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School HomeResearchPast Seminar informationApplied Mathematics

Past Applied Mathematics Seminars by Reverse Date

 


Applied Mathematics Seminars (Historical)

On coherence-incoherence transition in dynamical networks: spatial chaos and chimera states
Yuri Maistrenko (Potsdam)
19 Jul 2011Harrison 170 Tuesday 10amApplied Mathematics
We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Ro¨ssler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

 

The phase-amplitude description of neural oscillators.
Kyle Wedgewood (University of Nottingham)
11 Jul 2011Harrison 170 Monday 2pmApplied Mathematics
It is quite common to describe neural oscillators with a phase variable, thus reducing the model description to that of dynamics on a circle. However, if a limit cycle is not strongly attracting then this reduction may poorly characterise behaviour of the original system. Here we consider a coordinate transformation to a phase- amplitude framework that allows one to track the evolution of distance from the cycle as well as phase on cycle. A number of common models in computational neuroscience (primarily the Morris-Lecar model) are revisited in this framework and their response to pulsatile current forcing is investigated. We highlight the differences between phase and phase-amplitude descriptions, and show that the former can miss some substantial features of neuronal response. Finally, we discuss extensions of this work to consider the effects of off-cycle dynamics contributing to shear-induced chaos.

 

Weather, climate and renewable energy
David Brayshaw (University of Reading)
23 Jun 2011Harrison 209 Thursday 2pmApplied Mathematics
Securing a reliable electricity supply that is sufficient to meet demand is a vital concern for any modern economy. With the growth of renewable energy generation (particularly wind), it is important to understand the impacts of weather and climate variability on both supply and demand at national and international scales. At the day-to-day level, discussion in the UK often focuses on the issue of wind-supply during peak demand conditions – that is, the estimation of the minimum contribution that wind-power will make during extreme demand periods. Recorded power system data alone is insufficient to robustly estimate this wind “capacity value”, leading to the emergence of a rather confused picture in both the energy systems literature and the wider public debate. Weather-classification tools are proposed here as a means to address this problem. By identifying the relevant meteorological patterns associated with low-winds and peak-demand, it is demonstrated that the prevailing view of an anti-cyclonic "low-wind cold-snap" does not adequately describe peak-demand conditions. At longer timescales, large-scale low-frequency variability in the climate system can also have a marked impact on renewable generation, a fact that is often ignored during resource assessment and wind integration studies. A simple example is the North Atlantic Oscillation (NAO), variations in which are capable of yielding a difference in mean wind-power generation at UK sites of up to 10%. The NAO also correlates strongly with large-scale variations in seasonal-mean surface temperature and precipitation patterns, potentially affecting the demand for electricity and the availability of hydro-power, as well as wind generation. Such large-scale co-variability is likely to become increasingly important as cross-border transports within the European energy system increase. This talk presents ongoing research which seeks to better explore the links between weather, climate and energy. It will highlight some of the areas where meteorological information can be used to inform decision making in the UK and European electricity systems.

 

Why is the Arctic warming so fast?
James Screen (University of Melbourne)
21 Jun 2011Harrison 102 Tuesday 2pmApplied Mathematics
Recent climate change has been especially pronounced in the Arctic region, with surface temperatures rising two to four times faster than the global average and an accompanying rapid decline of sea ice. Both the Arctic warming and the sea ice loss are unprecedented over at least the last few thousand years. A multitude of climate feedbacks have been proposed that amplify the Arctic surface temperature response to climate forcing. This talk will discuss some of these, and explore whether they are already active and contributing to recent Arctic change. It will present evidence that strong ice-temperature feedbacks have emerged and that the decline in sea ice is playing a central role in Arctic temperature amplification. Both the sea ice loss and the warming have significant impacts on the Arctic moisture budget. These will be discussed in the context of changes in atmospheric water vapour content and in the phase of summer precipitation. There is evidence of humidity increases and a transition towards less snow and more rain. The causes, impacts, and feedbacks associated with these hydrological changes will be considered.

 

TBA
TBA
16 Jun 2011Harrison LT04 Thursday 2pmApplied Mathematics

 

TBA
TBA
9 Jun 2011Harrison LT04 Thursday 2pmApplied Mathematics

 

** postponed to 23rd June **
David Brayshaw (University of Reading)
2 Jun 2011Harrison LT04 Thursday 2pmApplied Mathematics
** postponed to 23rd June **

 

[symposium] Rotating Flow and Dynamo
Taylor and Francis sponsored symposium
2 Jun 2011Harrison 215 Thursday from 11amApplied Mathematics
Thursday, 2 June, 2011 at Room 215 Harrison Building 11:00--12:30 Tea/Coffee/Biscuits, Room 215 Harrison Building 12:30-2:00, Lunch at Xfi Building 2:00-2:30, Andrew Soward (Exeter) The onset of strongly localised thermal convection in rotating spherical shells. 2:30-3:00, Radostin Simitev (Glasgow), Effects of shell thickness and velocity boundary conditions on convective dynamos in rotating spherical shells. 3:00-3:30, Jun Zou (Hong Kong), Inverse Electromagnetic Obstacle Scattering. 3:30-4:30, Tea/Coffee/Biscuits, Room 215 Harrison Building; 4:30-5:00, Phil Livermore (Leeds) Dynamics of the tangent cylinder in rapidly-rotating inviscid flows, 5:00-5:30, Yannick Ponty (France) Large scale and small scale dynamos 5:30-6:00 Emilie Neveu (France) Multigrids for data assimilation on geophysics models 6:30--9:00 Conference dinner (the location to be confirmed) Friday, 3 June, 2011, at Room 215 Harrison Building 9:00-9:30 Steve Tobias (Leeds), Direct Statistical Simulation of Jet Formation 9:30-10:00 Emmanuel Dormy (France), Weak and Strong Field Dynamos 10:00-10:30 Paul Bushby (Newcastle), Dynamo action in rotating compressible convection 10:30-11:00 Tea/Coffee/Biscuits, Room 215 Harrison Building; 11:00--11:30 Keke Zhang (Exeter), Asymptotic solution for resonant flow in a spheroidal cavity driven by latitudinal libration. 11:30-12:00 Michael Chan (Hong Kong), Fluid motion and dynamos in a triaxial cavity driven by libration 12:00-13:30, Lunch at Xfi Building (THE END)

 

-- no seminar --
-- no seminar --
26 May 2011Harrison LT04 Thursday 2pmApplied Mathematics

 

Connecting mesoscale and macroscale models of cellular migration
Ruth Baker (University of Oxford)
19 May 2011Harrison LT04 Thursday 2pmApplied Mathematics
Continuum, partial differential equation (PDE) descriptions of cell movement are often employed in modelling studies because of their analytical tractability, and the wealth of numerical methods available for their solution. Derived from, for example, conservation of mass approaches these models describe how cell density changes with time due to random movements of cells, different types of taxes/kineses and cell proliferation/death. In the main, these processes are represented in the model equations in a phenomenological manner, providing gross descriptions not necessarily derived from the underlying cell behaviour. In this talk I will consider effects such as cell shape and volume exclusion, discussing how such phenomena may be modelled at the mesoscale, and how population-level macroscale models may be derived from these descriptions.

 

== COLLOQUIUM == Collective behaviour of swimming micro-organisms
Professor Tim Pedley (University of Cambridge)
12 May 2011Harrison LT04 Thursday 2pmApplied Mathematics
Suspensions of swimming micro-organisms exhibit a rich variety of collective behaviour, such as the bioconvection patterns seen for suspensions of upswimming cells that are denser than their surroundings, or the time-varying coherent structures seen in dense suspensions of swimming bacteria. Here we investigate the fluid dynamic mechanisms underlying these patterns, by means of (1) a continuum model for dilute suspensions, (2) hydrodynamic interactions between pairs of model micro-organisms, and (3) simulations and models for non-dilute suspensions. The talk will conclude with recent observations of ‘dancing’ algae.

 

Discrete Variational Derivative Methods for PDES
Chris Budd
9 May 2011Harrison 203 Monday 2pmApplied Mathematics

 

Time-stepping errors in weather and climate simulations
Paul Williams (University of Reading)
5 May 2011Harrison LT04 Thursday 2pmApplied Mathematics
Comprehensive assessments of uncertainty in weather and climate prediction models should in principle consider contributions from the discretised numerical schemes, as well as from the parameterised physics and other sources. The numerical contributions are often assumed to be negligible, however. This talk reviews the evidence for uncertainty arising from time-stepping schemes. Most contemporary weather and climate models still use the simple centred-difference (leapfrog) time-stepping scheme, in concert with the Robert-Asselin filter to stabilise the computational mode. This talk proposes a new alternative filter, known as the RAW filter, which substantially reduces the numerical errors and improves the formal accuracy. Examples are shown in which the new filter yields more skilful weather forecasts and reduces biases in climate models.

 

Calibrating computer simulators using ABC
Richard Wilkinson (University of Nottingham)
28 Mar 2011Harrison 209 Monday 3pmApplied Mathematics
Computer simulators are now used in nearly all scientific disciplines. Comparing simulators with observations of reality (in order to estimate parameters, quantify errors etc) is major challenge for statistics. In this talk I'll introduce a relatively new class of methods that can be used to calibrate simulators called Approximate Bayesian Computation (ABC) algorithms. I'll illustrate these methods on a problem from evolutionary biology.

 

Review of the Euler singularity problem (and our small contribution).
Andrew Gilbert (with Walter Pauls, University of Bielefeld).
23 Mar 2011Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

TBA
*no seminar - no room available*
21 Mar 2011Harrison 170 Monday 2pmApplied Mathematics

 

Chaotic mixing in a helix-like pipe with periodic variations in curvature and torsion
Mitsuaki Funakoshi (Kyoto University)
17 Mar 2011Harrison 170 Thursday 2pmApplied Mathematics
Chaotic motion of fluid particles by a steady viscous flow in a helix-like circular pipe caused by an axial pressure gradient, and mixing efficiency of this flow are numerically examined. This pipe is wound around a circular or elliptic cylinder with a constant pitch so that the curvature kappa and torsion tau of centerline of this pipe vary continuously and periodically. If both kappa and tau are small and slowly-varying, the cross-sectional motion of fluid particles is expected to be approximately governed by the sum of Dean's flow and the flow of rigid rotation. From Poincare sections and the values of an index of the extent of mixing, it is found that there is an intermediate range of Reynolds number Re of flow within which chaotic regions in Poincare sections are large and mixing efficiency in a short time is high. Moreover, larger chaotic regions and higher mixing efficiency are observed for pipes wound around a circular cylinder of smaller radius, and for pipes wound around a thinner elliptic cylinder. These results can be explained by the variation in characteristic ratio 12 tau / (kappa Re) in one period.

 

Unfolding of homoclinic and heteroclinic behaviour in a multiply-symmetric strut buckling problem.
Dr Khurram Wadee
16 Mar 2011Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Localized buckling in infinitely long structures has been at the forefront of furthering our understanding of homoclinic solutions in a class of reversible fourth-order systems. At criticality, the system encounters a sub-critical Hamiltonian-Hopf bifurcation from which emanate homoclinic (localized) solutions. These are unstable in the physical sense but the presence of higher order nonlinearity can act to stabilize the solutions. When appropriate stabilization is present, the homoclinic solution transforms into a heteroclinic solution with the propogation of a front. Careful analysis of the boundary layer between the zero solution and constant finite amplitude solution is the key to understanding how this transformation occurs. These predictions are then tested against numerical solutions of the governing equations.

 

Detecting the Interior Profile of Jupiter’s Differential Rotation by Gravity Science Techniques.
Dali Kong
9 Mar 2011Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
NASA’s JUNO Jupiter probe is going to be launched soon. One of its primary scientific goals is to determine the interior structure, and the deep atmosphere of Jupiter, by making detailed measurements of its complete gravity field from orbit tracking. The observations may help unveil the mechanism producing one of the most fascinating Jovian features, the persistent zonal jets and belts structure on Jupiter’s visible surface. In this work, for the first time, an up bound is given upon how much Jovian gravity field can be distorted, if a deep differential rotation model is assumed. The problem is discussed based on perturbed Maclaurin spheroid theory but is ready to be generalized to a more realistic physical state. It is suggested that the largest field expansion coefficient J_2 of Jupiter may be subject to a 10^{-3} relative change owing to the current observed zonal jet speed.

 

TBA
TBA
7 Mar 2011Harrison 209 Monday 3pmApplied Mathematics

 

On the applied Mathematics of Ocean Waves
Peter Janssen (ECMWF)
28 Feb 2011Harrison 170 Monday 2pmApplied Mathematics
For the (applied) Mathematician the subject of ocean waves, or to be more precise, surface gravity waves is an interesting problem because on the one hand it is a relatively simple and attractive while on the other hand the subject is very relevant for society. Nevertheless, due to its nonlinear character the problem has still not been solved, despite the fact that it received considerable attention for at least two centuries. Presently there is a renewed interest in the subject because of attempts to try to understand the generation of "freak" waves. After a brief historical account of the subject I will introduce the hamiltonian formulation of surface gravity waves. For weak nonlinearity there is a natural distinction between free and bound gravity waves. This distinction allows the introduction of a relatively simple evolution equation, which is called the Zakharov equation. From this evolution equation a number of interesting properties of weakly nonlinear water waves may be derived. In this talk I will concentrate on only one property, namely the instability of a uniform wave train which is an example of a four-wave interaction process. In fluid Mechanics this instability is called the Benjamin-Feir instability. It turns out that this instability, because it is a four-wave interaction, is also found in other fields. Examples are nonlinear Optics and Plasma Physics. In its most simple form the Benjamin-Feir Instability leads to the generation of envelope solitons which provides a possible explanation for the generation of "freak" waves. Because these extreme events are rare, forecasting of freak waves is difficult. Nevertheless, the probability of these extreme events can be estimated and at ECMWF probablistic forecasting of "freak" waves was introduced a number of years ago. This is the 32nd Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics".

 

**POSTPONED** Time-stepping errors in weather and climate simulations
**POSTPONED** Paul Williams (**POSTPONED** University of Reading)
21 Feb 2011Harrison 170 Monday 2pmApplied Mathematics
Comprehensive assessments of uncertainty in weather and climate prediction models should in principle consider contributions from the discretised numerical schemes, as well as from the parameterised physics and other sources. The numerical contributions are often assumed to be negligible, however. This talk reviews the evidence for uncertainty arising from time-stepping schemes. Most contemporary weather and climate models still use the simple centred-difference (leapfrog) time-stepping scheme, in concert with the Robert-Asselin filter to stabilise the computational mode. This talk proposes a new alternative filter, known as the RAW filter, which substantially reduces the numerical errors and improves the formal accuracy. Examples are shown in which the new filter yields more skilful weather forecasts and reduces biases in climate models.

 

Accelerating chaos control: how waiting can speed things up
Chris Bick (Max Planck Institute for Dynamics and Self-Organization, Goettingen)
15 Feb 2011Harrison 254 Tuesday 2pmApplied Mathematics

 

Huabing Yin
Microengineering biointerfaces for sensing and cell response (University of Glasgow)
14 Feb 2011Harrison 170 Monday 2pmApplied Mathematics
In the body, a cell senses and responds to its surrounding microenvironment. Increasingly, it has been demonstrated that this behavior is associated with important processes like stem cell differentiation, cancer cell invasion and wound healing. However, the natural habitat of a cell, the extracellular matrix (ECM), consists of interconnected physical, chemical and biological cues. Understanding the influence of these arrangements on cell function will have a profound impact in developing biomaterials that induce desired cellular responses. However, it remains an ongoing challenge. In this context, we have been developing microenvironments in vitro with the aim to closely mimic the multiplex cues found in vivo. Our work combines microfabrication, microfluidics and new surface chemistry to create functional biointerfaces, where multiple cues (both biological and physical) are spatially arranged on a length scale of nano- and micrometers. This interdisciplinary approach has enabled a flexible platform for a number of applications, ranging from high throughput drug screening for pharmaceutical development to the emerging fields of stem cell research. For example, discrete or gradient patterns of single or multiple biomolecules (e.g peptide and carbohydrates) have been reliably generated on a surface to investigate their collective roles in regulating cell migration, differentiation and elasticity (via AFM indentation). In this talk, I will discuss the rationales behind the design of these biointerfaces, their advantages and the challenges with our recent work in these areas.

 

TBA
TBA
7 Feb 2011Harrison 170 Monday 2pmApplied Mathematics

 

TBA
TBA
31 Jan 2011Harrison 170 Monday 2pmApplied Mathematics

 

Implicit hydrodynamic simulations of stellar convection
Maxime Viallet (Physics Dept, University of Exeter)
24 Jan 2011Harrison 170 Monday 2pmApplied Mathematics

 

Order vs. chaos when the space is discrete.
Franco Vivaldi (Queen Mary)
17 Jan 2011Harrison 170 Monday 2pmApplied Mathematics

 

Accounting for the limitations of quantitative models
Jonty Rougier (University of Bristol)
10 Jan 2011Harrison 171 Monday 2pmApplied Mathematics
There is a wide spectrum of modelling approaches for complex systems. However, in an area such as environmental science, even the most 'realistic' models tend to result in substantial system uncertainty. These realistic models are usually too unwieldy to be embedded within a statistical framework, necessary for performing the standard tasks of model criticism, model calibration, and system prediction. Instead, we consider whether it is possible to use much simpler 'phenomenological' models. The principles and practice are illustrated using a model for glacial cycles developed by Michel Crucifix as part of the ITOP project. The practice uses the very latest techniques from statistical computing, namely Particle Markov chain Monte Carlo (P-MCMC).

 

Passive scalar decay in chaotic flows with boundaries
Fatma Zaggout
14 Dec 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)
We study the decay rate of a passive scalar in two-dimensional chaotic flows, with a focus on the effect of boundary conditions for kinematically prescribed velocity fields with random or time periodic time-dependence. The boundary conditions on the scalar and flow in a subdomain are imposed by restricting to a subclass invariant under certain symmetry transformations. At late times the decay of the variance of a passive scalar, for example temperature, is exponential in time with rate $\gamma$. For a variety of different cases scaling laws of the form $\gamma(\kappa) \simeq C \kappa^\alpha$ are obtained with exponents $\alpha$ that depend on the boundary conditions mentioned before.

 

Dynamics of differential-delay equations with single, multiple and time--varying lags
Gabor Kiss (University of Bristol)
13 Dec 2010Harrison 170 Monday 2pmApplied Mathematics
We compare the stability properties of some families of delay differential equations with one delay to associated families of equations with distributed delays. With the aid of some examples, we indicate some differences between the non--linear oscillations of equations with one and distributed delays. Furthermore, we report on the existence of pullback attractors of multiple delayed equations.

 

Dispersion of Pollution by Transitional Atmospheric Boundary Layers
Alex Taylor
7 Dec 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)
We consider the dispersion of passive tracer particles within the atmospheric boundary layer through the development of two different methods, Lagrangian stochastic modelling and large-eddy simulation. Initially we focus on obtaining agreement with previous studies and observations for the case of a steady convective boundary layer, moving on to address the case of a typical evening 'decaying' convective boundary layer and investigating the role of residual convective turbulence on dispersion.

 

To snake or not to snake in the planar Swift-Hohenberg equation
Daniele Avitabile (University of Surrey)
6 Dec 2010Harrison 170 Monday 2pmApplied Mathematics
Localised stationary structures play an important role in many biological, chemical and physical processes. Such structures have been observed in a variety of experiments ranging from vertically-vibrated granular materials, liquid crystals, binary-fluid convection, autocatalytic chemical reactions, electrochemical systems to nonlinear optical devices. We investigate the bifurcation structure of stationary localised patterns in a prototypical model, the two- dimensional Swift-Hohenberg equation, on an infinitely long cylinder and on the plane. On cylinders, we find localised roll, square and stripe patches that exhibit snaking and non-snaking behaviour on the same bifurcation branch. Some of these patterns snake between four saddle-node limits: recent analytical results predict then the existence of a rich bifurcation structure to asymmetric solutions, and we trace out these branches and the PDE spectra along these branches. On the plane, we study the bifurcation structure of fully localised roll structures, which are often referred to as worms. We also show preliminary numerical results on oscillons, that is, time-periodic spatially-localised structures.

 

Uncertainty in Climate Projections.
Mat Collins
30 Nov 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)
We are not certain about how severe future climate change will be. Climate models that are used to make projections of the future are known to be inadequate at simulating past climate and climate change because of limitations in computing resources and because of limitations in our understanding of the climate system. Although models are constantly improved, inadequacies persist and policy makers are beginning to require quantitative information to plan for the future. This talk will discuss techniques for dealing with uncertainties using physical, mathematical and statistical approaches. A particular example will be future climate projections made for the UK under the UKCP09 project (http://ukcp09.defra.gov.uk/).

 

Convergence of fast-slow ODEs to stochastic differential equations
Ian Melbourne (University of Surrey)
29 Nov 2010Harrison 254 Monday 10amApplied Mathematics
A project started recently with Andrew Stuart investigates the convergence of certain deterministic systems to a stochastic differential equation. For (presently over-simplified) fast-slow systems, we prove, under very mild conditions on the fast variables (including the case where the fast equation is the Lorenz attractor), that the slow-variable solutions converge to solutions of a stochastic differential equation. A major difference between our approach and related projects is that we do not rely on decay of correlations for the fast variables (decay of correlations for flows is a notoriously difficult and poorly understood problem). Instead we use invariance principles (a generalisation of the central limit theorem giving convergence to Brownian motion) and large deviation estimates which have been derived for a very large class of systems in collaboration with Matthew Nicol.

 

Adaptive Mesh Modelling of the Global Atmosphere
Hilary Weller (University of Reading)
29 Nov 2010Harrison 170 Monday 2pmApplied Mathematics
The next generation of models for weather and climate prediction may look very different from the current, well optimised generation: Future models may use different grids which avoid the pole problem and use unstructured or adaptive meshes. During this talk I will demonstrate some advantages and disadvantages of a lat-lon grid, a cubed sphere and triangular and hexagonal icosahedral grids both with and without local refinement. I will then describe and demonstrate a mesh refinement criteria which anticipates mesh requirements many time steps into the future.

 

Robustness of funnel control in the gap metric.
Markus Mueller
23 Nov 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)
For m-input, m-output, finite-dimensional, linear systems satisfying the assumptions (i) minimum phase, (ii) relative degree one and (iii) positive high-frequency gain), the funnel controller achieves output regulation in the following sense: all states of the closed-loop system are bounded and, most importantly, transient behaviour of the tracking error is ensured such that its evolution remains in a performance funnel with prespecified boundary. As opposed to classical adaptive high-gain output feedback, system identification or internal model is not invoked and the gain is not monotone. Invoking the conceptual framework of the nonlinear gap metric we show that the funnel controller is robust in the following sense: the funnel controller copes with bounded input and output disturbances and, more importantly, it may even be applied to a system not satisfying any of the classical conditions (i)–(iii) as long as the initial conditions and the disturbances are “small” and the system is “close” (in terms of a “small” gap) to a system satisfying (i)–(iii).

 

Scaling properties of the spectrum for DDEs with large delay
Matthias Wolfrum (Weierstrass Institute for Applied Analysis and Stochastics, Berlin)
22 Nov 2010Harrison 170 Monday 2pmApplied Mathematics
Delay-differential equations play an important role in many applied problems including e.g. economy, neuroscience, and optoelectronics. For the dynamics of semiconductor lasers with optical feedback or coupling in many cases the delay caused by the finite speed of light has to be considered as large compared to the internal time scales of the laser being in the range of picoseconds. For a laser with optical feedback the classical Lang-Kobayashi model shows a large variety of dynamical behavior related to the large delay, including the coexistence of many periodic solutions with different stability properties, high dimensional chaos and other. Starting from these phenomena, we investigate typical phenomena in delay-differential equations (DDEs) where the delay time tends to infinity. We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudo-continuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continuous spectrum. We show that the spectral curves and strong spectral points provide a complete description of the spectrum for sufficiently large delay and can be comparatively easily calculated by approximating expressions. The abstract results will be illustrated by by some examples.

 

Zero dynamics and funnel control of linear differential-algebraic systems
Thomas Berger (Ilmenau University of Technology, Germany)
17 Nov 2010Harrison 101 Monday 2pmApplied Mathematics
We consider linear differential-algebraic equations of the form E\dot{x}_(t) = Ax(t) + Bu(t) y(t) = Cx(t) ; (1) for E,A \in R^{n \times n}, B,C^{T} \in R^{n \times m} and regular matrix pencil sE-A \in R[s]^{n \times n}, i.e. det(sE-A) \in R[s]\{0}. Furthermore we assume that the transfer function G(s) = C(sE-A)^{-1}B has proper inverse, i.e. G^{-1}(s) exists and lim _{s \rightarrow \infty} G^{-1}(s) = D for some D \in R^{m \times m}. For this class of systems a so called `zero dynamics form' which is a simple ("almost" a normal) form of the DAE is derived; it is a pendant to the well-known Byrnes-Isidori form for ODE systems. The `zero dynamics form' is exploited to characterize the zero dynamics of (1) by (A,E,B)-invariant subspaces; structural properties such as stable zero dynamics, minimum phase, and high-gain stabilizability are also characterized. Finally, the zero dynamics form is the main mathematical tool to show that the `funnel controller', that is a time-varying proportional output error feedback u(t) = -k(t)e(t), achieves for all DAE systems (1) with stable zero dynamics that the output signal y(\dot) tracks a reference signal y_{ref}(\dot) with respect to pre-specified transient behaviour.

 

Initialising Decadal Prediction in HadCM3 with RAPID Array Observations
Leon Hermanson (University of Reading/Met Office)
16 Nov 2010Harrison 101 Tuesday 3pmApplied Mathematics
The RAPID array consists of several moorings at about 26°N in the Atlantic that measure temperature and salinity from which the meridional overturning circulation (MOC) and its components at this latitude can be determined. The main aim of the VALue Of the RAPID array (VALOR) project is to assess the value of the RAPID array observations for predictions of the Atlantic MOC and its impact on climate. In addition, the project will explore a range of issues concerning the design of a potentional MOC prediction system. One of the models used in this work is the Hadley Centre HadCM3 model. In this work we have investigated the issues that arise when trying to initialise the HadCM3 model with the RAPID observations. This has initially been investigated in an idealised setting where pseudo-observations from the same model are used to reconstruct a known transport. Leon is a Research Fellow at University of Reading, but is currently seconded to the Met Office, where he is working in the Decadal Climate Prediction group. He is visiting the College for the entire week 15-9 Nov to work with Tom Fricker and Chris Ferro, so will be available to talk to about any aspect of his seminar, or his wider work, during that time.

 

Probabilistic transient envelope: Characterizing Disturbances and Perturbations.
Iakovos Matsikis
16 Nov 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)
We study the transient effect of deterministic or stochastic distrubances on a system that is perturbed deterministically or stochastically by constructing a transient envelope. The envelope is constructed with intensive simulation and it allows us to calculate the initial structures that cause amplification and attenuation over all time steps of interest, the biggest and smallest values the system might assume and the probability that the output belongs in certain bounded intervals. For application we use population projection matrices.

 

Fine-scale structure formation in Saturn's rings
Henrik Latter (University of Cambridge)
15 Nov 2010Harrison 170 Monday 2pmApplied Mathematics
Recent radio and UV occultation experiments carried out by the Cassini spacecraft have revealed that swathes of Saturn's A and B-ring support fine-scale axisymmetric patterns. This 'microstructure' is surprisingly regular, possessing wavelengths between 150 and 250 metres, and is probably driven by a pulsational instability of viscous origin. Using a simple hydrodynamical model, I show how this fine-scale quasiperiodic structure is related to nonlinear wave trains associated with the instability. I will also examine how variations and `defects' in the waves' phase and amplitude may relate to irregular features on larger-scales. This is the 31st Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics".

 

The climate and habitability of planets orbiting red dwarf stars
Manoj Joshi (NCAS Climate, Reading)
8 Nov 2010Harrison 170 Monday 2pmApplied Mathematics
The concept of the habitable zone, or the region in which a planet can support liquid water at its surface, is almost ubiquitous in studies of "astrobiology", or the study of life in the universe. The habitable zone becomes especially interesting when considering red dwarf stars, or those stars with a mass between 0.1 and 0.5 times that of the Sun. On the one hand, red dwarfs are far more common than sun-like stars, and are thought to maintain their mean luminosity for much longer; on the other hand a red dwarf's habitable zone is so close to the star that phenomena such as tidal locking and stellar flares might be important in determining whether or not a planet can support an atmosphere (or even life). In this talk I'll review research on the habitable zone, especially with regard to red dwarf stars; work which shows that while the tidal locking of planets orbiting red dwarfs is not a barrier to habitability, stellar activity might be; and finally how all this is relevant to present and future planet-finding space missions.

 

Buoyant plumes: simple models and large-eddy simulation
Ben Devenish (Met Office)
3 Nov 2010Harrison 106 Wednesday 2pmApplied Mathematics
NOTE - THIS IS THE SEMINAR POSTPONED FROM 27th OCTOBER. Examples of buoyant plumes abound in both natural and man-made situations: the recent eruption of Eyjafjallajokull in Iceland and the plume generated by the fire at the Buncefield oil depot in December 2005 are just two well-known examples. The ability to predict the dispersion of any resulting hazardous material was demonstrated with dramatic effect earlier this year and provides a clear motivation for the study of buoyant plumes. Despite their obvious complexity, buoyant plumes have been successfully described by relatively simple models. In this talk I will review these models and then consider what further insight can be gained from large-eddy simulations. I will also present results on more complicated but realistic scenarios such as the effect on the plume of a crosswind.

 

The role of global manifolds in the transition to chaos in the Lorenz system
Bernd Krauskopf (University of Bristol)
1 Nov 2010Harrison 170 Monday 2pmApplied Mathematics
joint work with Hinke Osinga (University of Bristol) and Eusebius Doedel (Concordia University). The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This talk addresses the role of two-dimensional stable manifolds of the origin and of saddle periodic orbits in organising the overall dynamics. These global objects need to be computed numerically with specialized algorithms. We present an approach that is based on the continuation of orbit segments, defined as solutions of suitable boundary value problems. In this way, we are able to study bifurcations of global manifolds as the Rayleigh parameter of the Lorenz system is changed. We show how the entire phase space of the Lorenz system is organised and how the manifolds change dramatically during the transition to chaotic dynamics. The delicate structure of global manifolds that we find also demonstrates the accuracy of the computations.

 

***** SEMINAR POSTPONED TO 3rd NOVEMBER *****
Ben Devenish (***** SEMINAR POSTPONED TO 3rd NOVEMBER *****)
27 Oct 2010Harrison 101 Wednesday 2pmApplied Mathematics
***** SEMINAR POSTPONED TO 3rd NOVEMBER *****

 

On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order
Klaus Boehmer (University of Marburg)
25 Oct 2010Harrison 170 Monday 2pmApplied Mathematics
For the first time, we present for the general case of fully nonlin- ear elliptic differential equations of second order a nonstandard C1 finite element method (FEM). We consider, throughout the paper, two cases in parallel: For convex, bounded, polyhedral domains in Rn, or for C2 bounded domains in R2, we prove stability and convergence for the corresponding conforming or nonconforming C1 FEM, resp. The classical theory of discretization methods is applied to the differential operator or the combined differential and the boundary operator. The consistency error for satisfied or violated boundary conditions on polyhedral or curved domains has to be estimated. The stability has to be proved in an unusual way. This is the hard core of the paper. Essential tools are linearization, a compactness argument, the interplay between the weak and strong form of the linearized operator and a new regularity result for solutions of finite element equations. An essential basis for our proofs are Davydov’s results for C1 FEs on polyhedral domains in Rn or of local degree 5 for C2 domains in R2. Our proof for the second case in Rn, includes the first essentially as special case. The method applies to quasilinear elliptic problems not in divergence form as well. A discrete Newton methods converges locally quadratically, essentially independently of the actual grid size by the mesh independence principle.

 

Flows on real networks
David Arrowsmith (Queen Mary)
18 Oct 2010Harrison 170 Monday 2pmApplied Mathematics

 

Evolution of magnetic helicity with the solar cycle: observations and dynamo theory
Kirill Kuzanyan ((1) IZMIRAN, Russian Academy of Sciences, Moscow (2) National Astronomical Observatories of China, B)
12 Oct 2010Harrison 101 Tuesday 9amApplied Mathematics
We review the long term systematic observation of solar vector magnetic fields at several observatories in the USA, China and Japan. The data sample at Huairou Solar Observing station of Chinese Academy of Sciences (Beijing) cover the whole period 1988-2005 which is the longest available systematic dataset of three-component magnetic field in solar active regions over the two consecutive solar cycles 22 and 23. We can apply to this sample a self-consistent averaging procedure which is the observational proxy to the averaging over the ensemble of turbulent pulsations. Thus we have obtained large-scale coherent structures resembling the mean magnetic field. It obeys Hale’s polarity rule for sunspots and magnetic fields in quiet photosphere, in accord with other observational results. We also use the data sample to compute current helicity and twist. They are important observational proxies of magnetic helicity which is the invariant in MHD flows. These helical parameters demonstrate hemispheric sign rule: in the northern/southern hemispheres their signs are predominantly negative/positive. However, based on the data sample covering almost overall 22 year magnetic solar cycle we have established specific areas in latitude and time when they are regularly inverted, mainly in the beginning at the end of the sunspot butterfly wings. In solar dynamo models helicity can be used as an important nonlinear drive controlling growth of the solar cycle, and at the same time it is a proxy of the alpha-effect which is a measure of regeneration of the poloidal field from the toroidal one. We discuss possible implications of our observational findings in the light of the solar dynamo. 30th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics".

 

Bifurcations in generalization of Kuramoto-Skaguchi model of coupled phase oscillators
Oleksandr Burylko (National Academy of Sciences of Ukraine)
11 Oct 2010Harrison 170 Monday 2pmApplied Mathematics
We consider the extension of popular Kuramoto (Kuramoto-Sakaguchi) model of globally coupled phase oscillators with the phase shift in coupling function that depends nonlinearly on the order parameter. This system was proposed by A.Pikovsky and M.Rosenblum (Phys. Rev. Lett. (2007), Physica D (2009). We discuss bifurcations of transition from full synchronization to desyncronization through different clustering states. We show that the typical way of this transition passes through different heteroclinic bifurcations. The obtained results are mostly based on the lemma about localization of equilibria that was proved. Also, we describe the multistability that occurs in the system.

 

Librationally driven flow in triaxial ellipsoids.
Keke Zhang
5 Oct 2010Harrison 101 Tuesday 9amApplied Mathematics (Internal)

 

The oscillations of rotating fluids and their applications to stars and planets
Michel Rieutord (Laboratoire Astrophysique de Toulouse)
4 Oct 2010Harrison 170 Monday 2pmApplied Mathematics
Stars and planets are all rotating. Due to the conservation of angular momentum, this leads to specific oscillations known as inertial oscillations. These oscillations modify the low-frequency oscillation spectrum of these bodies and introduce new phenomena which I shall try to describe in a simple manner. I'll present, for instance, some of the peculiarities of these oscillations (like singularities) and the role they play in the dynamics of tidally interacting bodies like stars harbouring a hot Jupiter. 29th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics".

 

California Hottest and Coldest Days: Their Large-scale Weather Patterns, Extreme Statistics, Downscaling, and Further Questions
Richard Grotjahn (Atmospheric Science Program, Univ. of California, Davis, U.S.A.)
19 Jul 2010Harrison 170 Monday 2pmApplied Mathematics
Extreme hot days as defined for the California central valley (CV) have a characteristic large scale structure that affects much of the west coast of North America as well. Extreme cold air outbreaks affect much of the southwestern United States. The patterns for both types of extreme events (EEs) will be briefly summarized, including statistically highly significant regions far from California. Simple statistics (boostrap resampling and simple tail tests) for assigning significance to parts of the EE patterns in both cases will be summarized. The EE patterns for the hottest 1% of summer days have been compared to daily weather maps in a simple calculation of a daily anomaly 'HDA index' to hindcast (and forecast) hottest days in daily anomaly values. The 'HDA index' captures ~1/2 of the hottest 1% days from a 25 year period using a peaks over a threshold test to find the highest 1% of HDA index and CV observed temperature. Perhaps unexpectedly, the HDA index has high correlation with maximum temperatures on near-normal and below-normal dates as well (overall correlation between daily maximum temperature at central valley stations and HDA index: 0.84). Remaining questions include how the large scale patterns develop dynamically and improved extreme statistics.

 

Simple statistical methods for complex ecological dynamics
Simon Wood (University of Bath)
21 Jun 2010Harrison 215 Monday 2pmApplied Mathematics

 

Mathematical analysis of circadian systems.
Ozgur Akman
15 Jun 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Circadian oscillations are universal, controlling 24-hour rhythms of metabolism, physiology and behaviour in organisms ranging from humans to cyanobacteria. The regulatory gene networks underlying these oscillations have proved to be useful systems for quantifying the relationship between the structures of biochemical systems and their higher order properties. By constructing mathematical models of key circadian organisms and analysing the models using techniques derived from nonlinear dynamics, insights can be obtained into the reasons why circadian networks have considerably more complex architectures than the minimal negative feedback loop required for entrainable oscillations. Recent results obtained from modelling a range of circadian species suggest that one of the possible benefits of the high feedback loop complexity characteristic clock networks is the increased functional flexibility that such architectures confer. Moreover, the techniques developed to construct and analyse the models have potential applicability to a broader range of signalling pathways, particularly with respect to parameter-fitting and sensitivity analysis.

 

Mathematical modelling of the active process of hearing in insects and mammals
Alan Champneys (University of Bristol)
14 Jun 2010Harrison 106 Monday 2pmApplied Mathematics
Hearing organs in mammals are remarkable in that a passive signal is electro-mechanically amplified over several orders of magnitude within the cochlear itself before any neural processing has taken place. In the insect world, the male mosquito also has a highly developed active hearing process, whose function is crucial to the mating process. It has recently been proposed, based on data from the bull frog, that the conceptual model of a Hopf bifurcation normal form captures all the features of the cochlear amplifier and that this might be a universal model across many species. The aim of this talk is to challenge this assertion and to show that there is no substitute for ab initio mathematical modelling that on the one hand attempts to capture the true physics and on the other hand is sufficiently simple to be amenable to qualitative as well as quantitative understanding. In particular I shall present recent work with Avitable and Homer based on the experiments in the lab of Robert in Bristol on a new mathematical model for the mosquito hearing organ. The organ is far more primitive than the mammalian cochlear and at bottom level can be described by a see-saw like lever arm that is attached to many threads that can provide mechanical stimulus in the form of a "twitch". The model is shown to capture the amplification of low-level sound, quenching of high input hysteresis and self-oscillation that is observed in live insects. I shall also present ongoing work with Szalai, Homer, O'Maoileidigh and Jülicher together with experimental teams in Bristol and Keele on mathematical models for the outer-hair cells that are thought to cause the active process within mammalian hearing. We show that this model displays a periodically forced cusp bifurcation, an unfolding of which is also able to show the characteristic 1/3-growth law that a Hopf bifurcation normal form displays. We also show how the dominant features of this model produce a very different kind of simple model, this is able to match experimental data in showing regions of active amplification with different amplitude-dependent exponents.

 

Evolution 1 - ID 0: One more case of biological complexity resolved.
Orkun Soyer
8 Jun 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The molecular basis of chemotaxis in the model organism Escherichia coli requires 7 signalling proteins, interacting in specific ways. The resulting dynamical system has non-trivial features including high sensitivity and precise adaptation. It remains unknown, how such a relatively complex system could have evolved and through which intermediary systems. This results in bacterial chemotaxis and the underlying signalling networks to be presented as an evolutionary puzzle. The lack of evolutionary understanding also limits our ability to extend the findings from E. coli to other species, which show remarkable differences to E. coli both in response dynamics and network structure. Using a mathematical approach we explore the potential evolutionary paths in chemotaxis. In particular, we reduce potential chemotaxis strategies to a simple formalism containing few key parameters that correspond to biological implementation of such strategies. We then compare the performance of such strategies under different parameter regimes. This yields a plausible evolutionary path from simple networks with straightforward dynamics to networks with adaptive dynamics. Interestingly, while the evolutionary transition can be driven only by selection for increased chemotaxis performance, the optimal performance can be achieved by different strategies under different parameter regimes (i.e. biological implementations).

 

Dynamical Systems and Complex Networks: Are such Theories Useful for Neuroscience and Earth Sciences?
Juergen Kurths (PIK, Potsdam)
7 Jun 2010Harrison 170 Monday 2pmApplied Mathematics
Complex networks were firstly studied by Leonhard Euler in 1736 when he solved the Königsberger Brückenproblem. Recent research has revealed a rich and complicated network topology in various model systems as well as in several fields of applications, such as transportation and social networks, or the WWW. It will be discussed whether this approach can lead to useful new insights into rather large complex systems or whether it is fashionable only to interpret various phenomena from this viewpoint and publish papers on that. A challenging task is to understand the implications of complex network structures on the functional organization of the brain activities. We investigate synchronization dynamics on the cortico-cortical network of the cat and find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Next we consider an inverse problem: Is there a backbone-like structure underlying the climate system? For this we reconstruct a global climate network from temperature data. Parameters of this network, as betweenness centrality, uncover relations to global circulation patterns in oceans and atmosphere. We especially study the role of hubs in the flows of energy and matter in the climate system. This new approach seems to be promising for understanding the dynamics of changing climate and its impacts.

 

Statistical Attractors and the Convergence of Time Averages
Ozkan Karabacak
1 Jun 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
There are various notions of attractor in the literature, including the ideas of measure (Milnor) attractors and statistical (Ilyashenko) attractors. We relate the notion of statistical attractor to that of the essential omega-limit set and prove some elementary results about these. In addition, we consider the convergence of time averages along trajectories. Ergodicity implies the convergence of time averages along almost all trajectories for all continuous observables. For non-ergodic systems, time averages may not exist even for almost all trajectories. However, averages of some observables may converge; we characterize conditions on observables that ensure convergence of time averages even in non-ergodic systems.

 

Excitability in ramped systems: The compost bomb instability.
Sebastian Wieczorek
25 May 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
About one year ago, Catherine Luke and Peter Cox reported (in one of our internal seminars) on the "combost-bomb instability" which represents a potential tipping point in the response of the climate system to anthropogenic forcing. In this strongly nonlinear phenomenon, biochemical heat release destabilizes peatland above some critical rate of global warming, leading to a catastrophic release of soil carbon into the atmosphere. This talk explains the "compost-bomb instability" as a novel type of excitability where a stable quiescent state exists for different fixed settings of a system's parameter but enormous excitable bursts appear when the parameter is increased gradually (ramped) from one setting to another. We show that an excitable system with a ramped parameter forms a singularly perturbed problem with at least two slow variables and focus on the case with locally folded critical manifold. Analysis of the desingularised flow identifies an excitability threshold as a canard trajectory through a folded singularity and leads to the analytical formula for the critical rate of global warming.

 

Normalized coprime representations for time-varying linear systems
Markus Mueller
18 May 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
By considering the behaviour of stabilizable and detectable, linear time-varying state-space models over doublyinfinite continuous time, we establish the existence of so-called normalized coprime representations for the system graphs; that is, stable and stably left (resp. right) invertible, image (resp. kernel) representations that are normalized with respect to the inner product on L2(−oo,oo). The approach is constructive, involving the solution of timevarying differential Riccati equations with single-point boundary conditions at either +oo or −oo.

 

CANCELLED Interfacial instabilities in a two-layer system with vertical electric current
Sergei Molokov (University of Coventry)
17 May 2010cancelled cancelled cancelled cancelledApplied Mathematics
CANCELLED 28th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics". abstract TBA

 

Evidence for Rotational Parametric Instability in Earth's Core from Analysing Relative Paleointensity Data
Keith Aldridge (York University, Canada)
11 May 2010Harrison 170 Tuesday 12noonApplied Mathematics
29th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics" Evidence for Rotational Parametric Instability in Earth's Core from Analysing Relative Paleointensity Data Abstract We have developed an algorithm to search records of relative paleointensity for evidence of a parametric instability in Earth's core. Under the assumption that the spectrum of magnetic field intensity is a proxy for that of fluid velocity, the presence in Earth's core of a parametric instability will be seen in records of the magnetic field intensity. As long as the strain rate produced by either precessional or tidal forces exceeds the dissipation rate, a parametric instability will grow and subsequently decay repeatedly as observed in laboratory experiments. In the event that the externally imposed strain rate is close to the dissipation rate, a balance will result in what we call a steady state. Our algorithm has searched records of relative paleointensity from sedimentary cores from the past 2 million years. We smooth the data and set a threshold of significant change in the field which is segmented into intervals of growth, decay or steady state. According to our model of parametric instability, adjacent decays and growths recovered by our algorithm can be combined to give the magnitude of the external strain rate. Application of this algorithm to the SINT2000 data reveals distinct maxima that correspond to all the reversals of the field in the interval studied. Thus our model for parametric instability in Earth's core is consistent with the occurrence of magnetic field reversals at times when the external straining is largest.

 

What can convection teach us about the nature of turbulence?
Fritz Busse (University of Bayreuth)
11 May 2010Harrison 170 Tuesday 11amApplied Mathematics
27th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics". abstract: TBA

 

Self-consistent nonlinear MHD
David Hughes (University of Leeds)
10 May 2010Harrison 170 Monday 2pmApplied Mathematics
26th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics". The majority of astrophysical dynamo modelling is performed using mean field MHD, an elegant theory of MHD turbulence in which small-scale interactions are captured by various transport coefficients, most notably the alpha-effect. Here I shall extend the standard mean field approach from a kinematic one - treating the instability of a magnetic field to a purely hydrodynamic basic state - so as to consider fully MHD basic states (with both flow and field). It is then vital to treat the momentum and induction equations on the same footing. This leads to a description of any resulting instability in terms of four tensors, two familiar and two new.

 

Control Engineering Approaches to Systems Biology Research
Declan Bates (University of Exeter)
4 May 2010Harrison 170 Monday 4pmApplied Mathematics

 

Constraints on the relaxation of magnetic fields.
Antonia Wilmot-Smith (University of Dundee)
4 May 2010Harrison 170 Tuesday 2pmApplied Mathematics
23rd Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics" full abstract: TBA

 

Deciphering the Swine-flu pandemics of 1918 and 2009
Richard Goldstein ((NIMR, Mill Hill))
30 Apr 2010Harrison 170 (visualisation suite) Friday 2pmApplied Mathematics
The devastating ‘Spanish flu’ of 1918 killed an estimated 50 million people worldwide, ranking it as the deadliest pandemic in recorded human history. It is generally believed that the virus transferred from birds directly to humans shortly before the start of the pandemic, subsequently jumping from humans to swine. By modelling how the viral sequences changes in human, avian, and swine hosts, we find it likely that the Spanish flu of 1918, like the current 2009 pandemic, was a 'swine-origin' influenza virus. Now that we are faced with a new pandemic, can we understand how influenza is able to change hosts? Again by modelling the evolutionary process, we can identify locations that seem to be under different selective constraints in humans and avian hosts, identifying changes that may have facilitated the establishment of the 2009 swine-origin flu in humans.

 

Rules and Tools for Directed Evolution
Florian Hollfelder (University of Cambridge)
9 Apr 2010Harrison 170 Friday 2pmApplied Mathematics
I will address approaches leading up to directed evolution of functional proteins. First the observation of catalytic promiscuity is used to define functional relationships in enzyme superfamilies as a basis for phylogentic relationships for catalysis. Promiscuous activities could be remnants from the evolutionary ancestor that has been gene duplicated and adapted to fullfill a new function. Alternatively the observation of promiscuity could indicate that an enzyme is ‘pregnant’ with another activity, i.e. has the potential to be mutated or evolved into a new catalyst Specifically we demonstrate this principle with observations of strong promiscuous activities with rate accelerations between 109 and 1016 in a class of hydrolytic enzymes that share an unusual formylglycine active site nucleophile. Promiscuity in these enzymes is not limited to a single activity, but allows the same active site to catalyse up to six activities efficiently in addition to its native activity.. Evolution experiments should ideally analysed by high-throughput approaches, but require the development of special technologies. The quantitative assessment of large numbers of experiments is possible in water-in-oil emulsion droplets that act as discrete picolitre reactors. These droplets, originally introduced by Dan Tawfik and Andrew Griffiths, are so small that high-throughput experiments on the order of > 108 become possible. Recent experiments to this end - in vitro expression, cell-based assays and continuous PCR reactions – will be discussed. See: http://www.bio.cam.ac.uk/~fhlab/index.html

 

Validation of mesospheric analyses
David Long
1 Apr 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The Met office produce analyses of the middle atmosphere on a daily basis. The project is concerned with validating these analyses against observational satellite data, namely profiles obtained from the EOS MLS and SABER experiments. Systematic baises in the dataset will be presented and concluesions drawn. Particular attention will be made to the operational gravity wave paramterisation scheme used at the Met Office and it's contribution to the accurate representation of the middle atmospheric circulation and temperature fields. The design of experiments with the aim of reducing the described systematic baises will be presented, with particular attention to the impact of including turbulent heating (due to gravity wave dissipation) in the operational parameterisation scheme.

 

Flux Rope Instabilities in Coronal Mass Ejections
Bernhard Kliem (Potsdam)
29 Mar 2010Harrison 170 Monday 2pmApplied Mathematics
25th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics" Images of erupting prominences typically suggest the magnetic structure of a single line-tied flux rope. Many prominence eruptions and coronal mass ejections (CMEs) begin with an approximately exponential rise, suggesting an instability. I will present numerical simulations of two relevant flux rope instabilities, the well-known helical kink instability and the torus instability, using the force-free line-tied flux rope equilibrium by Titov and Demoulin as initial condition. The properties of these instabilities indicate which parameters of the initial configuration control whether the eruption stays confined or becomes ejective, evolves into a fast or a slow CME, shows strong or weak writhing. Exponential as well as power-law rise profiles can be modelled. Supporting quantitative comparison of the simulations with several well observed eruptions will be included.

 

Averaging, passages through resonances, and captures into resonance in dynamics of charged particles
Anatoly Neishtadt (Loughborough University)
26 Mar 2010Harrison 170 (visualisation suite) Friday 3pmApplied Mathematics
A study of motion of charged particles in the field of an electromagnetic or electrostatic wave propagating in plasma in the presence of a uniform stationary background magnetic field is a classical problem in plasma physics. Under different relations between parameters of this problem completely different dynamical phenomena take place. In this talk I am planning to describe phenomena of capture into resonance and scattering on resonance that occur in the case of slow high frequency waves and a weak background magnetic field. Capture into resonance may lead to unlimited particle acceleration along the front of the wave (so called surfatron acceleration).

 

Population Modelling of Montastraea annularis
Heather Burgess
25 Mar 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
We are studying the reef-building coral Montastraea annularis. Previously we have modelled a population of coral patches using Population Projection Matrices. This involves the discretization of size. This discretization is restrictive because there is not enough data to accurately assign transition rates between some of these discretized size classes. Therefore we are now aiming to build an Integral Projection Model for this population which assumes continuous size classes. Some initial results are presented together with a comparison to our PPM approach.

 

Geomagnetic reversals from low order dynamo models
Graham Sarson (Newcastle University)
22 Mar 2010Harrison 170 Monday 2pmApplied Mathematics
24th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics" TBA

 

CANCELLED
Ozgur Akman
18 Mar 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

High-Frequency Self-Excited Oscillations in 3D Collapsible Tube Flows
Robert Whittaker (University of Oxford)
15 Mar 2010Harrison 170 Monday 2pmApplied Mathematics
Experiments show that steady flow along an elastic-walled tube can become unstable to large-amplitude oscillations involving both the tube wall and the fluid. We consider a 'Starling resistor' setup - a finite length elastic tube attached to rigid end sections, through which an axial flow is driven by either a steady flux at the downstream end or a steady pressure drop between the ends. I shall describe a theoretical analysis of small-amplitude high-frequency long-wavelength oscillations. We first consider the fluid mechanics (prescribed oscillations) and then the solid mechanics (to derive an appropriate tube law) in isolation. The two strands of work are then combined to investigate the full fluid--structure interaction problem for self-excited oscillations. We determine the form of the normal modes and obtain expressions for the growth rate and frequency of the oscillations. The predictions from our modelling show good agreement with numerical simulations performed using the oomph-lib C++ library.

 

Dynamics of microscale swimmers
Andrew Gilbert (with Feodor Ogrin, Peter Petrov and Peter Winlove)
11 Mar 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The problem of swimming on small scales, for example microorganisms, has a long and rich history. On such scales fluid may be thought of as very viscous (i.e. low Reynolds number) and one has to imagine swimming in treacle. It turns out that motions that are not time-reversible need to be adopted to have persistent motion in one direction, the so-called 'scallop theorem'. Such swimmers need to break the symmetry, and biological organisms have evolved a variety of ways of achieving this. With interest now in micromachines and microscale processing of chemical and biological materials - the idea of the lab-on-a-chip - there is interest in developing tiny scale pumps, valves, gels, and machines that can swim, perhaps to deliver a drug very precisely. Recently a microscale swimming device has been developed here in Physics by the Biomedical Physics Group, consisting of elastically coupled magnetic beads whose motion is driven by an external magnetic field. The seminar will discuss the mathematical modelling of such swimmers, regimes, parameters and mechanisms.

 

Molecular Programming
Luca Cardelli (Microsoft Research)
10 Mar 2010Harrison 215 Wednesday 2pmApplied Mathematics
Nucleic acids (DNA/RNA) encode information digitally, and are currently the only truly 'user-programmable' entities at the molecular scale. They can be used to manufacture nano-scale structures, produce physical forces, act as sensors and actuators, and do computation in between. Eventually we will be able to interface then with biological machinery to detect and cure diseases at the cellular level under program control. The technology to create and manipulate them has existed for many years, but the imagination necessary to exploit them has been evolving slowly. Recently, some very simple computational schemes have been developed that are autonomous (run on their own once started) and involve only short (easily synthesizable) DNA strands with no other complex molecules. We need programming abstractions and tools that are suitable for molecular programming. Low-level molecular design is required to produce molecules that interact in the desired controllable ways. On that basis one can then design various kinds of 'logic gates' and 'computational architectures', which is where much of the imagination is currently needed. Then one needs programming languages both at the level of gate implementation (Andrew Phillips at Microsoft Research Cambridge has built a strand-level DNA language and simulator), and at the level of circuit implementation (I will describe a Strand Algebra for implementing e.g. automata and Petri nets). Since DNA computation is massively concurrent, some tricky and yet familiar issues arise: the need to formally verify gate designs to avoid subtle deadlocks and race conditions, and the need to design high-level languages that exploit concurrency and stochasticity.

 

Micro-chaos in switched control systems with digital sampling
Piotr Kowalczyk (University of Manchester)
8 Mar 2010Harrison 170 Monday 2pmApplied Mathematics
TBA

 

Stability Analysis of Three Linearly Coupled Laser Oscillators
Nicholas Blackbeard
4 Mar 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Coupled nonlinear oscillators exhibit rich and complex dynamics. Semiconductor lasers are particularly interesting and technologically relevant examples of nonlinear oscillators that feature an intrinsic amplitude-phase coupling, quantified by the alpha-parameter. This characteristic nonlinearity causes different dynamics that can be utilised for a wide variety of applications. Many of these require the use of laser arrays - where the desired behaviour ranges from a high power coherent radiation to that of robust chaos. We study a system of three lasers with nearest neighbour coupling as a first step towards understanding the complexity of larger arrays.

 

Double Diffusive Magnetic Buoyancy Instability
Lara Silvers (City University)
1 Mar 2010Harrison 170 Monday 2pmApplied Mathematics
The generation of magnetic field by velocity shear and the field’s subsequent evolution are of great importance to an understanding of the operation of the solar dynamo. While the current dynamo paradigm contains many complex interacting components, an integral part of all current large-scale solar dynamo models is the creation of strong toroidal magnetic structures in the tachocline. Strong toroidal magnetic field is thought to be induced by the stretching action of the differential rotation on any background poloidal field. Subsequently, magnetic buoyancy instabilities of the generated field are invoked as the mechanism for the creation of distinct magnetic structures and their subsequent rise toward eventual emergence at the solar surface as active regions. In this talk I will focus on double diffusive magnetic buoyancy instabilities. I will discuss the criterion for this form of the instability to exist and show the first images from numerical simulations of this instability. This is the 22nd Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics"

 

For Whom the Bell Tolls -The mute (silent) bell in Cologne cathedral as a dynamical system
Tassilo Kuepper (University of Cologne)
25 Feb 2010Harrison 170 (vis suite) Thursday 2pmApplied Mathematics
The “Kaiserglocke” in the cathedral of Cologne is known as a spectacular example of a bell withstanding to ring since the clapper remained in the center of the bell, hence showing synchronous oscillations with the bell. Based on a mathematical model describing the motion of clapper and bell as two connected pendula Veltmann has shown that such synchronous oscillation may exist if only 4 characteristic parameters (“length” and mass of clapper and bell) satisfy a specific relation, which turned out to hold in the case of the “Kaiserglocke”. To prove, though, that under such constellation it is never possible for a bell to ring requires more advanced mathematical tools which had not yet been developed a 100 years ago. In this talk we will supplement Veltmann's argument with regard to stability considerations. The system of clapper and bell can serve as a nice illustration for modern mathematical investigations. Since Veltmann has only be interested to derive reasons for non-ringing of bells, he only needed to consider motions without contact between clapper and bell. True ringing relies on that contact. Mathematically that requires an extension from the classical system of differential equations used by Veltmann by “impacts”. This leads to the class of non-smooth dynamical systems, an area of present research. Our analysis shows how the interaction between bell and clapper influences the motion; for example we also show how various forms of ringing may result from a change of the coupling between clapper and bell.

 

The Theory of Configuration of Rapidly Rotating Giant Planets
Da-Li Kong
18 Feb 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The classical homogeneous Maclaurin ellipsoid model for rapidly rotating planets is extended to a more realistic two-layer configuration by making use of a minimized energy principle combined with the hydrostatic free surface condition. By adopting oblate spheroidal coordinates, a universal semi-analytical method is derived. The details about coordinate system, spheroidal harmonics, physical principles and special numerical integration techniques are intensively investigated.

 

Recurrence and extreme behaviour in dynamical systems
Mark Holland
11 Feb 2010Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
We explore the statistical properties of chaotic dynamical systems, including case studies of the Lorenz and Henon attractors. We examine questions such as the long term distribution of typical solution trajectories and how frequently they visit a prescribed region of the space. We also discuss the issue of asymptotic (in)dependence: how long do we have to wait until the system settles down to some equilibrium and does this equilibrium dependent on the initial conditions?

 

Condensation and metastability in stochastic particle systems
Stefan Grosskinsky (University of Warwick)
1 Feb 2010Harrison 170 Monday 2pmApplied Mathematics
The zero-range process is a recently well studied stochastic particle system that exhibits a condensation transition. When the total density exceeds a critical value, a finite fraction of all particles condenses on a single lattice site, which can be characterized mathematically by the equivalence of ensembles via convergence in specific relative entropy. Although the transition is continuous, finite systems exhibit interesting metastable behaviour and phase coexistence. We establish a law of large numbers for the excess mass fraction in the maximum, which turns out to jump from 0 to a positive value at the critical point. The metastable states can be characterized heuristically as fixed points of a simple effective dynamical system.

 

Amplified stochastic oscillations
Alan McKane (University of Manchester)
18 Jan 2010Harrison 170 Monday 2pmApplied Mathematics
I discuss a systematic approach to the modelling of various biological systems which starts from individual-based models, and then goes on to derive from these the corresponding deterministic equations (which are valid when the size of the system is large) and the leading order stochastic correction to them. The individual-based models are formulated as master equations, which allows use to be made of well-established methods from the theory of these equations to analyse their behaviours. In many cases large and well-defined stochastic cycles arise, even though the corresponding deterministic equations predict the system will approach a fixed point. Application of these ideas to predator-prey dynamics, epidemiology, cellular systems and autocatalytic reactions, amongst others, will be discussed.

 

Generalized stochastic resonance models for abrupt climate changes
Istvan Daruka (Eotvos University, Budapest)
14 Dec 2009Harrison 170 (3D vis suite) Monday 9.30amApplied Mathematics
The glacial-interglacial changes observed in Paleoclimatic temperature data of the middle to late Pleistocene epochs are analyzed in terms of two generalized stochastic resonance models including memory effects. The simple models account for the asymmetric, saw-tooth shaped temperature oscillations occurring both at Milankovitch (100kyr) and millennial time scales.

 

Long-term behavior of linear, stochastic, discrete time systems: Asymptotic amplification and attenuation in covariance
Iakovos Matsikis
10 Dec 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Lyapunov exponents are the tool widely used in studying the long-term dynamics of systems under the influence of randomness. They do not, however, take into account the effect of initial conditions and in general are difficult to compute. In this talk we will employ second mean analysis and ideas from linear algebra and will present the new notions of asymptotic amplification and attenuation in covariance. These new mathematical tools are depended on initial conditions, are easily computed and together with the second mean exponent they provide a framework of study for linear stochastic systems. Specifically they can be used in the construction of envelopes that capture the system's dynamics and make visible its asymptotic properties. We will finally apply our results to a population dynamics model.

 

On the existence of quasipattern solutions of the Swift-Hohenberg equation.
Alastair Rucklidge ( University of Leeds)
9 Dec 2009Harrison HAR170 Wednesday 10amApplied Mathematics

 

Assimilating data into ocean models
Chris Jones (University of Warwick)
7 Dec 2009Harrison 170 Monday 2pmApplied Mathematics
Abstract: The technology-enabled increase in data acquisition is well matched by that coming from computational modeling. The subject of Data Assimilation (DA) addresses the issue of making optimal use of both sides of this equation. Bayes’ Theorem provides a framework for DA, but this is only the beginning of what is interesting mathematically. I have come at this subject from the perspective of Lagrangian DA, which aims at assimilating data from ocean instruments that "go with the flow". I will argue that Lagrangian DA is both exciting and promising exactly because the Lagrangian flow can be very complicated (highly nonlinear, chaotic etc) even though the fluid flow field may be tame. I will suggest that this leads to a guiding principle for DA as a whole.

 

Palaeoclimate and dynamical systems : challenges and promises
Michel Crucifix (Université Catholique de Louvain)
3 Dec 2009Harrison 170 (3D suite) Thursday 2pmApplied Mathematics
Palaeoclimate data present important challenges to the climate modeller : sparse data, dating uncertainties, high non-stationarities, and unknown physical constraints at these time scales. On which basis may one formulate tractable problems in such difficult conditions ? First, palaeoclimate do indeed show spatio-temporal structures owing to the effect of orbital elements, and phenomena of bifurcation may be visualised with continuous wavelet transforms. These offer opportunities of empirical model validation and selection, in spite of dating uncertainties. Other methods of identification, for example clustering methods to determine the number of regimes, show promise but will not be adressed here. Second, we do have a physical knowledge of the climate system, but often the physical models employed nowadays lack the dynamical range required to tackle palaeoclimate time scales. Consider this : building a 3000-m-thik ice sheet over 80,000 years imply a yearly mass imbalance of 37 cm/year : arguably below the precision of current models. Furthermore, physical mechanisms proper to palaeoclimate time scales, such as ice sheet instability, have received little attention in current models. The strategy is therefore to reduce empirically general circulation models, and build on this basis parameterisations that may be used and calibrated at more ambitious time scales. Several challenges, especially regarding stochastic parameterisations and carbon cycling remain unmet. Third, statisticians have been creative at developing parameter estimation methods suitable for dynamical systems. Here we show examples based on an implementation of the particle filter with auxiliary sampling, adapted for the parameter estimation problem. Such algorithm provide a basis to formulate the model calibration and selection problem on a sound statistical basis, making use of prior information obtained with more sophisticated models. The lecture will be articulated around these three themes, with examples based on Pleistocene palaeoclimate time series, simulations with the LOVECLIM earth system model of intermediate complexity, and particle filtering of simple dynamical systems.

 

New nonlinear mechanisms of midlatitude atmospheric low-frequency variability
Alef Sterk (University of Groningen)
30 Nov 2009Harrison 170 Monday 2pmApplied Mathematics
In this talk we will discuss the dynamical mechanisms potentially involved in the so-called atmospheric low-frequency variability, occurring at midlatitudes in the Northern Hemisphere. This phenomenon is characterised by recurrent non-propagating and temporally persistent flow patterns, with typical spatial and temporal scales of 6000-10000 km and 10-50 days, respectively. We study a low-order model derived from the 2-layer shallow water equations on a $\beta$-plane with bottom topography, which is forced by relaxation to an imposed westerly wind. The low-order model is obtained by a Galerkin projection retaining only the Fourier modes with wavenumbers 0, 3 (zonal) and 0, 1, 2 (meridional). The amplitude of the bottom topography and magnitude of zonal wind forcing are used as control parameters to study bifurcations of equilibria and periodic orbits. In the low-order model equilibria destabilise through Hopf bifurcations, which can be interpreted in terms of mixed barotropic/baroclinic instabilities. These Hopf bifurcations give birth to two families of periodic orbits with different spatio-temporal characteristics. In turn, the periodic orbits bifurcate into strange attractors via the following codimension-1 routes to chaos: period-doublings, break-down of 2-tori, and intermittency. The dynamics on these strange attractors are associated with low-frequency variability: the vorticity fields show weakening and amplification of non-propagating planetary waves on time scales of 10-200 days. These spatio-temporal characteristics are ``inherited'' (by intermittency) from the two families of periodic orbits and are detected in a relatively large region of the parameter plane. This scenario differs fundamentally from those proposed in the literature so far, which mainly rely on theories involving multiple equilibria. This is joint work with Renato Vitolo (Exeter), Henk Broer (Groningen), Carles Simo (Barcelona), and Henk Dijkstra (Utrecht)

 

Vertical Discretisations for Coupling the Atmospheric Boundary Layer with the Large Scale Dynamics
Dan Holdaway
26 Nov 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
It is now well understood that for modelling the equations describing the large scale atmosphere the Charney-Phillips grid is preferable to the Lorenz grid. Not only does the Lorenz grid give a poorer representation of the dispersion relation, it also supports a single zero frequency computational mode. For modeling the atmospheric boundary layer it is preferable to use a Lorenz grid, otherwise an averaging is required in order to compute the Richardson number. We show, through linearisation and comparison of transients, that vertical configurations can be systematically compared for the boundary layer type problem. This can then be used in order to compare configurations of the complete coupled system and thus to aid in understanding the affect that the boundary layer has on both the computational mode and the overall dispersion relation.

 

Numerical experiments for $L_1$-norm regularisation in variational data assimilation.
Melina Freitag (University of Bath)
23 Nov 2009Harrison 170 Monday 2pmApplied Mathematics
In this talk we give a brief introduction to data assimilation and we show that data assimilation using 4DVar (4D Variation) can be interpreted as some form of Tikhonov regularisation, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that $L_1$-norm penalty regularisation recovers sharp edges in the image better than the $L_2$-norm penalty regularisation. We apply this idea to 4DVar for problems where shocks are present and give some examples where the $L_1$-norm penalty approach performs much better than the standard $L_2$-norm regularisation in 4DVar.

 

Evolution of biological system dynamics
Orkun Soyer
19 Nov 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Systems biology aims to understand the structure and dynamics of biological networks that underlie physiological responses, while synthetic biology ultimately aims to implement such networks. A fundamental question at the crossroads of these two fields is; what is the repertoire of biological networks that can underlie a given response dynamics? Answering this question could allow us to understand how networks underlying a given response would differ in different species and whether there are minimal networks, more amenable for synthetic biology implementations. In this talk, I will illustrate how evolutionary and mathematical approaches can be employed towards reaching such an understanding.

 

SUPR Models : Models for the Study of the Uncertainty in PalaeoClimate Reconstruction.
John Haslett (Trinity College, Dublin)
18 Nov 2009Harrison LT04 Wednesday 3pmApplied Mathematics
We present some modelling challenges that have arisen in the context of our work on palaeoclimate reconstruction. The simplest version of the the problem is as follows. A 10m core of lake sediment contains pollen deposited over the past several millennia. Samples ($n =150$) from along the core are examined under a microscope; each sample is rendered as a multivariate count vector $y^a_i$ of `ancient' pollen. Such vectors describe the composition of the ancient `pollen rain'. As such they provide information on the surrounding vegetation at times in the past; that is, ancient pollen is a `proxy' for ancient climate, for we know from modern data that vegetation composition reflects the climate $c$. Models built on such data, $D^m$, provide information on the probability distribution $\pi[y|c, D^m]$. This in turn permits inference $\pi[c|y^a_i,D^m]$ on the ancient climates corresponding to the samples. Variations on this are applied to other proxies (eg diatoms) in other archives (eg ocean sediment). At its simplest, palaeoclimate reconstruction returns `best climates' $\hat c^a_i$ corresponding to each $y^a_i$. Our concern in this paper lies with the underlying uncertainties and with the statistical models that we have found to be useful. For example there are many cores, and sample counts thus have spatial and temporal location $(s_i, t_i)$. Individually each $\pi[c|y^a_i,D^m]$ is a statement of uncertainty concerning an aspect of a common latent space-time process $C(s,t)$. How can we formalise the joint statistical inference? Our approach has been Bayesian, and has rested on stochastic process models including: Gaussian (Markov) Random Fields; a novel monotone stochastic process with continuous sample paths, based on a bivariate renewal process; and long tailed random walks with Normal Inverse Gaussian increments. The talk will illustrate their use in this joint inference, and some of the many remaining challenges. There are of course several scientific challenges to the underlying methodology, for example: To what extent can we rely on modern data to tell us about ancient climate-vegetation relationships? Is climate-change the only driver of vegetation change. We look forward to some of the statistical challenges that these questions pose. This work has involved collaboration with, and stimulation from, many including Brian Huntley, Andrew Parnell, Mike Salter-Townshend, Havard Rue, Alan Gelfand and Caitlin Buck. It has been supported by several grants from Science Foundation Ireland and by a welcome sojourn with Durham University's Institute of Advanced Study.

 

Codimension two bifurcations arising in a system of phase coupled oscillators
Ann-Katrin Becher (Cologne University, Germany)
17 Nov 2009Harrison 170 Tuesday 2pmApplied Mathematics
A model of phase coupled oscillators is introduced describing a network with both excitatory and inhibitory interactions. The phase dynamics are modelled by a Kuramoto-like system but without symmetries with regard to coupling. The coexistence of inhibitory and excitatory interactions and the asymmetry of coupling give rise to several different scenarios of synchronization. We study the model from the standpoint of bifurcation theory of low-dimensional dynamical systems. Therefore we focus on different configurations of coupling which lead to various bifurcation phenomenons with codimension >1.

 

Chimera states in heterogeneous Kuramoto networks
Carlo Laing (Massey University)
16 Nov 2009Harrison 170 Monday 2pmApplied Mathematics
Since 2002 several groups have studied "chimera states" in networks of identical phase oscillators, in which some oscillators synchronise while the remainder are incoherent. However only in the simplest case did the authors study the stability of such states. I show how to greatly generalise these results to other networks, deriving time-evolution PDEs with as many spatial dimensions as the network. The results emphasise the commonality of the dynamics of different networks, and provide stability information that was previously inferred.

 

Visualising probabilistic forecasts
Tim Jupp
12 Nov 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
We consider the problem of creating maps of ternary probabilistic forecasts. As in traditional (binary) methods, continuous forecast distributions are projected onto discrete ternary forecasts, in which probabilities are assigned to three categories defined by quantiles of the current climatology. Our innovation is to think geometrically and consider each ternary forecast as a point in the triangle of barycentric coordinates (i.e. a 2-simplex). This allows us to assign a unique colour to each forecast from a continuum of colours defined on the triangle. We show that a single easy-to-interpret map can convey full information from a ternary forecast in addition to a measure of the past skill of the forecasting system. Specifically, the forecast at each location is expressed by a circle whose colour encodes the ternary forecast and whose radius encodes past skill. We use the natural symmetries in the problem to assign colours to forecasts using the hue-saturation-value colour system. We derive mathematical measures of subjective certainty H, dominant category theta and misfit R. These measures are used to assign strong colours to forecasts that differ greatly from the climatology, and large circles to regions of high skill. Finally, we show how the concepts of uncertainty, reliability, resolution and calibration (which are usually taken to apply to binary forecasts) can be extended to ternary forecasts. Methods for interpreting these quantities geometrically are proposed. These ideas are illustrated with probabilistic precipitation forecast data from climate model runs, processed using "R" and displayed using "Google Earth".

 

Using model reduction methods from control theory within variational data assimilation
Caroline Boess (University of Reading)
9 Nov 2009Harrison 170 Monday 2pmApplied Mathematics
In this talk the use of model order reduction methods from control theory within variational data assimilation is discussed. The focus is on four-dimensional variational assimilation – a method which requires the minimization of a series of simplified cost functions. These simplified functions are usually derived from a spatial or spectral truncation of the full system being approximated. In this talk a new method for deriving these simplified problems is proposed, based on control theoretic model reduction methods. Moreover, a new model reduction approach for unstable systems is considered. It is shown that this performs well within the state estimation problem occurring in data assimilation.

 

What really matters in data assimilation?
Dan Cornford (Aston University)
5 Nov 2009Harrison 101 Thursday 2pmApplied Mathematics
In this talk I will consider the state of the art in data assimilation theory, focussing on our recent variational Bayesian approaches, but also discussing path sampling, particle filtering, 4DVAR and ensemble Kalman filters. I will then consider the question of what really matters in data assimilation - in particular I will consider the formulation of the data assimilation problem from a statistical perspective, and try to relate this to the real world application of data assimilation methods in operational settings.

 

Dynamics and geometry near resonant bifurcations
Sijbo Holtman (University of Groningen, NL)
29 Oct 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
In this talk we focus on non-linear parameter dependent dynamical systems exhibiting resonance. This phenomenon occurs if oscillatory subsystems interact, while the corresponding frequencies are rationally related. Such a situation appears in many real-world scenarios, e.g., coupled pendula, the moon-earth system, and electric circuits. The main goal is to explain the parameter dependence of the qualitative behavior of the dynamics. In particular, we consider the geometry of parameter values for which resonance occurs. It turns out that in the non-degenerate case the geometry is given by the well-known 2-dimensional Arnol'd resonance tongue. A mildly degenerate case corresponds to a more complicated 4-dimensional geometry, which we describe in detail. We also present so-called recognition conditions determining to which of these two cases a given resonant family of dynamical systems belongs.

 

Compressible Hartmann and mixed Ekman-Hartmann boundary layers.
Krzysztof Mizerski (University of Leeds)
26 Oct 2009Harrison 170 Monday 2pmApplied Mathematics
21st Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics" We consider the effect of compressibility in mixed Ekman-Hartmann boundary layers on an infinite plane ($z=0$), in the presence of an external magnetic field oblique to the boundary. The aim is to investigate the influence of the magnetic pressure on the fluid density, and hence, via mass conservation, on the mass flow into or out of the boundary layer. We find that if the $z$-component of vorticity in the main flow, immediately above the boundary layer, is negative, then there is a competition between Ekman suction and the magnetic pressure effect. Indeed, as the magnetic field strength is increased, the magnetic pumping may overcome the Ekman suction produced by anti-cyclonic main flow vortices. Such competition may play a role in the solar tachocline, the region of strong shear at the base of the convective zone and a plausible site for the solar dynamo. Here field must be confined until it becomes sufficiently strong that, on escaping, it can rise to the solar surface relatively unscathed, thus giving rise to active regions. The Ekman-Hartmann boundary layer is the simplest model of a thin region with large shear and a magnetic field; our simplified model may therefore describe some of the important physics of the tachocline.

 

A model for physics-dynamics coupling
Bob Beare
22 Oct 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Formulations of numerical weather prediction and climate models divide conveniently into the resolved dynamical core and the sub-grid physical parametrizations. Improving these components is an ongoing area of research and development. Arguably less examined, however, is the coupling between these components. More research on the physics-dynamics coupling might therefore lead to significant improvements in future model performance. Here, we demonstrate a new approach to physics-dynamics coupling. We compare a full dynamics model with a model explicitly constrained to balance the large scale dynamics and the boundary layer parametrization.

 

Using constraint-based optimization to model multilayer buckling phenomena
Rorie Edmunds (University of Bath)
19 Oct 2009Harrison 004 Monday 2pmApplied Mathematics
A constraint-based methodology will be presented which has successfully been applied to a solid, elastic, frictional model for parallel folding. Conceived from investigations of the engineering design process, the constraint-based methodology has helped design engineers identify and understand the initial constraints and limitations placed on a system. Written as a set of algebraic expressions the design objectives and constraints can be formulated and optimal solutions found using numerical optimization techniques. A bespoke Constraint Modeller has been created to embrace the methodology. This is able to resolve large systems comprising of over 100 degrees-of-freedom using a variety of optimization routines. Parallel folding is representative of multilayer geological systems undergoing buckling deformation and modelling the evolution of folds poses a significant problem. Simplifying down to a two layer formulation, the behaviour of the central interface is modelled using a number of points whose movement is constrained. Looking for least energy solutions, the small-deflection model closely matches the sequential nature seen in experiments. Using the full large-deflection energy formulation, further phenomena are found which match experimental evidence. Additionally, by altering some of the parameters, the parallel folding model can admit solutions that are kink band-like in structure. Thus insight is given into the transition between the different folding-types seen in nature.

 

Geoengineering the climate: unthinkable last resort or optimal solution?
Peter Cox
15 Oct 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

The liquid top: precession and tides in planetary cores
Andreas Tilgner (University of Goettingen, Germany)
5 Oct 2009Harrison 004 Monday 2pmApplied Mathematics
20th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics"

 

Binocular rivalry - a new model
Peter Ashwin
2 Jul 2009Harrison 106 Wednesday 3.30pmApplied Mathematics (Internal)
The effect of binocular rivalry is a well-known phenomenon in the psychology of perception, where the brain will move between recognition of two conflicting images presented to each eye. It is particularly interesting as a system where the brain constantly "changes its mind" in the absence of any change to the input. This talk will discuss a newly developed model of the author and A Lavric, based on heteroclinic switching.

 

Anomalous diffusion of migrating biological cells
Rainer Klages (Queen Mary, University of London)
29 Jun 2009Harrison 101 Monday 2pmApplied Mathematics

 

Harper operators, equations and maps: a laboratory for strange nonchaotic attractors
Joaquim Puig (Universitat Politecnica de Catalunya, Barcelona, Spain)
15 Jun 2009Harrison 101 Monday 2pmApplied Mathematics
This talk is part of the workshop "Global Dynamics and Applications" held on 15/16 June 2009 in SECaM, University of Exeter. (http://secamlocal.ex.ac.uk/people/staff/rv211/woglodyn09.html)

 

Phase transitions in statistical physics models
Barrie Cooper
11 Jun 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
From a physical point of view, macroscopic properties of a material such as its temperature, structure and magnetisation are determined by the properties and interactions of its constituent microscopic particles. A primary aim of statistical physics is to study these emergent properties of complex systems. Of particular importance are phase transitions, whereupon there is a qualitative change in the macroscopic properties of a system, such as the spontaneous demagnetisation of a ferromagnet at the Curie point. I will describe a family of statistical physics models exhibiting phase transitions and explore how representation theory and the algebraic properties of the operators in such models can help drastically reduce the complexity of the numerical calculations required to detect such a phase transition.

 

Boundary layer dynamics in extra-tropical cyclones
Ian Boutle (University of Reading)
8 Jun 2009Harrison 101 Monday 2pmApplied Mathematics
19th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal "Geophysical and Astrophysical Fluid Dynamics"

 

Wave propagation on adapting, inhomogeneous and unstructured grids
John Thuburn
4 Jun 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Solitons, homoclinic orbits and exponentially small phenomena in reversible systems
Tomas Lazaro (Universitat Politecnica de Catalunya, Barcelona, Spain)
1 Jun 2009Harrison 101 Monday 2pmApplied Mathematics

 

Asymmetric Desynchronization and Ratcheting in Networks of Coupled Oscillators
Ozkan Karabacak
28 May 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
We analyze an example system of four coupled phase oscillators and discover a novel phenomenon that we call “heteroclinic ratchet”; a particular type of robust heteroclinic network on torus where connections wind in only one direction. We show that, for coupled phase oscillators, this type of heteroclinic network can exist as an attractor in phase space resulting in asymmetric desynchronization of certain pairs of oscillators. In other words, oscillators with natural frequencies w1 and w2 break synchrony for w1-w2>0 but not for w1-w2<0. Similarly, when w1=w2, arbitrary small noise results in a break of synchrony such that after the desynchronization the observed frequencies W1 and W2 satisfy W1>W2.

 

The effect of mechanical forcing on buoyancy-driven flows
Remi Tailleux (University of Reading)
18 May 2009Harrison 101 Monday 2pmApplied Mathematics

 

Reconnection in braided magnetic fields
Gunnar Hornig (University of Dundee)
11 May 2009Harrison 101 Monday 2pmApplied Mathematics

 

A catalogue of singularities
Jens Eggers (University of Bristol)
27 Apr 2009Harrison 101 Monday 2pmApplied Mathematics

 

TBC
Andrew Gilbert (University of Exeter)
12 Mar 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

TBA
Chris Jones (University of Leeds)
9 Mar 2009Harrison 101 Monday 2pmApplied Mathematics

 

A Hamiltonian approach to variational data assimilation
Ian Roulstone (University of Surrey)
2 Mar 2009Harrison 101 Monday 2pmApplied Mathematics

 

Extending semi-geostrophic theory to include boundary layer diffusion
Bob Beare (University of Exeter)
26 Feb 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Since the seminal work of Hoskins (1975), the semi-geostrophic model has proved invaluable in describing the dynamics of meteorological fronts and cyclone formation. The model has also been a focus for the mathematically inclined as, for example, the equations can be proved to be well-posed and can be interpreted in terms of variational principles. However, a weakness of the semi-geostrophic model as an interpretive framework for climate models is that it contains no inclusion of the sub-grid physical processes such as boundary layer diffusion. In this talk, I will review some of the existing approaches to including boundary layer diffusion in semi-geostrophic theory and propose a more accurate formulation.

 

Localised pattern formation
Jonathan Dawes (University of Bath)
23 Feb 2009Harrison 101 Monday 2pmApplied Mathematics

 

TBC
Svitlana Popovych (University of Cologne)
19 Feb 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Dynamical networks and graph theory
Markus Kirkilionis (University of Warwick)
16 Feb 2009Harrison 101 Monday 2pmApplied Mathematics
Non-linearities like mass-action kinetics describe events created by collisions of molecules in a well-mixed environment giving them locally the same probability to meet each other. Moreover this probability is only dependent on the concentration of the mutual partners. In a deterministic approximation the dynamical system describing the evolution of molecular concentrations over time can be interpreted as defining a dynamical network, for example linking species together by the ability to be transformed into each other. Different feedback loops encoded in the non-linearities will determine the qualitative behaviour of the system. In this talk we are looking at dynamical networks and ask a fundamental but unfortunately hard mathematical question which is currently discussed in many branches of complex systems theory and systems biology: What is the relationship between network topology and qualitative behaviour of such a dynamical network? The answer to this question will depend on what kind of information can be retrieved from different graphs associated to the dynamical system. In this talk I will discuss several such graphs that have been constructed for reaction systems which here will serve as a basic example of a dynamical network in general.

 

Smoothing geometric maps and applications to KAM theory.
Alejandra Gonzalez-Enriquez (University of Exeter)
12 Feb 2009Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
We show that finitely differentiable diffeomorphisms which are either symplectic, volume-preserving, or contact can be approximated with analytic diffeomorphisms that are, respectively, symplectic, volume-preserving or contact. We prove that the approximating functions are uniformly bounded on some complex domains and that the rate of convergence, in $C^{r}$-norms, of the approximation can be estimated in terms of the size of such complex domains and the order of differentiability of the approximated function. As an application to this result, we give a proof of the existence, the local uniqueness and the bootstrap of regularity of KAM tori for finitely differentiable symplectic maps.

 

Numerical Methods For Weather and Climate Models
James Kent (University of Exeter)
5 Feb 2009Harrison 101 Thursday 2pmApplied Mathematics (Internal)
Numerical models for weather and climate have finite resolution in space and time; the governing equations are solved on the resolved scales while important processes occurring on smaller scales must be represented by sub-grid models. The numerical schemes used to solve the resolved scales are not perfect; they suffer from truncation errors. A controversial issue is whether the truncation errors, by accident or by design, can be interpreted as representing some sub-grid processes.

 

Computer assisted rigorous hyperbolicity estimates in one-dimensional dynamics
Stefano Luzzatto (Imperial College)
2 Feb 2009Harrison 101 Monday 2pmApplied Mathematics

 

Damped wave equations with supercritical nonlinearities
Sergey Zelik (University of Surrey)
26 Jan 2009Harrison 101 Monday 2pmApplied Mathematics

 

Bifurcation analysis of heteroclinic chains involving periodic orbits
Thorsten Riess
10 Dec 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The bifurcation analysis of heteroclinic chains is important for many applications; such chains arise for example in biological models (cells) or physical models (lasers), and their existence is often connected with a rich variety of nearby dynamics. Recently, some of the theoretical and computational tools for the analysis of heteroclinic chains connecting hyperbolic equilibria have been extended to chains connecting hyperbolic equilibria and hyperbolic periodic orbits. The analytical results obtained via an extension of Lin's method can readily be applied to an equilibrium-to-periodic-orbit cycle (EtoP cycle), giving rise to bifurcation equations for homoclinic orbits near the EtoP cycle. These analytical results are confirmed by numerical evidence for a concrete example, which is obtained by a computational method to find and continue EtoP connections in parameters. This numerical method is also based on the theoretical framework of Lin's method.

 

The mean field approach to the transport of magnetic field
Alice Courvoisier (University of Leeds)
8 Dec 2008Harrison 101 Monday 2pmApplied Mathematics
18th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics'

 

Stochastic approximation of fast chaotic Hamiltonian degrees of freedom
Wolfram Just (Queen Mary, University of London)
1 Dec 2008Harrison 101 Monday 2pmApplied Mathematics
We restate the problem whether the Hamiltonian dynamics of slow variables coupled to a small number of fast chaotic degrees of freedom can be modelled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining drift and diffusion terms and the accuracy of the stochastic approximation on all time scales.

 

TBC
Renato Vitolo (University of Exeter)
26 Nov 2008Harrison 215 Wednesday 10amApplied Mathematics (Internal)

 

Applications of delay differential equations in science and engineering
Thomas Erneux (Universite Libre de Bruxelles, Belgium)
24 Nov 2008Harrison 101 Monday 2pmApplied Mathematics

 

The Holm Navier-Stokes-alpha equation
Andrew Soward (University of Exeter)
19 Nov 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Multifractal analysis for non-uniformly hyperbolic dynamical systems
Thomas Jordan (University of Bristol)
17 Nov 2008Harrison 101 Monday 2pmApplied Mathematics

 

Modelling and Dynamics of coupled laser
Hartmut Erzgraber (University of Exeter)
12 Nov 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Heteroclinic structures in small motifs of Hodgkin-Huxley neurons? Indication from a numerical study
Thomas Nowotny (University of Sussex)
10 Nov 2008Harrison 101 Monday 2pmApplied Mathematics

 

Comparing deterministic and stochastic models for cell motility and domain growth
Ruth Baker (University of Oxford)
3 Nov 2008Harrison 101 Monday 2pmApplied Mathematics

 

Probing the temporal power-law characteristics of the global atmospheric circulation
Dmitry Vyushin (University of Toronto, Canada)
30 Oct 2008Harrison 103 Thursday 2pmApplied Mathematics
Climate variability on timescales longer than a year is often characterized by temporal scaling ("power law") behaviour for which spectral power builds up at low frequencies in contrast to red-noise behaviour for which spectral power saturates at low frequencies. We estimate temporal power-law exponents ("Hurst exponents") for the global atmospheric circulation of pre-industrial control and 20th century simulations for the troposphere and stratosphere. We consider 17 most established climate models from the CMIP3 archive. We show that current-generation climate models generally simulate the spatial distribution of the Hurst exponents well. We also use simulations of an atmospheric GCM with different climate forcings to explain the Hurst exponent distribution and to account for discrepancies in scaling behaviour between different observational products. Our analysis demonstrates that at the surface regions of large power law exponents coincide with the regions of strong decadal variability, namely northern North Atlantic, northern and tropical Pacific, and the Southern Ocean. In the free atmosphere these regions are confined to the tropical and subtropical troposphere and stratosphere. The spectral steepness in the former is explained by its strong coupling to the surface and in the later by its sensitivity to the volcanic aerosols. We conclude that this analysis of how climate models capture the falloff of spectral power with frequency provides valuable physical insight into climate variability.

 

Cointegration: an econometric time-series tool applied to the carbon cycle
Tim Jupp (University of Exeter)
29 Oct 2008Harrison 101 Wednesday 10amApplied Mathematics (Internal)

 

Designing the dynamics of coupled oscillators
Peter Ashwin (University of Exeter)
22 Oct 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Vortices, waves and numerical schemes for mesoscale atmospheric dynamics
Peter Bartello (McGill University, Montreal, Canada)
20 Oct 2008Harrison 101 Monday 2pmApplied Mathematics
An overview of recent research on the wave/vortex dynamics of the mesoscale range of the atmospheric energy spectrum will be presented. The presence or absence of these dynamics in a variety of "realistic" models will also be discussed. A few of these reproduce the correct spectrum while most do not. It is argued that this may be attributed to their numerics and/or parameterisation schemes.

 

Flood rich periods and flood poor periods in the UK's hydrological record - a new way of thinking through 21st century flood risk?
Stuart Lane (University of Durham)
20 Oct 2008Harrison 106 Monday 2pmApplied Mathematics

 

Small Gain Theorems and Feedback Loops - Can They Really Be Relevant in Modelling Endangered Plants?
Stuart Townley (University of Exeter)
15 Oct 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

A lattice Boltzmann formulation for magnetohydrodynamics with current-dependent resistivity
Paul Dellar (University of Oxford)
13 Oct 2008Harrison 101 Monday 2pmApplied Mathematics

 

Astrophysical applications of self-similar flows
Yu-Qing Lou (Tsinghua University, China)
6 Oct 2008Harrison 101 Monday 2pmApplied Mathematics
17th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics' *** Astrophysical research activities at Tsinghua University China are briefly described. We present new results on self-similar hydrodynamics and magnetohydrodynamics under self-gravity. Astrophysical applications include star formation, planetary nebulae, stellar collapses, rebound shocks of supernovae, galactic bulge evolution and so forth. We also describe astrophysical voids in self-similar expansion.

 

Reconciling an emissions model with a climate change model
Peter Cox and Owen Kellie-Smith (University of Exeter)
13 Jun 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Some climate models take (as inputs or control variables) scenarios of future greenhouse gas emissions and output measures of climate change. The altered climate does not necessarily feed back into the emission scenarios. This work-in-progress aims to identify the space of feasible emission scenarios, via a highly simplified economic model in which emissions are fed back as a model output.

 

Determining Convergence Rates: Order of Accuracy vs Function Continuity.
Dan Holdaway (University of Exeter)
30 May 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
The relation between order of accuracy and convergence rate for simple linear finite difference schemes for differentiation and advection is examined theoretically and empirically. When a function is sufficiently smooth convergence will be given by the order of accuracy of the scheme. For less smooth functions convergence rate for differentiation can be determined from the function's spectral slope. Convergence for advection of a non smooth function involves an interaction between order of accuracy and spectral slope.

 

Dynamics of aircraft on the ground
Bernd Krauskopf (University of Bristol)
29 May 2008Harrison 170 Thursday 2pmApplied Mathematics

 

Systematic strategies for stochastic modelling of climate variability
Christian Franzke (British Antarctic Survey, Cambridge)
19 May 2008Harrison 203 Monday 2pmApplied Mathematics
The climate system has a wide range of time scales for important physical processes, ranging from organized synoptic scale weather systems on a daily time scale, extra-tropical low-frequency variability on a time scale of 10 days to months, to decadal time scales of the coupled atmosphere-ocean system. An understanding of the processes acting on these different time scales is important since all these processes interact with each other due to the nonlinearities in the governing equations. The spatial structure of extra-tropical variability can be described by only a few teleconnection patterns. The two most prominent examples are the North Atlantic Oscillation (NAO) and the Pacific-North American (PNA) pattern. These teleconnection patterns explain a large amount of the total variability, have a strong impact on surface climate and are related to climate change. In atmosphere-ocean science, slowly evolving large-scale structures like the NAO and PNA, and their statistical behavior, are often of the most interest, and yet the computational power of complex climate models is spent on resolving the smallest and fastest variables in the system. Reduced models for only the most important teleconnection patterns provide computationally feasible alternatives for calculating the statistical behavior of the climatologically relevant slow variables. These reduced models give also insight into the dynamics of the slow variables and their interaction with the unresolved variables. In these reduced models the fast variables are systematically represented by stochastic processes. In my presentation I will discuss systematic strategies to extract reduced stochastic models from data of complex atmospheric circulation models. The stochastic mode reduction strategy accounts systematically for the effect of the unresolved degrees of freedom and predicts the functional form of the effective reduced equations. These procedures extend beyond simple Langevin equations with additive noise by predicting nonlinear effective equations with both additive and multiplicative (state-dependent) noises. The stochastic mode reduction strategy predicts rigorously closed form stochastic models for the slow variables in the limit of infinite separation of time-scales. Even though there is only a very moderate time-scale separation in the atmospheric flows the reduced stochastic models reproduce well the statistics of the complex circulation models. The reduced models have about 10 or less degress of freedom while the complex atmospheirc models have about 1000 degress of freedom.

 

The phase relation between poloidal and toroidal magnetic fields in latitude and longitude observed in the cycles 22-23
Valentina Zharkova (University of Bradford)
12 May 2008Harrison 203 Monday 2pmApplied Mathematics

 

Numerical wave propagation on the Hexagonal C-Grid
John Thuburn (University of Exeter)
9 May 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

TBA
Ingo Fischer (Heriot-Watt University, Edinburgh)
8 May 2008Harrison 170 Thursday 2pmApplied Mathematics

 

Using the past to predict the future: what can we learn from 20th century and last millennium temperature changes?
Gabi Hegerl (University of Edinburgh)
28 Apr 2008Harrison 203 Monday 2pmApplied Mathematics
16th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics'

 

Modelling the atmospheric boundary layer
Bob Beare (University of Exeter)
14 Mar 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

The atmospheric boundary layer is the turbulent layer above the Earth's surface with a thickness between 100m and 2km. It is responsible for exchange of momentum, heat and moisture between the surface and the free atmosphere, so is an important component of the climate system.

This talk describes simulations of the atmospheric boundary layer as it changes from it's weak turbulence state at night to its strong turbulence in the day. The mixed phase state between the night and day time turbulence is defined more precisely than before and is shown to scale strongly with wind shear.

 

Stability of rolls in rotating magnetoconvection with physically realistic boundary conditions
Olga Podvigina (Russian Academy of Sciences, Moscow, Russia)
12 Mar 2008Harrison 173 Wednesday 11amApplied Mathematics
15th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics' *** We consider small amplitude Boussinesq convection in a horizontal layer rotating about a vertical axis with an imposed vertical magnetic field. Rigid electrically insulating no slip horizontal boundaries held at constant temperature are assumed. Depending on parameter values, convection at the onset can be steady or oscillatory. For the steady onset of convection rolls can emerge in a supercritical or subcritical bifurcation of the trivial steady state, and they can be unstable with respect to the same rolls flow rotated by an arbitrary angle. We study, for which parameter values convection at the onset is steady or oscillatory, and how stability of small amplitude rolls depends on the parameters.

 

Optimization of ergodic averages
Oliver Jenkinson (Queen Mary, University of London)
10 Mar 2008Harrison 209 Monday 2pmApplied Mathematics

 

Mean-field equations for weakly non-linear two-scale perturbations of forced hydromagnetic convection in a rotating layer
Vladislav Zheligovsky (Russian Academy of Sciences, Moscow, Russia)
10 Mar 2008Harrison 203 Monday 11amApplied Mathematics
14th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics' *** We consider stability of regimes of hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the evolution of weakly non-linear mean perturbations are derived under the assumption that the alpha-effect is insignificant in the leading order (e.g., due to a symmetry of the system). The mean-field equations generalise the standard equations of hydromagnetic convection: New terms emerge - a second-order linear operator representing the combined eddy diffusivity, and quadratic terms associated with the eddy advection. If the perturbed CHM regime is non-steady and insignificance of the alpha-effect in the system does not rely on the presence of a spatial symmetry, the combined eddy diffusivity operator also involves a non-local pseudodifferential operator. If the perturbed CHM state is almost symmetric, alpha-effect terms appear in the mean-field equations as well. Near a point of a symmetry-breaking bifurcation, cubic nonlinearity emerges. All the new terms are in general anisotropic.

 

Convection in rotating cylinders: asymptotic theory and numerical simulations
Keke Zhang (University of Exeter)
7 Mar 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Forecasting complex systems: it's about dynamics, it's not about statistics
Kevin Judd (University of Western Australia, Perth, Australia)
6 Mar 2008Laver 320 Thursday 12.00Applied Mathematics
In 1963 Edward Lorenz published a paper that changed the way scientists think about the prediction of geophysical systems. Two years earlier, Rudolf Kalman had published a paper that changed the way engineers thought about prediction of electronic and mechanical systems. In recent years geophysicists have become increasingly interested in Kalman filters, where as engineers have become increasingly interested in chaos. I will argue that prediction of complex systems like the weather has more to do with nonlinear dynamics than it has to do with linear statistics. A position with which I think both Lorenz and Kalman would likely agree. I will attempt to show why attractors, shadowing trajectories, nonlinear filters, optimal control, and other concepts from nonlinear dynamics are important in weather prediction, by first illustrating the ideas with Lorenz's 1963 example of a chaotic system, then confirming these results by experiments with an operational weather forecasting model.

 

Revealing the ghost in the machine: noise and population dynamics
Tim Benton (University of Leeds)
3 Mar 2008Harrison 101 Monday 2pmApplied Mathematics

 

A dwell-time approach to the stability of switched linear systems
Özkan Karabacak (University of Exeter)
29 Feb 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Switched linear systems arise as examples or generalizations of hybrid systems, especially in control engineering. A switched system consists of a family of different subsytems and a set of signals that controls the switching between these subsystems. In this talk switched linear systems and its stability problems will be introduced in general. One of these, namely, finding a sufficient condition on the minimum dwell time of the switching signal that guarantees the stability of switched linear systems will be considered and a new approach to this problem will be presented. The proposed method interprets the stability of switched linear systems through the distance between the eigenvector sets of subsystem matrices. Thus, an explicit relation in view of stability is obtained between the family of the involved subsytems and the set of admissible switching signals.

 

Zeeman's nerve impulse model
Martin Krupa (New Mexico State University, Las Cruces, NM, USA)
28 Feb 2008Newman D Thursday 2pmApplied Mathematics
In early 1970's E.C. Zeeman proposed a three dimensional model of the dynamics of a neuron. The model is a slow/fast ODE with one fast variable and two slow ones and is a caricature of the Hodgking-Huxley equation. In this talk we analyze the model of Zeeman using methods of geometric singular perturbation theory and blow-up, veryfying the numerical predictions of the dynamics of the model. As a part of the analysis we discuss the dynamics near a singularly perturbed cusp.

 

Magneto-seismology of the solar atmosphere: does really wag the tail the dog?
Robert Erdelyi (University of Sheffield)
25 Feb 2008Harrison 209 Monday 2pmApplied Mathematics

 

Magnetic fields in star formation
Daniel Price (University of Exeter)
22 Feb 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Magnetic fields are observed in sufficient strengths to be important at every stage of the star formation process, from the dynamics of the interstellar medium in galaxies, in turbulent molecular clouds and in individual star forming cores. I will discuss our attempts to incorporate magnetic fields into numerical simulations of the fragmentation of dense cores and of star cluster formation from turbulent initial conditions using a Smoothed Particle Magnetohydrodynamics algorithm.

 

Estimation of the correlation decay rate for chaotic intermittency maps
David Natsios (University of Liverpool)
18 Feb 2008Harrison 203 Monday 11amApplied Mathematics
Chaotic intermittency maps give a non-linear, non-Gaussian method of generating long memory time series. In particular we study the symmetric cusp map, the asymmetric cusp map, polynomial maps and logarithmic maps. In previous studies by Bhansali and Holland, it has been shown that these maps can simulate stationary time series with a full range of values for the long memory parameter, including d = 0.5 which is usually considered non-stationary, d = 0 which is usually considered short memory and d < 0 which is usually intermediate memory. This gives us the opportunity to carry out a simulation study to investigate the robustness of various long memory estimation techniques in extreme cases and when the assumptions of linearity and Gaussian distribution no longer hold. We show that standard methods can give large bias and we introduce an extended dual parameter long memory model, which includes the standard one-parameter fractional difference model as a special case and also accommodates a boundary behaviour of the type not admissible in the standard model. We also consider extensions of the chaotic intermittency maps, including stochastic versions and a bivariate version of the polynomial map. Our dual parameter methods of long memory parameter estimation are once again compared to standard methods and methods of distinguishing between the stochastic maps are introduced.

 

Machine learning in astronomy: time delay estimation in gravitational lensing
Peter Tino (University of Birmingham)
18 Feb 2008Harrison 209 Monday 2pmApplied Mathematics
A ray of light (or any other form of electromagnetic radiation, e.g. radio or x-rays) travels along a geodesic, which could be locally curved due to the gravitational effect of clumps of matter like stars or galaxies. This is known as gravitational lensing. Gravitational lensing, caused by intervening matter along the line of sight, can give rise to interesting cosmic illusions like magnified and seriously distorted images of distant sources, sometimes splitting into multiple images. Since the distortion of the images depends on the distribution of matter in the lensing object, this is the most direct method of measuring matter (which is often dark) in the Universe. Quasar Q0957+561, an ultra-bright galaxy with a super massive central black hole was the first lensed source to be discovered and it is the most studied so far. Gravitational lens creates two distinct images of Q0957+561. We attempt to recover the phase shift in the 2 lensed images of Q0957+561 using a model based approach formulated within the framework of kernel regression. In a set of controlled experiments emulating presence of realistic observational gaps, irregular observation times and noisy observations, we compare our method with other state-of-art statistical methods currently used in astrophysics. We then apply the method to actual observations doubly imaged quasar Q0957+561 at several radio and optical frequencies.

 

Nanoflares in the solar corona
Mitchell Berger (University of Exeter)
15 Feb 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

Solar flares are magnetic storms in the sun's atmosphere. The distribution of flare energies is a power law over several orders of magnitude. The smallest flares (nanoflares) may be responsible for heating the coronal plasma to over a million degrees. The nature of nanoflares is unknown, as they are below observational resolution. In the 1980s Parker suggested that nanoflares occur when braided magnetic flux tubes reconnect. This talk gives a model of flux tube braiding and reconnection similar to self-organized forest fire models, with a power law energy distribution.

 

Bayesian learning from the last glacial maximum on climate sensitivity
Hermann Held (Potsdam Institute for Climate Impact Research, Potsdam, Germany)
11 Feb 2008Harrison 209 Monday 2pmApplied Mathematics
13th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics'

 

The Impenetrable Hedge – some thoughts on propriety, equitability and consistency
Ian Jolliffe (University of Exeter)
8 Feb 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

In weather and climate forecasting, hedging is said to occur whenever a forecaster’s judgment and forecast differ, and it is usually taken as evident that hedging is undesirable. Forecasts are often judged by computing a verification measure or score. A number of different scores are available in most circumstances, and to choose between them, various desirable properties of scores have been defined.

Three ‘desirable’ properties of scores are linked to the idea that hedging should be avoided, namely propriety, equitability and consistency. It is fair to say that none of these properties is fully understood.

This talk will provide some clarification and new insights, as well as some historical background. Nearly as many questions are raised as are answered.

 

Control of beams and plates: a mathematical perspective
Mark Opmeer (University of Bath)
4 Feb 2008Harrison 209 Monday 2pmApplied Mathematics

 

The dynamics of wheel shimmy or good memory causes trouble
Gabor Orosz (University of Exeter)
1 Feb 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

The lateral vibration of towed wheels, called shimmy, may appear on airplane landing gears, motorcycle wheels, caravans, rear wheels of semi-trailers and articulated buses, and it usually presents a safety hazard. The dynamics of wheel shimmy is studied when the vibrations are related to the elasticity of the tyre. In the corresponding stretched-string tyre model, the non-holonomic rolling constraint is described by a partial differential equation (PDE) that is coupled to an integro-differential equation (IDE) governing the lateralwheel motion. The coupled PDE-IDE system can be transformed to a delay differential equation (DDE) by assuming travelling wave solutions along the contact patch. Investigating the stability of the stationary rolling motion reveals intricate stability charts where instabilities lead to periodic and quasi-periodic vibrations. These vibrations are found by numerical simulation and verified by experiments.

 

Aerosol modelling in the Unified Model and their importance in global weather and climate
Duncan Ackerley (University of Reading)
28 Jan 2008Harrison 209 Monday 2pmApplied Mathematics

 

Second mean analysis of stochastically perturbed population dynamics
Iakovos Matsikis (University of Exeter)
25 Jan 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

Population Projection Matrices (PPM's) are mathematical models that describe the evolution of age- or stage-classified populations. These models usually are stochastically perturbed, due to environmental reasons and their asymptotic dynamics are governed by the resulting spectra (Lyapunov exponents). This mean asymptotic analysis however, do not give satisfactory answers regarding the PPM's transient behavior.

In this talk we study stochastically perturbed PPM's using second mean techniques. We plot pseudospectra and variance envelopes which capture the transient dynamics and discuss non-normality of matrices and its implications in the population's transient evolution.

 

The acoustics and stability of swirling flow
Nigel Peake (University of Cambridge)
21 Jan 2008Harrison 209 Monday 2pmApplied Mathematics

 

Towards the seamless prediction of weather and climate
Tim Palmer (ECMWF, Reading)
14 Jan 2008Harrison 203 Monday 2pmApplied Mathematics

 

Bursting dynamics in the neuronal systems
Abul Kalam Al-Azad (University of Exeter)
11 Jan 2008Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

Bursting is a relatively slow rhythmic alternation between an active phase of rapid spiking and a quiescent phase. It is exhibited by a wide range of nerve and endocrine cells, including pancreatic beta-cells, respiratory pacemaker neurons, dopaminergic neurons of the mammalian midbrain, thalamic relay cells, and pyramidal neurons of the neocortex.

One of the major challeges in the theoretical neuroscience is to understand the dynamical and computational properties of bursters, and their underlying physiological mechanism both in the single cell and network levels.

We examine synchronization phenomena in varying parameter regime for the bursting neuronal systems governed by standard minimal models, and emergence of clustering in the ensuing dynamics. We also present a method to compute the stability of the subspace formed by partial synchronous clusters.

 

Convection and magnetic stability of the planetary cores
Sergey Starchenko (IZMIRAN, Troitsk, Russia)
7 Jan 2008Harrison 209 Monday 2pmApplied Mathematics

 

Invasion Dynamics: Resilient vs. Vulnerable Populations
Stuart Townley (University of Exeter)
7 Dec 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
In this talk we consider two interacting populations - a resident and an invader.

From uncertain models of each population we want to determine if the invader, initiated with negligible density, can dislodge the resident from steady state carrying capacity. Adopting robustness tools from control engineering, we show that resilience (robustness of non invasion) and vulnerability (non robustness and transient interactions) can be captured from pseudospectrum plots of linearised invasion matrices.

 

Palaeomagnetic field and palaeoclimatic changes: observations from China
Yongxin Pan / Rixiang Zhu (Chinese Academy of Sciences, Beijing, China)
3 Dec 2007Harrison 209 Monday 2pmApplied Mathematics
12th Taylor & Francis sponsored seminar -- Taylor & Francis are publishers of the journal 'Geophysical and Astrophysical Fluid Dynamics'

 

A model for the pure bending of isotropic tubes: beyond the Brazier effect
Khurram Wadee (University of Exeter)
30 Nov 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
Tubular structures are common in engineering and biological settings. They provide an efficient way of carrying load but are also susceptible to elastic instabilities. Under conditions of pure bending, thin tubes are known to ovalize; the basic theory was formulated exactly 80 years ago but assumed that the ovalization occurs uniformly along the length of the tube. In this talk a novel treatment will be presented which identifies other routes to instability that provide a better approximation to the real behaviour of tubes. Furthermore, this new formulation is applicable to tubes made of auxetic or orthotropic materials.

 

Asymptotics of large bound states of localised structures
Jon Chapman (University of Oxford)
26 Nov 2007Harrison 209 Monday 2pmApplied Mathematics

 

Cat's eyes and Landau poles
Matt Turner (University of Exeter)
23 Nov 2007Harrison 254 Friday 10 amApplied Mathematics (Internal)

The relaxation of a smooth two–dimensional vortex to axisymmetry is examined, after an instantaneous, weak external strain field is applied. In this limit the disturbance decays exponentially in time at a rate that is linked to a pole of the associated linear inviscid problem (known as a Landau pole). As a model of a typical vortex distribution that can give rise to cat’s eyes, here distributions are considered that have a basic Gaussian shape but whose profiles have been artificially flattened about some radius rc . A numerical study of the Landau poles for this family of vortices shows that as the location rc is varied, so the decay rate of the disturbance moves smoothly between poles as the decay rates of two Landau poles cross.

Cat’s eyes which occur in the nonlinear evolution of a vortex lead to an axisymmetric azimuthally averaged profile with an annulus of approximately uniform vorticity, rather like the artificially flattened profiles investigated. It is found that finite thickness cat’s eyes can persist (i.e. the mean profile has a neutral mode) at two distinct radii, and in the limit of a thin flattened region the result that vanishingly thin cat’s eyes only persist at a single radius is recovered. The decay of non–axisymmetric perturbations to these flattened profiles for larger times is investigated and a comparison with the result for a Gaussian profile is made.

 

Maximum-entropy velocity profiles and boundary layer theory in turbulent flow
Robert Niven (University of New South Wales, Canberra, Australia)
21 Nov 2007Harrison 107 Wednesday 2pmApplied Mathematics
The maximum entropy method of Jaynes (1957) is used to determine the "most probable" steady-state velocity profile u(y) in several "classical" fluid flow systems, including axial flow in a cylindrical pipe (Poiseuille flow) and flow between parallel plates. In each case, the analysis yields an analytical solution for the velocity profile over the complete spectrum of laminar to turbulent flow, as a function of the maximum velocity u_{max} and a momentum parameter M. In each case, the predicted profile reduces to the well-known laminar solution at M = 0, whilst for M > 0 it gives an equation which supersedes the semi-empirical correlations commonly used for turbulent flow profiles. The main steps of the analysis and the predicted profiles are presented here. The analysis is then used to derive a new maximum-entropy laminar-turbulent boundary layer theory, for the velocity profile in steady flow along a flat plate. For M = 0, this reduces to the laminar boundary layer theory given in some texts, which approximates the Prandtl-Blasius solution to the Navier-Stokes equation. For turbulent flow, it yields a previously unreported set of solutions.

 

Solitary surface waves on fluids in electric fields
Paul Hammerton (University of East Anglia)
19 Nov 2007Harrison 209 Monday 2pmApplied Mathematics

 

Maximum Entropy Production in planetary atmospheres
Tim Jupp (University of Exeter)
16 Nov 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

Atmospheric motions constitute a heat engine. As energy flows down temperature gradients from the tropics to the poles, so entropy is produced. Observations, and numerical simulations, suggest that the terrestrial atmosphere produces entropy at the "maximum possible rate". The currently developing theory of Maximum Entropy Production (MEP) provides a framework for interpreting these observations.

In this talk I shall give an overview of MEP theory and its application to planetary atmospheres. In particular, the influence of surface drag on atmospheric entropy production is examined. A simple dynamical model is used to give insight into previous numerical results. The dependence of the MEP state on parameters such as planetary radius and rotation rate is then used to extrapolate the results to other planets.

Link to talk

Link to MEP reference material

 

Invariant polygons in systems with grazing-sliding
Robert Szalai (University of Bristol)
12 Nov 2007Harrison 209 Monday 2pmApplied Mathematics

 

Relaxation Oscillations arising in the Thermal Convection of Rapidly Rotating Spherical Systems
Ed Blockley (University of Exeter)
9 Nov 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
This work will make up the final chapter of my thesis and is concerned with studying the behaviour of the following PDE system:
which has been modified from the complex Ginzburg-Landau equation (CGLE) studied in previous work by the addition of a temperature gradient and thermal diffusion time-scale .
Starting from the limit (for which we recover the CGLE featured in Blockley et. al.) we reduce and observe how the behaviour of the system changes becoming quasi-periodic before breaking down to chaos.

 

Pattern transformation induced by an elastic instability
Tom Mullin (University of Manchester)
5 Nov 2007Harrison 209 Monday 2pmApplied Mathematics

 

A Review of Mantle Convection
Francisco Pla (Depto. de Matematicas, Facultad de Ciencias Quimicas and IMACI, Universidad de Castilla-La Mancha)
2 Nov 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

The formation of the rocks indicates that viscosity in the interior of the Earth and planets strongly depends on temperature, and this influence is the fundament for understanding the mantle convection and subduction motions. This is the goal for which a convection problem with temperature-dependent viscosity in the Navier-Stokes equations is studied. The dimensionless hydrodynamics equations are considered in which the viscosity is an exponential function of the temperature ν(T ) = ν0 · exp(−γT ).

This work studies the time-dependent solutions in codim-2 zones for different aspect-ratios, Rayleigh numbers, exponential rate γ and other parameters.

A bifurcation study with the stability results for constant viscosity and variable viscosity are also exposed.

This work is by Francisco Pla and Henar Herrero, Depto. de Matematicas, Facultad de Ciencias Quimicas and IMACI, Universidad de Castilla-La Mancha and Ana Maria Mancho, Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas.

 

Delay dynamics in semiconductor laser systems
Vicky Crockett and Hartmut Erzgräber (University of Exeter)
26 Oct 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

Vicky Crockett

Lasers with optical feedback can exhibit a wide range of complicated dynamics which can be useful or problematic depending on the desired application. In either case we need to know how to understand laser instabilities to achieve and control the desired type of dynamics.

Much work has been done on a laser with little light reflected back in from a distant external mirror, modeled with delay differential equations. For a laser with a nearby external mirror and a large amount of reflected light, the composite cavity model is more appropriate. In such an approach, the system is modeled by ordinary differential equations coupled to a set of algebraic equations for the modes. The mode equations are dependent on the coupling mirror transmission, , and optical length difference between the laser and external cavity, dLo. Bifurcation analysis is used to find regions of stable and chaotic dynamics on the plane of (T,dL).

Hartmut Erzgräber

Mathematical modeling and understanding the dynamics of coupled laser devices is of importance for many modern laser applications and holds various interesting problems for fundamental research. In the weak coupling approach a laser coupled to a filter can be modeled by delay-differential equation, which has an infinite dimensional phase space. We will present a comprehensive bifurcation analysis with respect to the relevant parameters. This reveals several codimension-two points as organizing centers. The calculated bifurcation diagrams show qualitative agreement with experiments.

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The persistence of disease in an SIR model with self-regulation and seasonal birth rate
Ben Mestel (Open University)
22 Oct 2007Harrison 209 Monday 2pmApplied Mathematics

 

Modelling the Atmosphere
Dan Holdaway and James Kent (University of Exeter)
19 Oct 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

This seminar will consist of two twenty minute talks on numerically modelling the atmosphere.

Numerical solutions to the Governing Equations cannot resolve all relevant scales. Processes that are larger than the grid length can be included in the model, however there are many processes that occur on a subgrid level. These subgrid process can interact with the resolved scale processes and affect the large scale flow. The large scale quantities can be solved by the numerical method, while the small subgrid scale processes need to be parametrized.

Numerical Methods for Weather and Climate Models. Subgrid Models (SGM) can be added to the numerical scheme to act as the effect of the subgrid processes. All numerical schemes contain errors. If these errors equal the effect of the subgrid processes then there is no need for an explicit SGM. The numerical errors associated with the numerical scheme solving the resolved scale equations could provide an implicit subgrid model for the unresolved scales.

Physics Dynamics Coupling. Proper coupling between the SGMs and the resolvable dynamics is key in obtaining accurate weather and climate forecasts. By examining the normal modes of the solutions, the spatial aspects of the coupled system are examined. Questions of particular interest are, what choice of thermodynamic variable works best? What choice of vertical staggering works best? What are the effects of nonuniform grid spacing?

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The transition to turbulence in confined shear flows
Ashley Willis (University of Bristol)
15 Oct 2007Harrison 209 Monday 2pmApplied Mathematics

 

Spatio-temporal code generation with globally coupled oscillators
John Wordsworth (University of Exeter)
12 Oct 2007Harrison 106 Wednesday 3pmApplied Mathematics (Internal)
For systems of globally coupled phase oscillators it is possible to find attractors that form symmetrical and robust heteroclinic networks. By detuning the natural frequencies of the oscillators it is then possible to break the symmetry of these networks. These dynamics can then be used to generate a spatio-temporal code from the input that has been fed into the system by means of detuning and this code can be used to classify the input accordingly.

 

Controlling neurons
Jeffrey Moehlis (University of California, Santa Barbara, USA)
8 Oct 2007Harrison 209 Monday 2pmApplied Mathematics
The phase response curve (PRC) for a nonlinear oscillator describes the phase-shift of the oscillation due to an impulsive perturbation as a function of the phase at which the perturbation occurs. We consider how knowledge of the PRC for a neuron can be used to determine external currents which control the time at which the neuron fires. We first use variational methods to determine the optimal currents that elicit spikes at a desired time, showing that there is a unique current that minimizes a square-integral measure of its amplitude. For intrinsically oscillatory models, we further demonstrate that the form and scaling of this current is determined by the model's PRC. We then propose a novel feedback control mechanism which allows one to control the phase of an oscillation, assuming only that the PRC is known and that a once-per-period marker event, such as the time at which a neuron fires, can be detected. This work represents a first step toward feedback-based treatment of ailments such as Parkinson's disease by using electrical deep brain stimulation, in which current is injected into the appropriate brain region to try to desynchronize pathologically synchronized neurons.

 

The dynamics of the North Atlantic Oscillation and Annular Modes
Edwin Gerber (Columbia University, USA)
24 Sep 2007Harrison 209 Monday 2pmApplied Mathematics
The North Atlantic Oscillation (NAO) and Annular Modes are the dominant patterns of intraseasonal variability in the extratropical atmosphere. The NAO in particular characterizes a significant fraction of the wintertime variability in Eastern North America and Europe, and has been recognized in some form since the eighteenth century. I'll begin with a simple model based on random walks to explain why these patterns of variability always dominate statistical analyses of the extratropical circulation. I'll then move to a more realistic model, a dry general circulation model of the atmosphere, to probe the dynamics of the variability. Annular Mode and NAO-like patterns are created with the addition of idealized topography and heating anomalies approximating land-sea contrast. We find that the NAO arises from the confluence of topographic and thermal forcing, and is best understood in terms of the eddy life cycle. We also find a parameter sensitive coupling between eddies and the large-scale flow that extends the persistence of the variability on timescales of 10-100 days. The feedback loop, however, is very sensitive to zonal asymmetries. This sensitivity is explored with a coupled oscillator model to illustrate the impact of standing waves on the eddy-mean flow feedback.

 

Global transient behaviour: basins of attraction in experimental nonlinear dynamics
Lawrie Virgin (Duke University, USA)
13 Sep 2007Harrison 170 Thursday 2pmApplied Mathematics

 

Periodicity and recurrence in a map with two half-planes
Arek Goetz (San Francisco State University)
7 Aug 2007Harrison 004 Tuesday 2pmApplied Mathematics

 

A Changing Climate for Prediction
Peter Cox (University of Exeter)
20 Jul 2007Harrison 254 Friday 12 noonApplied Mathematics (Internal)
Standard climate model projections, which have shown the significance of global warming, must be redesigned to inform climate change adaptation and mitigation policy. In this seminar, Peter Cox explains the modelling that informed his & David Stephenson's paper in "Science" of 13.7.07, and invites discussion on climate prediction as an initial value problem.

 

The seasonal cycle of gravity wave drag in the middle atmosphere estimated by an assimilation technique
Manuel Pulido (UNNE, Corrientes, Argentina)
26 Jun 2007Harrison 209 Tuesday 2pmApplied Mathematics
11th TAYLOR AND FRANCIS sponsored lecture. T&F are publishers of the Journal Geophysical and Astrophysical Fluid Dynamics// A novel technique to estimate gravity wave drag from global scale analyses will be presented. It is based on the principles of four-dimensional variational data assimilation using a dynamical model of the middle atmosphere and its adjoint. The control variables are solely the horizontal components of gravity wave drag so that the minimum of the cost function that measures the differences between model states and observations gives the optimum gravity wave drag.// The assimilation technique is applied to estimate gravity wave drag using Met Office analyses as the initial conditions and the observations for the year 2002. The seasonal variations of the one-year gravity wave drag estimation will be presented and analysed. Vertical variations in the sign and pattern of the estimated drag suggest filtering of the gravity wave spectrum by the background flow.

 

Introduction to the new Nature Geosciences Journal
Heike Langenberg (Editor of Nature Geosciences)
19 Jun 2007Harrison 209 Tuesday 12pmApplied Mathematics

 

Forecast verification of extremes: Use of Extreme Value Theory
Rick Katz (NCAR, Boulder, Colorado, USA)
11 Jun 2007Harrison 107 Monday 4pmApplied Mathematics
Evaluating the ability of a weather forecasting system to predict extremes should be an important consideration in forecast verification, particularly given the well known societal impacts of extreme events. Yet statistical methods devised for extreme values have only rarely been applied. // I adopt a distributions-oriented approach to forecast verification, making use of the calibration-refinement factorization of the joint distribution of forecasts and observations. The exceedance of a high (or falling below a low) threshold by the weather variable is modeled by a conditional Poisson distribution, whose rate parameter is expanded as a function of the forecast. Likewise, the excess over a high (or deficit below a low) threshold of the weather variable is modeled by a conditional generalized Pareto distribution, whose scale parameter depends on the forecast. In this way, whether or not there is any skill (or how much skill exists) in forecasting weather extremes corresponds to determining whether or not (or to what extent) using the forecast as a covariate improves the fit (e.g., via a likelihood ratio test). // The proposed method is applied to a set of specialized NWS minimum temperature forecasts and observations at Yakima, WA, USA. Because of the risk of damage to fruit buds from freezing during their development, these forecasts were made available to orchardists each spring.

 

Unfolding of codimension-two grazing-sliding bifurcations
Piotr Kowalczyk (University of Exeter)
5 Jun 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

A new global analysis of precipitation
Mathew Sapiano (University of Maryland, USA)
31 May 2007Harrison 171 Monday 2pmApplied Mathematics
Many merged multi-source global analyses of precipitation exist, including the Global Precipitation Climatology Project (GPCP) analysis and the CPC Merged Analysis of Precipitation (CMAP). The multi-source nature of these datasets allows them to use the best data available to produce the most accurate estimate of precipitation for any given place and time. However, this strength can lead to weaknesses in the form of discontinuities in the longer record, which raise questions regarding their suitability for trend analysis. Additionally, high latitude precipitation is poorly determined in these datasets since the available estimates originate from either gauges (which suffer from problems related to under-catch of solid precipitation) or satellite data (which exhibit large errors at high latitudes due to ice-contamination issues). We aim to produce a new global analysis of precipitation using Optimum Interpolation (OI) that will overcome both of these issues by using the relatively long consistent precipitation record (~20 years) from the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) and forecast precipitation from the ERA-40 reanalysis. An additional advantage of the OI methodology is its facility in the calculation of errors associated with the analysis, which are needed for most applications. I will start by showing results from an inter-comparison of the several commonly used precipitation algorithms for SSM/I. Next I will discuss issues associated with the OI and show some early results from our analysis. Finally, I will describe our plans to extend the analysis back in time by using proxy records tied to the reanalysis precipitation and calibrated by the SSM/I data. Our goal is that this extended record of precipitation will be suitable for the assessment of changes in global precipitation in the latter part of the 20th Century at all latitudes.

 

Stability of patterns for the complex Ginzburg-Landau equation
Jorge Diosdado (CIMAT, Guanajuato, Mexico)
29 May 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Aspects of feedbacks and forcing in stochastic dynamics
Stuart Townley (University of Exeter)
22 May 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

On the dynamics and adjustment of the Atlantic thermohaline circulation
David Marshall (University of Oxford)
21 May 2007Harrison 107 Monday 2pmApplied Mathematics

 

What controls the rate of mixing of passive scalars in smooth flows?
Peter Haynes (DAMTP, University of Cambridge)
14 May 2007Harrison 107 Monday 2pmApplied Mathematics

 

Networks that draw networks or honeybees on scent
Gabor Orosz (University of Exeter)
8 May 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

A new asymptotic solution for stellar dynamo
Dmitry Sokoloff (Moscow State University, Russia)
30 Apr 2007Harrison 107 Monday 2pmApplied Mathematics
10th TAYLOR AND FRANCIS sponsored lecture. T&F are publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Compressible convection in rapidly rotating spherical shells
Kirill Kuzanyan (University of Leeds)
24 Apr 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

The dynamics of the Antarctic slope front
Peter Baines (Quantifying Earth Systems, QUEST, Earth Sciences, University of Bristol)
23 Apr 2007Harrison 107 Monday 2pmApplied Mathematics

 

The precession-driven dynamo in a plane layer
Paul Roberts (IGPP, UCLA, USA)
23 Mar 2007Harrison 107 Friday 2pmApplied Mathematics
9th TAYLOR AND FRANCIS sponsored lecture. T&F are publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Interpolation by vector-valued analytic functions, with applications to the controllability of linear systems
Jonathan Partington (University of Leeds)
15 Mar 2007Harrison 215 Monday 2pmApplied Mathematics

 

Parametric instability of the helical dynamo
Marine Peyrot (LEGI, Grenoble)
13 Mar 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Efficient data assimilation for spatially extended systems: a local ensemble transform Kalman filter
Brian Hunt (University of Maryland, USA)
12 Mar 2007Harrison 107 Monday 4pmApplied Mathematics
8th TAYLOR AND FRANCIS sponsored lecture. T&F are publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Exactly solvable problems for excitons in two dimensions
Misha Portnoi (University of Exeter)
6 Mar 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

The dynamics of deep convection and large-scale tropical wave motion
Glenn Shutts (Met office)
5 Mar 2007Harrison 107 Monday 2pmApplied Mathematics

 

Transient dynamics - are they just a passing trend or ... ?
Stuart Townley (University of Exeter)
27 Feb 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Are the fractal skeletons the explanation for the plankton paradox and the in-stent restenosis?
Celso Grebogi (University of Aberdeen)
26 Feb 2007Harrison 107 Monday 2pmApplied Mathematics
Nature is permeated by phenomena in which active processes, such as chemical reactions and biological interactions, take place in environmental flows. They include the dynamics of growing populations of plankton in the oceans and the evolving distribution of ozone in the polar stratosphere. I will show that if the dynamics of active particles in flows is chaotic, then necessarily the concentration of particles have the observed fractal filamentary structures. These structures, in turn, are the skeletons and the dynamic catalysts of active processes, yielding an unusual singularly enhanced productivity. I will argue that this singular productivity could be the hydrodynamic explanation for the plankton paradox, in which an extremely large number of species are able to coexist, negating the competitive exclusion principle that asserts the survival of only the most perfectly adapted to each limiting resource. I will then suggest that the presence of such fractal skeletons in arterial flow could be the explanation for the eventual restenosis of arteries after a stent-assisted angioplasty.

 

Simulations of nonlinear pore-water convection in spherical shells
Zhifeng Dai (University of Exeter)
20 Feb 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Quaternions and particle dynamics in the Euler equations
John Gibbon (Imperial College London)
19 Feb 2007Harrison 107 Monday 2pmApplied Mathematics

 

Practical bifurcation analysis of piecewise smooth systems
Daniel Pagano (University of Bristol)
15 Feb 2007Harrison 107 Thursday 2pmApplied Mathematics
The lack of smoothness in these systems precludes the application of local analysis tools (so useful in differentiable dynamics) and then, as a consequence, the separation between local and global issues has a fuzzy character, if it actually exists. Therefore, the bifurcation analysis in this context turns out to be cumbersome and specific for each concrete case. We will show how to proceed in order to obtain bifurcation sets in representative families of planar Filippov systems, and comment the difficulties to overcome in non-solved cases.

 

Marginal stability of planetary convection and magnetism
Sergey Starchenko (IZMIRAN, Troitsk, Russia)
13 Feb 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Numerical methods for solving electromagnetic problems
Jun Zou (The Chinese University of Hong Kong)
12 Feb 2007Harrison 107 Monday 2pmApplied Mathematics
7th TAYLOR AND FRANCIS sponsored lecture. T&F are publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Dynamo action in a helical pipe
Leszek Zabielski (Warsaw University of Technology)
5 Feb 2007Harrison 107 Monday 2pmApplied Mathematics

 

Reduced atmospheric models using dynamically motivated basis functions
Frank Kwasniok (University of Exeter)
30 Jan 2007Harrison 209 Wednesday 2pmApplied Mathematics (Internal)

 

Overcoming essential instabilities induced by coupling delay
Jan Sieber (University of Aberdeen)
29 Jan 2007Harrison 107 Monday 2pmApplied Mathematics
Realistic tests in mechanical engineering often involve bidirectional real-time coupling between computer simulations and mechanical experiments. If this coupling occurs at a fixed joint then arbitrarily small delays in the coupling can result in an essential instability, that is, the linearization has infinitely many unstable eigenvalues. A general theorem (see, for example, the textbook of Hale/Verduyn-Lunel) implies that this kind of instability is impossible to compensate. We discuss an approach that is potentially able to overcome this difficulty. This is joint work with Yuliya Kyrychko (Bristol).

 

Nonlinear dynamics of lasers
Sebastian Wieczorek (University of Exeter)
23 Jan 2007Harrison 203 Wednesday 1pmApplied Mathematics (Internal)

 

Solitons in photonic crystal fibers
Dmitry Skryabin (University of Bath)
22 Jan 2007Harrison 107 Monday 2pmApplied Mathematics

 

Modelling atmospheres
Beccy Mitchell, Dan Holdaway and James Kent
19 Jan 2007Harrison 107 Wednesday 3pmApplied Mathematics (Internal)

 

Data inversion in solar radio spectroscopy: application to the flares
Gregory Fleishman (Ioffe Physico-Technical Institute, St. Petersburg, Russia)
16 Jan 2007Harrison 107 Wednesday 1pmApplied Mathematics (Internal)

 

Design of parametrically forced patterns
Alastair Rucklidge (University of Leeds)
15 Jan 2007Harrison 170 Monday 2pmApplied Mathematics

 

Some dynamical systems without ergodicity
Peter Ashwin (University of Exeter)
9 Jan 2007Harrison 107 Wednesday 1pmApplied Mathematics (Internal)

 

Equation-free modeling of inelastic collapse
Mark Muldoon (University of Manchester)
8 Jan 2007Harrison 107 Monday 2pmApplied Mathematics
A hard sphere gas whose particles collide inelastically lacks a straightforward hydrodynamic limit and its evolution is poorly described by PDEs. Such gasses undergo a so-called "inelastic collapse", after which most particles are confined to slow-moving, high-density clusters. Here we apply the recent, "equation-free" methods of Kevrekides and collaborators---which combine short bursts of stochastic simulation with Euler-like time stepping---to a prototypical example of inelastic collapse, a one-dimensional gas originally studied by Du, Li and Kadanoff.

 

Solar differential rotation: a new proposal for the tachocline
Michael McIntyre (DAMTP, University of Cambridge)
4 Dec 2006Harrison 107 Monday 2pmApplied Mathematics

 

Sediment transport above rippled beds
Vanesa Magar (University of Plymouth)
28 Nov 2006Harrison 107 Wednesday 1pmApplied Mathematics (Internal)

 

Quadratic differential forms and (some of) their applications
Paolo Rapisarda (University of Southampton)
27 Nov 2006Harrison 107 Monday 2pmApplied Mathematics
Often when dealing with dynamical systems it is important to describe and analyze the interplay of dynamics and functionals of the variables of the system and their derivatives; for example, in the case of linear systems, quadratic functionals are of paramount importance in filtering, estimation, optimal control, etc. Recently, the formalization of these functionals using two-variable polynomial matrices has been proposed by Willems and Trentelman in a framework in which there is no need to use first-order (i.e. state) representations of a dynamical system as it is customary to do, and one can work with descriptions of the dynamics in terms of systems of higher-order differential equations. In this talk the basic features and some applications of the calculus of these so-called quadratic differential forms are presented.

 

The effect of mantle conductivity on the super-rotating jets near the liquid core surface
Konrad Bajer (Warsaw University, Poland)
23 Nov 2006Harrison 107 Thursday 2pmApplied Mathematics

 

Rapid mixing and other statistical properties of Lorenz attractors
Mark Holland (University of Exeter)
14 Nov 2006Harrison 107 Wednesday 1pmApplied Mathematics (Internal)
I will survey the statistical properties of Lorenz maps and Lorenz flows and in particular give details about the mixing properties of the classical Lorenz attractor (work in progress).

 

Vortex multipoles and vortex quasimodes: the parallels and differences between coherent structures of fluids and plasmas
Lorena Barba (University of Bristol)
13 Nov 2006Harrison 107 Monday 2pmApplied Mathematics
A column of electrons surrounded by a conducting wall and confined by a strong magnetic field is an excellent manifestation of two-dimensional vortices in an inviscid fluid. The equations governing the drift motion of a magnetized electron column are isomorphic to the Euler equations for incompressible, 2D flow. This isomorphism implies, for example, that surface charge perturbations on the electron column (called diocotron modes) are equivalent to surface waves on vortex columns (called Kelvin waves). In the plasma literature, a quasimode is a vorticity perturbation which is weakly damped, and behaves like it was a single azimuthally propagating wave on the vortex edge. In fluids, a multipole is an arrangement of two or more peaks of vorticity which is compact, coherent and long-lived. The topology of quasimodes and multipoles can appear quite similar. But, is there any inherent physical relationship between the core quasimodes, basically explained by wave phenomena, and the hydrodynamic multipoles, which are more readily explained by the nonlinear interaction of vorticity?

 

Bringing mathematical insights to the climate change problem
Peter Cox (University of Exeter)
7 Nov 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

Analytic invariants associated with a parabolic fixed point in C^2
Vincent Naudot (University of Warwick)
6 Nov 2006Harrison 107 Monday 2pmApplied Mathematics
Near a parabolic fixed point 0 in R^2, a real analytic diffeomorhism can be embedded in a smooth autonomous flow. We show that in the complex-analytic case the situation is completely different. We construct 2 analytic invariants with respect to local analytic changes of coordinates. One invariant vanishes for time-1 maps of analytic flows but generically not equal to 0.

 

An efficient phase-field model for polycrystaline grain growth
Prasad Patnaik (University of Exeter)
31 Oct 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

Slow flow between concentric cones
Oskar Hall (University of Exeter)
24 Oct 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

The helicity conservation in delta-Omega and alpha-delta-Omega and its impact to eleven year solar torsional oscillations
Valery Pipin (Institute Solar-Terrestrial Physics, Irkutsk, Russia)
23 Oct 2006Harrison 107 Monday 2pmApplied Mathematics
This is the 5th TAYLOR AND FRANCIS sponsored lecture. Taylor and Francis are the publishers of the Journal Geophysical and Astrophysical Fluid Dynamics.

 

Asymptotic receptivity and the Parabolized Stability Equation: a combined approach to boundary layer transition
Matthew Turner (University of Exeter)
17 Oct 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

Spatio-temporal epidemic modelling for public health protection
Ian Hall (Health Protection Agency: Porton Down)
16 Oct 2006Harrison 107 Monday 2pmApplied Mathematics

 

Regulation of primary photosynthetic processes and problems of ecological monitoring
Andrei Rubin (Moscow State University)
10 Oct 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

Connections between discrete control theory and numerical methods for ODEs
Adrian Hill (University of Bath)
9 Oct 2006Harrison 107 Monday 2pmApplied Mathematics
We write a general linear method for the numerical integration of ODEs as a discrete control system. The positive real lemma, the Z-transform and perturbation methods are used to explore the stability of such numerical methods.

 

Numerical Rossby wave propagation on the C-grid
John Thuburn (University of Exeter)
3 Oct 2006Harrison 106 Wednesday 1pmApplied Mathematics (Internal)

 

Decay of correlations for Lorentz gases
Ian Melbourne (University of Surrey)
2 Oct 2006Harrison 107 Monday 2pmApplied Mathematics

 

Verifying deterministic forecasts of extreme events
Chris Ferro (Department of Meteorology, University of Reading)
25 Sep 2006Harrison 254 Monday 2pmApplied Mathematics
Forecast verification, the practice of assessing forecast quality, is difficult for at least two reasons when the event being forecasted is rare. First, sampling variability of quality measures may be high if only a small number of events has been observed. Second, many quality measures necessarily degenerate to trivial values as events become rarer. These problems will be mitigated by means of a statistical model based on extreme-value theory that quantifies the relationship between observations and forecasts. The model's two parameters can be interpreted as measures of forecast quality that do not degenerate with event rarity. The model also predicts the values of standard quality measures as event rarity increases. These model estimates are more efficient than evaluating the measures directly and show that different standard measures can indicate opposing changes in forecast quality as rarity increases. The model will be used to assess forecast quality for some extreme weather events.

 

The dynamo bifurcation in rotating spheres
Emmanuel Dormy (Ecole Normale Superieure, Paris)
22 Sep 2006Harrison 170 Friday 2pmApplied Mathematics
This is the 4th TAYLOR AND FRANCIS sponsored lecture. Taylor and Francis are the publishers of the Journal Geophysical and Astrophysical Fluid Dynamics.

 

Feel sick? Follow the money!
Dr. Dirk Brockmann (Max-Planck-Institute for Dynamics and Self-Organization)
22 Jun 2006Harrison B74 Thursday 2pmApplied Mathematics
In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic the knowledge of dynamical and statistical properties of human travel is of fundamental importance. A quantitative assessment of these properties on geographical scales still remains elusive and the assumption that humans disperse diffusively still prevails in models.
In 1998 Hank Eskin invented the internet game wheresgeorge.com, an online bill tracking system.
The idea behind the game is simple. Users can register at the website, mark individual dollar bills, report them to the website, reenter them into circulation and subsequently monitor their geographic dispersal as other users make reports to the website. We have analysed the wheresgeorge.com dataset and used the dispersal of nearly half a million dollar bills as a proxy for human travel. We were thus able to assess the statistical properties of human travel with a high spatio-temporal precision. We found that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as Lévy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraic tails which attenuate the superdiffusive spread. We were able to show that human travel can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process.

 

Periodicity in a system of two rotations (joint work with Anthony Quas)
Prof Arek Goetz (San Francisco State University)
13 Jun 2006Harrison 170 Tuesday 12 noonApplied Mathematics

 

Relating forced climate change to natural variability
Owen Kellie-Smith
23 May 2006Harrison 106 Wednesday 12 noonApplied Mathematics (Internal)
Link to slides

 

The validity of Boussinesq and anelastic equation sets in convecting atmospheres: A normal mode analysis
Rebecca Mitchell (Exeter)
16 May 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Delay induced dynamics of a nonlinear transmission line oscillator model
David Barton (Bristol Centre for Applied Nonlinear Mathematics, University of Bristol)
9 May 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Pseudospectra
Dominic Mc-Carthy (UIniversity of Exeter)
2 May 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Dynamos in flows with cat's eyes
Andrew D Gilbert (Exeter)
25 Apr 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Multistability in the Kuramoto model with synaptic plasticity
Yuri Maistrenko (Institute of Medicin and Virtual Institute of Neuromodulation, Research Centre Jülich)
28 Mar 2006Harrison 106 Wednesday 11amApplied Mathematics (Internal)

 

A high order WENO finite difference scheme for incompressible fluids and magnetohydrodynamics
Paul Roberts (IGPP, UCLA, USA)
27 Mar 2006Harrison 170 Monday 2pmApplied Mathematics
Sponsored by TAYLOR AND FRANCIS, publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Computed eigenmodes of planar regions
Nick Trefethen (University of Oxford)
16 Mar 2006Harrison 170 Thursday 2pmApplied Mathematics
Recently developed numerical methods make possible the high-accuracy computation of eigenmodes of the Laplacian for a variety of "drums" in two dimensions, or as some physicists prefer to call them, problems of "quantum billiards". A number of computed examples will be presented together with a discussion of their implications concerning bound and continuum states, symmetry and degeneracy, eigenvalue avoidance, resonance, localization, eigenvalue optimization, perturbation of eigenvalues and eigenvectors, and the problem of "can one hear the shape of a drum?".

 

Dependence of magnetic field generation by convective flows in a plane layer on the kinematic Prandtl number
Olga Podvigina (International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac.Sci.)
14 Mar 2006Harrison LT6 Tuesday 12pmApplied Mathematics
Sponsored by TAYLOR AND FRANCIS, publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Dependence of magnetic field generation by convective flows in a plane layer on the kinematic Prandtl number
Olga Podvigina (International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac.Sci.)
14 Mar 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)
Sponsored by TAYLOR AND FRANCIS, publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Weakly nonlinear stability of convective hydromagnetic systems with insignificant alpha-effect in a plane rotating layer to perturbations involving large scales
Vlad Zheligovsky (International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac.Sci.)
7 Mar 2006Harrison LT6 Tuesday 12pmApplied Mathematics
Sponsored by TAYLOR AND FRANCIS, publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Weakly nonlinear stability of convective hydromagnetic systems with insignificant alpha-effect in a plane rotating layer to perturbations involving large scales
Vlad Zheligovsky (International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Ac.Sci.)
7 Mar 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)
Sponsored by TAYLOR AND FRANCIS, publishers of the Journal Geophysical and Astrophysical Fluid Dynamics

 

Prehistoric demography and the spread of the Neolithic: Models based on radiocarbon dates
Anvar Shukurov (University of Newcastle upon Tyne)
6 Mar 2006Harrison 170 Monday 2pmApplied Mathematics

 

The dynamincs of coupled phase oscillators
John Wordsworth (Exeter)
28 Feb 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Bifurcation and non-uniqueness of exact Navier-Stokes solutions: Is it consistent to neglect far-field boundaries?
Rich Hewitt (University of Manchester)
27 Feb 2006Harrison 170 Monday 2pmApplied Mathematics

 

The onset of almost adiabatic planetary convection
Sergey Starchenko (Rybinsk State Avian-Technical Academy)
23 Feb 2006Harrison 170 Thursday 2pmApplied Mathematics

 

Jeffery-Hamel flow between two cones
Oscar Hall (Exeter)
21 Feb 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Transport of momentum and particle in hydrodynamic and magnetohydrodynamic turbulence
Eun-jin Kim (University of Sheffield)
20 Feb 2006Harrison 170 Monday 2pmApplied Mathematics

 

Synchronization of globally coupled chaotic maps: clusters and quasi-clusters
Anastasiya Panchuk (NAS of Ukraine, Kiev)
16 Feb 2006Harrison 170 Thursday 2pmApplied Mathematics

 

What on earth is a Normalized Bi-Conjugate Minimum Residual Gradient Method? - A brief introduction to Krylov subspace methods"
John Thuburn (Exeter)
14 Feb 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Describing and modeling biofilm mechanics
Isaac Klapper (Montana State University)
9 Feb 2006Harrison 170 Thursday 2pmApplied Mathematics

 

Wave Train Solutions in Spherical Couette Flow
Ed Blockley (Exeter)
7 Feb 2006Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Finite-dimensional attractors of randomly-forced PDEs
David Broomhead (University of Manchester)
30 Jan 2006Harrison 170 Monday 2pmApplied Mathematics

 

Nonlinear dynamics of warped accretion discs
Gordon Ogilvie (University of Cambridge)
23 Jan 2006Harrison 170 Monday 2pmApplied Mathematics

 

Approximate iterative methods for variational data assimilation
Amos Lawless (University of Reading)
16 Jan 2006Harrison 170 Monday 2pmApplied Mathematics

 

Nucleation of localised 2D patterns
David Lloyd (University of Surrey)
9 Jan 2006Harrison 170 Monday 2pmApplied Mathematics
Localised patterns have been observed in a variety of physical experiments from vibrated granular materials to nonlinear optics. We present the results of Umbanhowar et al. Nature 382 (1996) for the vibrated granular material problem and propose a new process for pattern formation and selection in 2-dimensions. We demonstrate this new process by taking a toy model, namely the Swift-Hohenberg equation. Taking our guidance from known 1D results, we develop analytical and numerical techniques to explore the nucleation of localised patterns in 2D. Finally, I present results showing the rich bifurcation structure of these patterns and suggest avenues for on going research.

 

Understanding turbulence through the sequence-of-bifurcation approach
Fritz Busse (University of Bayreuth)
8 Dec 2005Harrison 170 Thursday 2pmApplied Mathematics

 

Bifurcations and heteroclinic-like oscillations in highway traffic models with reaction-time delay
Gabor Orosz (University of Exeter)
22 Nov 2005Harrison LT6 Tuesday 12 noonApplied Mathematics (Internal)

 

Coupled systems: Theory and examples
Marty Golubitsky (University of Houston)
21 Nov 2005Harrison 170 Monday 2pmApplied Mathematics
A coupled cell system is a collection of interacting dynamical systems. Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We ask: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much depends on the specific equations? The ideas will be illustrated through a series of examples and theorems. One theorem classifies spatio-temporal symmetries of periodic solutions and a second gives necessary and sufficient conditions for synchrony in terms of network architecture.

 

Convectons
Edgar Knobloch (University of California, Berkeley)
17 Nov 2005Harrison 170 Thursday 2pmApplied Mathematics
Recent simulations of binary fluid convection reveal the presence of multiple numerically stable spatially localized steady states we have called 'convectons'. These states consist of a finite number of rolls embedded in a nonconvecting background and are present at supercritical Rayleigh numbers. The convecton length decreases with decreasing Rayleigh number; below a critical Rayleigh number the convectons are replaced by relaxation oscillations in which the steady state is gradually eroded until no rolls are present (the slow phase), whereupon a new steady state regrows from small amplitude (the fast phase) and the process repeats. The Swift-Hohenberg equation, both variational and nonvariational) provides much insight into this behaviour. This equation contains several classes of localized steady states whose length grows in a characteristic 'snaking' fashion as they approach spatially periodic states, and the associated dynamics resemble the binary fluid simulations. The origin of the snaking and the stability properties of the associated states will be elucidated, and the results used to shed light on the remarkable complexity of these simple systems.

 

Climate Sensitivities via a Fokker-Planck Adjoint Approach
John Thuburn (University of Exeter)
15 Nov 2005Harrison LT6 Tuesday 12 noonApplied Mathematics (Internal)

 

Stability of magnetic flux tubes subject to external flows
Antonio Ferriz Mas (Universidad de Vigo, Spain)
14 Nov 2005Harrison 170 Monday 2pmApplied Mathematics

 

Uncertain Matrix Systems: From Pseudospectra to Kharitonov Theorems.
Stuart Townley (Universty of Exeter)
8 Nov 2005Harrison LT6 Tuesday 12 noonApplied Mathematics (Internal)

 

Metric approximations in global weather forecasting
Andy White (Met. Office)
7 Nov 2005Harrison 170 Monday 2pmApplied Mathematics
Weather forecasting by national meteorological centres such as the Met Office is guided by the output of numerical models of the atmosphere's motion and thermodynamics. Most centres use models based on the so-called hydrostatic primitive equations, which in a global context make an assumption of shallowness that involves neglect of part of the Coriolis force. Met Office models have been based on more accurate underlying equations since 1992, and on non-hydrostatic equations since 2002. Recent work has identified a hierarchy of consistent approximated equation sets that are at least as accurate as the hydrostatic primitive equations. The hierarchy includes the hydrostatic primitive equations themselves, the Met Office's equation sets, and a non-hydrostatic formulation used by the Canadian Environment Service. An equation set is said to be consistent if it possesses good conservation properties (for energy, angular momentum and potential vorticity) and if it can be directly derived from Lagrange's equations of motion. Four consistent formulations arise as two approximations are made or not made: (a) an assemblage of approximations known collectively as the shallow atmosphere approximation; (b) neglect of the time derivative in the vertical component of the momentum equation. These may be concisely regarded in terms of approximations of metrics - in one case, of metric factors that describe the assumed geometry, in the other case, of the velocity metric that appears in the definition of kinetic energy.

 

Uncertainty Intervals, Stability and Kharitonov’s Theorem
Dominic McCarthy (University of Exeter)
2 Nov 2005Harrison LT6 Wednesday 12 noonApplied Mathematics (Internal)

 

Spatiotemporal chaos in Rayleigh-Benard convection
Mike Cross (Caltech)
31 Oct 2005Harrison 170 Monday 2pmApplied Mathematics

 

Uncertain Matrix Systems: From Pseudospectra to Kharitonov Theorems
Stuart Townley (University of Exeter)
25 Oct 2005Harrison LT6 Tuesday 12 noonApplied Mathematics (Internal)

 

Two-dimensional flows in slowly deforming domains
Jacques Vanneste (University of Edinburgh)
24 Oct 2005Harrison 170 Monday 2pmApplied Mathematics

 

Modelling of nucleation kinetics
Lindsay Greer (University of Cambridge)
20 Oct 2005Harrison 170 Thursday 2pmApplied Mathematics
Most phase transitions proceed by growth from particular nucleation sites, which either appear sporadically or are pre-determined. In recent decades great progress has been made in the quantitative analysis of growth kinetics, but nucleation remains notoriously difficult to model quantitatively. Yet nucleation is important in so many ways: not only in materials (casting of metals, transparency of polymers), but in medicine (CJD, kidney stones), environment (meteorology, crop damage). This presentation will introduce some of the issues in the mechanisms of nucleation, the consequences for how it is modelled and for mathematical techniques. There are, for example, nucleation phenomena that are in general understood, but where the complexity as yet precludes prediction of nucleation rates. Different forms of analysis may be needed at different length scales. Despite the difficulties, recent work shows that there are cases in which sound quantification and prediction are possible. Nucleation is often regarded as an intrinsically stochastic process, yet the recent work focuses on deterministic behaviour.

 

Timestepping methods for linearly stiff systems
Paul Matthews (University of Nottingham)
10 Oct 2005Harrison 170 Monday 2pmApplied Mathematics

 

The linked twist map approach to fluid mixing
Rob Sturman (University of Bristol)
3 Oct 2005Harrison 170 Monday 2pmApplied Mathematics

 

The analytic structure of Euler flow
Uriel Frisch (Observatoire de Nice)
19 Sep 2005Harrison 170 Monday 2pmApplied Mathematics

 

Probabilistic aspects of recurrence in dynamical systems
Sandro Vaienti (Luminy, Marseille)
16 Sep 2005Harrison B74 Friday 2pmApplied Mathematics

 

Where Strategic and Evolutionary Stability Depart - A Study of Minimal Diversity Games
Dieter Balkenborg (Exeter (Economics))
28 Jun 2005Harrison 170 Tuesday 3.40pmApplied Mathematics
The paper is concerned with the connection between two different approaches to game theory: evolutionary game theory and equilibrium refinement. The literature on learning and evolution studies the evolution of simple forms of adaptive behaviour. It asks, for instance, under which conditions evolutionary selection or learning will in the long run lead to rational behaviour and Nash equilibrium.

In contrast, the literature on refinement presupposes highly rational individuals. Its starting point is the observation that many interesting games have Nash equilibria that are unconvincing as solutions to a game and that additional criteria are needed to refine among them. The most developed notion of equilibrium refinement is the concept of strategically stable sets of Nash equilibria as introduced by Kohlberg and Mertens and as further developed by Mertens.

A number of papers indicate a strong connection between evolutionary and strategic stability. Recently De Michelis and Ritzberger have shown for a very general class of dynamics that model evolutionary or learning processes between different populations that an asymptotically stable Nash equilibrium component must contain a strategically stable set if its Euler characteristic is not zero.

We ask whether, conversely, a strict equilibrium set containing a Mertens stable set must have non-zero Euler characteristic.

We address this question for a special class of games that we call minimal diversity games. In a minimal diversity game each member of a team of I players must independently and simultaneously choose one of the numbers k=1,...,K. Each player gets payoff -1 if all players name the same number and payoff 0 otherwise.

Minimal diversity games have two equilibrium components. One consists of an isolated mixed strategy Nash equilibrium where each player takes each choice with equal probability. The other consists of the set of efficient Nash equilibria where at least two players choose different pure strategies. The mixed strategy Nash equilibrium is strategically stable, but not evolutionary stable. The efficient component is shown to be a topological sphere of dimension (I-1)*(K-1)-1. It has hence zero Euler characteristic iff it is odd dimensional, i.e. if I or K is odd. Therefore it contains a strategically stable set if it is an even dimensional sphere. For the cases I=2 and K odd we show that it does not contain a strategically stable set.

Closely related (and proved with the same construction) is the fact that for nearby payoff perturbations of the game generically no trajectory of an evolutionary dynamic converges. It is not yet known whether the finding extend to other minimum diversity games with three of more players.

 

Master equation approach to the study of phase change processes in data storage media
Konstantin Blyuss (Exeter)
28 Jun 2005Harrison 170 Tuesday 4.30pmApplied Mathematics
The dynamics of crystallization in phase-change materials is investigated using a master equation approach. We develop a novel model using the thermodynamics of the processes involved. Some partial analytical results are obtained for the isothermal case and for large cluster sizes, but principally numerical simulations are used to investigate the model.

 

Real-time dynamic substructuring: stability and Hopf bifurcation in a neutral delay differential system
Yuliya Kyrychko (Bristol)
28 Jun 2005Harrison 170 Tuesday 1.30pmApplied Mathematics
Real-time dynamic substructuring is a powerful testing method which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the experimental structure with a numerical model, connected by a transfer system. In order to provide reliable results, the hybrid system has to remain stable during the whole test. One of the problems with the method is the presence of delay due to several technical factors. This delay can lead to destabilization and failure. In this talk we consider a hybrid system, consisting of a pendulum attached to a mass-spring-damper. The latter is replaced by a numerical model and the transfer system is an actuator. The model we use is a system of two coupled second order neutral delay differential equations. We carry out a stability analysis of the system and identify possible regions of instability and the number of stability switches depending on parameters and delay time. Using the parameters from a real experiment, we perform numerical simulations which confirm our analytical findings, and show regions of periodic and quasi-periodic behaviour.

 

Robustness tools in ecology
Stuart Townley (Exeter)
28 Jun 2005Harrison 170 Tuesday 2.20pmApplied Mathematics

 

A conservation of fragility law and its consequences for biochemical network dynamics
Jorge Gonçalves (Cambridge University)
19 May 2005Harrison 170 Thursday 2pmApplied Mathematics
Robustness is a defining feature of successful complex systems. In this talk I will describe a fundamental limit on the robustness of complex systems achievable through feedback control. Based on a generic formulation of the control problem, we define /fragility/ in terms of the sensitivity of an output to a disturbance and derive an integral constraint (lower-bound) on the net fragility of a system. Put simply, reducing the sensitivity to disturbances at one range of frequencies by feedback control will necessarily amplify disturbances at other frequencies. For the special case of linear feedback systems, this result reduces to Bode's integral formula. We illustrate the implications of this robustness tradeoff for biological systems, and identify feedforward control and buffering as strategies for ameliorating the tradeoff. Finally, the theory provides an alternate interpretation of Shannon's channel capacity theorem for nonlinear control systems.

 

Inaugural Lecture: The mathematical basis for numerical weather and climate models: past successes; future challenges
John Thuburn (University of Exeter)
9 May 2005XFI centre - Monday 6pmApplied Mathematics

 

A unifying explanation of the transition to seizure states via a model of Human EEG
John Terry (Loughborough)
28 Apr 2005Harrison 209 Thursday 4pmApplied Mathematics

 

Terascale simulation using byte-size pieces
Lee Margetts (University of Manchester)
25 Apr 2005Harrison 170 Monday 2pmApplied Mathematics

 

On phase transitions in coupled map lattices
Wolfram Just (Queen Mary University of London)
14 Mar 2005Harrison 170 Monday 2pmApplied Mathematics
Coupled map lattices are a paradigm for studying fundamental questions in spatially extended dynamical systems. Within this tutorial we focus on qualitative changes of the motion which are intimately related with the limit of large system size. Similar to equilibrium phase transitions, such qualitative changes are an ubiquitous feature of dynamical systems with a large number of degrees of freedom. Within the first part we present an overview and some phenomenological facts of phase transitions in coupled map lattices. The following two parts describe in some details analytical tools which are useful for understanding phase transition behaviour in dynamical systems beyond plain numerical simulations. We explain how coupled map lattices are linked with the canonical equilibrium physics of spin systems when techniques of symbolic dynamics are applied. Using a simple model we explain how coupled map lattices are linked with phase transitions in equilibrium spin models. In the last part we describe an alternative approach in terms of kinetic spin models linking the dynamics of coupled map lattices with equilibrium and nonequilibrium statistical mechanics.

 

A model for the pure bending of isotropic tubes: localized buckling and the Brazier effect
Khurram Wadee (University of Exeter)
14 Mar 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

Using a dynamical systems approach to study the dyanmics of model reference adaptive control systems
David Wagg (University of Bristol)
7 Mar 2005Harrison 170 Monday 2pmApplied Mathematics

 

Nonlinear dynamo action in hydrodynamic instabilities driven by shear
Pu Zhang (University of Exeter)
7 Mar 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

A simple model of the dynamics of sudden stratospheric warmings
Gavin Esler (University College London)
28 Feb 2005Harrison 170 Monday 2pmApplied Mathematics

 

How to compute using globally coupled oscillators
Jon Borresen (University of Exeter)
28 Feb 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

Slumping of granular media
Rich Kerswell (University of Bristol)
21 Feb 2005Harrison 170 Monday 2pmApplied Mathematics

 

Mixing of passive scalars in Baker's maps
Andrew Gilbert (University of Exeter)
21 Feb 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

A conservation of fragility law and its consequences for biochemical network dynamics (POSTPONED until 19 May)
Jorge Gonçalves (Cambridge University)
17 Feb 2005Laver LT321 Thursday 2pmApplied Mathematics
Robustness is a defining feature of successful complex systems. In this talk I will describe a fundamental limit on the robustness of complex systems achievable through feedback control. Based on a generic formulation of the control problem, we define /fragility/ in terms of the sensitivity of an output to a disturbance and derive an integral constraint (lower-bound) on the net fragility of a system. Put simply, reducing the sensitivity to disturbances at one range of frequencies by feedback control will necessarily amplify disturbances at other frequencies. For the special case of linear feedback systems, this result reduces to Bode's integral formula. We illustrate the implications of this robustness tradeoff for biological systems, and identify feedforward control and buffering as strategies for ameliorating the tradeoff. Finally, the theory provides an alternate interpretation of Shannon's channel capacity theorem for nonlinear control systems.

 

Synchronization in Kuramoto-like model of globally coupled oscillators
Alexander Burilko (Kiev)
14 Feb 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

Interactions between vortices, boundaries and bottom topography
Ted Johnson (University College London)
7 Feb 2005Harrison 170 Monday 2pmApplied Mathematics

 

Eddy scaling for poleward heat transport in Earth's atmosphere
John Thuburn (UIniversity of Exeter)
7 Feb 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

Hilbert's 16th problem - some analytic and algebraic aspects
Colin Christopher (University of Plymouth)
31 Jan 2005Harrison 170 Monday 2pmApplied Mathematics
The second part of Hilbert's 16th problem deals with the number of limit cycles of polynomial vector fields in the plane. It remains one of the few of the original 23 problems that have not been substantially solved over the past century. However, over the past twenty years or so, insights from the theory of foliations and algebraic geometry as well as improved analytic techniques have brought many new advances to our understanding of this old problem. My aim in the talk is to give a brief survey of some of these recent advances as well as the many open questions which surround the study of polynomial vector fields in the plane.

 

Quasi-geostrophic approximation revisited
Keke Zhang (University of Exeter)
31 Jan 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

High-dimensional chaos in the Kuramoto model
Yuri Maistrenko (Kiev)
24 Jan 2005Harrison 106 Monday 10amApplied Mathematics (Internal)

 

Corner eddies: new variations on an old theme
Keith Moffatt (Cambridge University)
17 Jan 2005Harrison 170 Monday 2pmApplied Mathematics

 

Dynamics of delayed relay systems
Jan Sieber (University of Bristol)
10 Jan 2005Harrison 170 Monday 2pmApplied Mathematics

 

TBA
Achim Ilchmann (Ilmenau, Germany)
10 Dec 2004Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

A numerical scheme for stochastics PDEs
Gabriel Lord (Heriot-Watt University)
6 Dec 2004Harrison 170 Monday 2pmApplied Mathematics

 

New Effects in Mean-Field Magnetic Dynamos
Igor Rogachevskii (Ben-Gurion University, Beer-Sheva, Israel)
3 Dec 2004Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Rates of mixing in hyperbolic flows
Mike Field (University of Houston, USA)
29 Nov 2004Harrison 170 Monday 2pmApplied Mathematics

 

TBA
Paolo Rapisarda (University of Southampton)
27 Nov 2004Harrison 254 Monday 2pmApplied Mathematics

 

Stellar differential rotation
Guenther Rudiger (Potsdam, Germany)
26 Nov 2004Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

This seminar has been cancelled owing to illness
 

 

Unpredictability in population dynamics
Josef Hofbauer (University College London)
22 Nov 2004Harrison 170 Monday 2pmApplied Mathematics

 

Quasi-geostrophic approximation revisited
Keke Zhang (Mathematical Sciences)
19 Nov 2004Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

This seminar has been postponed until early in the new year - date to be advised
 

 

Different limiting mechanisms for nonlinear dynamos
Dave Galloway (University of Sydney, Australia)
15 Nov 2004Harrison 170 Monday 2pmApplied Mathematics

 

Piecewise Isometric Disk Packings and the Arbelos
Marcello Trovati (Mathematical Sciences)
12 Nov 2004Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Cycling cycles: Dynamics near a heteroclinic network
Claire Postlethwaite (Cambridge University)
8 Nov 2004Harrison 170 Monday 2pmApplied Mathematics

 

The role of inertia in the evolution of spherical dynamos
Binod Sreenivasan (Mathematical Sciences)
5 Nov 2004Harrison LT3 Wednesday 2pmApplied Mathematics (Internal)

 

How long can left and right handed life forms coexist?
Axel Brandenburg (NORDITA, Copenhagen, Denmark)
1 Nov 2004Harrison 170 Monday 2pmApplied Mathematics

 

Zonal flows and magnetic fields in laboratory plasmas
Pat Diamond (University of California, San Diego, USA)
25 Oct 2004Harrison 170 Monday 2pmApplied Mathematics

 

A mechanism of solar variability influence on climate
Alexander Ruzmaikin (JPL, Pasadina, USA)
18 Oct 2004Harrison 170 Monday 2pmApplied Mathematics

 

Matrix functions: Theory and algorithms
Nick Higham (University of Manchester)
11 Oct 2004Harrison 170 Monday 2pmApplied Mathematics

 

The slow-fast myth in geophysical fluid dynamics
David Dritschel (University of St Andrews)
4 Oct 2004Harrison 170 Monday 2pmApplied Mathematics

 

A model of cross-contamination by wind in genetically modified oilseed rape
Martin Hoyle (Biological Sciences)
24 Sep 2004Harrison L40 Wednesday 11amApplied Mathematics (Internal)

 

Asymptotic structure of biological excitability equations
Vadim Biktashev (University of Liverpool)
8 Dec 2003Harrison 170 Monday 2pmApplied Mathematics

 

Nonlinear Schroedinger equations as models of superfluidity
Natalia Berloff (Cambridge University)
1 Dec 2003Harrison 170 Monday 2pmApplied Mathematics

 

Magnetic fields in numerical simulations of the interstellar medium
Graeme Sarson (University of Newcastle)
24 Nov 2003Harrison 170 Monday 2pmApplied Mathematics

 

Stability of Hamiltonian relative equilibria and applications to underwater vehicles
Claudia Wulff (University of Surrey)
17 Nov 2003Harrison 170 Monday 2pmApplied Mathematics

 

Qualitative behaviour of thin liquid metal layers at low magnetic Reynolds number
Paul Dellar (Oxford University)
10 Nov 2003Harrison 170 Monday 2pmApplied Mathematics

 

Robust control of 2D and 3D channel flow with CFD validation
Eric Rogers (University of Southampton)
3 Nov 2003Harrison 170 Monday 2pmApplied Mathematics

 

Renormalization in interval translation maps
Henk Bruin (University of Surrey)
27 Oct 2003Harrison 170 Monday 2pmApplied Mathematics

 

Formation of vortices and jets in rotating convection on a beta-plane: Jupiter's belts and zones in the laboratory
Peter Read (Oxford University)
20 Oct 2003Harrison 170 Monday 2pmApplied Mathematics

 

Two MHD problems: Helical dynamos and the pulsar magnetosphere
Jonathan Mestel (Imperial College)
13 Oct 2003Harrison 170 Monday 2pmApplied Mathematics

 

Dynamics of impacting systems: Theory and experiments
Marian Wiercigroch (Aberdeen University)
6 Oct 2003Harrison 170 Monday 2pmApplied Mathematics

 

Strange attractors and their basins
Yongluo Cao (Suzhou University)
18 Sep 2003Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Quasipatterns in surface waves
Alastair Rucklidge (Leeds University)
10 Sep 2003Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Shape optimization for induction hardening
Jan Sokolowski ('Henrie Poincare University, Nancy')
11 Jul 2003Harrison 170 Monday 2pmApplied Mathematics

 

Dynamos and convection: mean flow generation
Jon Rotvig (University of Exeter)
13 Jun 2003Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Partial stability and stabilization. Part 2
Reza Rokni Lamooki (University of Exeter)
6 Jun 2003Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Partial stability and stabilization. Part 1: an introduction
Reza Rokni Lamooki (University of Exeter)
30 May 2003Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Integrability of Hamiltonian systems: from Poincare to Ziglin.
Alexei Tsygvinstev (University of Exeter)
19 May 2003Harrison 170 Monday 2pmApplied Mathematics

 

Pinching without branch points: new mechanism for absolute instability
Jonathan Healey (Keele University)
12 May 2003Harrison 170 Monday 2pmApplied Mathematics

 

Chaotic mixing and eigenfunctions
Jean-Luc Thiffeault (Imperial College)
28 Apr 2003Harrison 170 Monday 2pmApplied Mathematics

 

Characterization of a family of two-roll mill flows
Jonathan Kobine (University of Dundee)
17 Mar 2003Harrison 170 Monday 2pmApplied Mathematics

 

The structure of periodic causal operators on L2
George Weiss (Imperial College London)
10 Mar 2003Harrison 170 Monday 2pmApplied Mathematics

 

Energy, helicity and crossing number relations for complex flows
Renzo Ricca (University College London)
3 Mar 2003Harrison 170 Monday 2pmApplied Mathematics

 

Nonlinear waves in diverging flows
Rich Kerswell (University of Bristol)
24 Feb 2003Harrison 170 Monday 2pmApplied Mathematics

 

Parametrisation of attractors and Takens embedding thereom
James Robinson (University of Warwick)
17 Feb 2003Harrison 170 Monday 2pmApplied Mathematics

 

The application of the method of matched asymptotic expansions to problems arising in reaction-diffusion theory
John Leach (University of Reading)
10 Feb 2003Harrison 170 Monday 2pmApplied Mathematics

 

Revisiting scaling laws for the magnetic and velocity fields
Glenn Ierley (University of California San Diego)
31 Jan 2003Harrison 170 Monday 2pmApplied Mathematics

 

Marangoni-Benard convection in square and almost square containers
Edgar Knobloch (University of Leeds)
27 Jan 2003Harrison 170 Monday 2pmApplied Mathematics

 

Instabilities of the Stewartson layer
Rainer Hollerbach (University of Glasgow)
20 Jan 2003Harrison 170 Monday 2pmApplied Mathematics

 

Transient vortex events in turbulence
Bob Kerr (University of Warwick)
13 Jan 2003Harrison 170 Monday 2pmApplied Mathematics

 

Zonal flows on Jupiter
Chris Jones (University of Exeter)
13 Dec 2002Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

New observational constraints on the geodynamo
Richard Holme (University of Liverpool)
9 Dec 2002Harrison 170 Monday 2pmApplied Mathematics

 

Nature of torsional oscillations in the solar convection zone
Reza Tavakol ('Queen Mary, University of London')
2 Dec 2002Harrison 170 Monday 2pmApplied Mathematics

 

Some bifurcation results for differential-algebraic equations
Robert Beardmore (Imperial College)
25 Nov 2002Harrison 170 Monday 2pmApplied Mathematics

 

A new proof of the uniqueness of elastic surface waves
Yibin Fu (University of Keele)
18 Nov 2002Harrison 170 Monday 2pmApplied Mathematics

 

Validity of various approximations of the fully-compressible atmospheric equation as inferred from normal-mode analysis
'Andrew Staniforth, Terry Davies and Nigel Wood' (Met Office)
11 Nov 2002Harrison 170 Monday 2pmApplied Mathematics

 

Magnetic fields in barred galaxies
David Moss (University of Manchester)
4 Nov 2002Harrison 170 Monday 2pmApplied Mathematics

 

Magnetic damping of surface gravity waves
Binod Sreenivasan (University of Exeter)
1 Nov 2002Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Virial functional in fluid mechanics
Vladimir Vladimirov (Univeristy of Hull)
28 Oct 2002Harrison 170 Monday 2pmApplied Mathematics

 

Impulse differential inclusions: Towards a viability theory of hybrid systems
John Lygeros (University of Cambridge)
21 Oct 2002Harrison 170 Monday 2pmApplied Mathematics

 

A new test for chaos in deterministic nonlinear dynamical systems
Ian Melbourne (University of Surrey)
14 Oct 2002Harrison 170 Monday 2pmApplied Mathematics

 

Fractal asymptotics
Carl Dettmann (University of Bristol)
7 Oct 2002Harrison 170 Monday 2pmApplied Mathematics

 

On the relationship between the discrete and continuous Painleve equations
Peter Clarkson (University of Kent)
10 Jun 2002Harrison 170 Monday 2pmApplied Mathematics

 

Explicitly time-dependent alpha-quenching
Axel Brandenburgh (NORDITA)
27 May 2002Harrison 170 Monday 2pmApplied Mathematics

 

Stochastic population dynamics
Xuerong Mao (University of Strathclyde)
13 May 2002Harrison 170 Monday 2pmApplied Mathematics

 

Quantum monodromy
Holger Dullin (Loughborough University)
29 Apr 2002Harrison 170 Monday 2pmApplied Mathematics

 

Composition convection due to the decrease of the rapidly rotating shell
Serguey Starchenko (GFO Borok)
22 Apr 2002Harrison 170 Monday 2pmApplied Mathematics

 

Shear and magnetic buoyancy instabilities in the solar tachocline
Steve Tobias (University of Leeds)
11 Mar 2002Harrison 170 Monday 2pmApplied Mathematics

 

Vortex equilibria of the Euler equations
Darren Crowdy (Imperial College)
4 Mar 2002Harrison 170 Monday 2pmApplied Mathematics

 

Thin layer theories
Richard Craster (Imperial College)
25 Feb 2002Harrison 170 Monday 2pmApplied Mathematics

 

Localisation of patterns in convection
Stephen Cox (University of Nottingham)
18 Feb 2002Harrison 170 Monday 2pmApplied Mathematics

 

Pattern selection and symmetry in rotating Rayleigh-Benard convection
Jon Dawes (University of Cambridge)
11 Feb 2002Harrison 170 Monday 2pmApplied Mathematics

 

The role of the heating mode of the mantle in intermittent reorganisation of plate velocities
Julian Lowman (University of Leeds)
4 Feb 2002Harrison 170 Monday 2pmApplied Mathematics

 

MHD in metallurgical processes
Peter Davidson (University of Cambridge)
28 Jan 2002Harrison 170 Monday 2pmApplied Mathematics

 

Fast dynamo problem
Oleg Kozlovski (University of Warwick)
21 Jan 2002Harrison 170 Monday 2pmApplied Mathematics

 

Jets, waves and vortices in the Jovian atmosphere
POSTPONED
Yasuhiro Yamazaki (University of Oxford)
14 Jan 2002Harrison 170 Monday 2pmApplied Mathematics

 

Deterministic and random products of Euclidean transformations
CANCELLED
Ian Melbourne (University of Surrey)
7 Jan 2002Harrison 170 Monday 2pmApplied Mathematics

 

Global bifurcation to travelling waves in spherical Couette flow
Andrew Soward (University of Exeter)
7 Dec 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Adaptive controllers and the gap metric
Mark French (University of Southampton)
3 Dec 2001Harrison 170 Monday 2pmApplied Mathematics

 

A new generation of geodynamo models
Keke Zhang (University of Exeter)
30 Nov 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Oscillations in small aspect ratio magnetoconvection
Mike Proctor (University of Cambridge)
26 Nov 2001Harrison 170 Monday 2pmApplied Mathematics

 

Nonlinear models of rotating spherical convection
Steve Cole (University of Exeter)
23 Nov 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Galactic magnetic fields
Steven Cowley (Imperial College)
19 Nov 2001Harrison 170 Monday 2pmApplied Mathematics

 

Hopf bifurcation with the symmetry of the cube
Pete Ashwin (University of Exeter)
16 Nov 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Particles in a random field
Andrew Stuart (University of Warick)
12 Nov 2001Harrison 170 Monday 2pmApplied Mathematics

 

Some issues in stochastic control
Stuart Townley (University of Exeter)
9 Nov 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Shear propagation into the solar radiative zone
Pascale Garaud (University of Cambridge)
5 Nov 2001Harrison 170 Monday 2pmApplied Mathematics

 

Energy fluxes and dissipation in planetary cores
Chris Jones (University of Exeter)
2 Nov 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Statistics, symmetry and skew products
Mike Field (University of Houston)
29 Oct 2001Harrison 170 Monday 2pmApplied Mathematics

 

Vorticity, mixing and motion
Andrew Gilbert (University of Exeter)
26 Oct 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Kinematic dynamos at high magnetic Reynolds number
Graeme Sarson (University of Newcastle upon Tyne)
22 Oct 2001Harrison 170 Monday 2pmApplied Mathematics

 

Scaling properties of spatial and temporal spectra of the geomagnetic field
Roberta Tozzi (Rome)
19 Oct 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Weak disjointness in topological dynamics
Xiangdong Ye (University of Science and Technology of China)
25 Sep 2001Harrison 170 Monday 2pmApplied Mathematics

 

Numerical modelling of star formation
Matthew Bate (University of Exeter (Physics))
15 Jun 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Packing properties of invariant disks for some planar piecewise isometries
Xin-Chu Fu (University of Exeter)
8 Jun 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Quantum turbulence in superfluid helium
Tomasz Lipniacki (University of Warsaw)
1 Jun 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Evolution of sharp edged planar vortices
Ian Hall (University of Exeter)
25 May 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Routes to chaos, channel capacity and the representation of numbers in non-integer bases'
Paul Glendinning (UMIST)
21 May 2001Harrison 170 Monday 2pmApplied Mathematics

 

Instabilities induced by the differentially rotating inner core and mantle
Pu Zhang (University of Exeter)
18 May 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Chaotic Dynamics in Semiconductor Lasers
Pieter Collins (University of Liverpool)
14 May 2001Harrison 170 Monday 2pmApplied Mathematics

 

Fourier series on spheres
Paul Earnshaw (University of Exeter)
11 May 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

'Numerical exterior algebra, with applications in hydrodynamic stability and dynamical systems'
Tom Bridges (University of Surrey)
23 Apr 2001Harrison 170 Monday 2pmApplied Mathematics

 

Dynamics of a Sigma-Delta modulator as a piecewise isometry
Jonathan Deane (University of Surrey)
30 Mar 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

'Typical magneto-convection values in the interiors of Jupiter, Saturn and the Earth'
Sergey Starchenko ('GFO Barok, Russia')
13 Mar 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Modulating pulse solutions for a class of nonlinear wave equations
Mark Groves (University of Loughborough)
12 Mar 2001Harrison 170 Monday 2pmApplied Mathematics

 

MHD shear layers in spherical Couette flow
Andrew Soward (University of Exeter)
9 Mar 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Stochastic bifurcation: concepts and examples
Ludwig Arnold ('Universitat Bremen')
5 Mar 2001Harrison 170 Monday 2pmApplied Mathematics
Part of the %http://www.maths.ex.ac.uk/Research/applDSC/events/ndc.html%Southern Bifurcation Meeting%

 

Quasi-invariant sets in Piecewise Isometries
Miguel Mendes (University of Surrey)
2 Mar 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Neutral Rayleigh waves in Hagen-Poiseuille flow
Andrew Walton (Imperial College)
26 Feb 2001Harrison 170 Monday 2pmApplied Mathematics

 

Non-orientable manifolds in three-dimensional vector fields
Hinke Osinga (University of Exeter)
23 Feb 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Receptivity of boundary layers to free-stream disturbances
Paul Hammerton (University of East Anglia)
19 Feb 2001Harrison 170 Monday 2pmApplied Mathematics

 

Convection in a semi-infinite layer above a flat plate
Andrew Bassom (University of Exeter)
16 Feb 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

'Dynamo action in the stretch, fold, shear model'
Andrew Gilbert (University of Exeter)
9 Feb 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

The magneto-rotational instability in a Couette-type flow
Wolfgang Dobler (University of Newcastle upon Tyne)
5 Feb 2001Harrison 170 Monday 2pmApplied Mathematics

 

The anatomy of some non-holonomic oscillators
Ciprian Coman (University of Exeter)
2 Feb 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Rotational instabilities of contained fluids; laboratory experiments and applications to the Earth's core
Keith Aldridge (York University, Canada)
29 Jan 2001Harrison 170 Monday 2pmApplied Mathematics

 

Using constrained variational techniques to improve numerical weather prediction
Ian Roulstone (University of Reading)
22 Jan 2001Harrison 170 Monday 2pmApplied Mathematics

 

Bifurcations in nonlinear dynamos driven by ABC forcing
Olga Podvigina (University of Moscow)
19 Jan 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

%http://www.maths.ex.ac.uk/~PAshwin/workshop_15_1_01.html%Dynamics and Intermittency%
(WORKSHOP)
15 Jan 2001Harrison 170 Monday 2pmApplied Mathematics

 

Multi-scale space-periodic kinematic dynamos
Vlad Zheligovsky (University of Moscow)
12 Jan 2001Harrison 106 Wednesday 3pmApplied Mathematics (Internal)

 

Is intermittency that nonlinear?
Sergei Nazarenko (University of Warwick)
8 Jan 2001Harrison 170 Monday 2pmApplied Mathematics