Many nonlinear dissipative distributed systems of varied physical, chemical and biological origin display excitable behaviour; the return from a perturbed state to a single stable equilibrium state may be achieved by two qualitatively different routes, one of which entails a large excursion from equilibrium, the so called ``excitation''. Examples of excitability abound in chemical systems, notably in the celebrated Belousov-Zhabotinsky reaction, but also in the context of spontaneous ignition of stored solids or of leaking reactant fluids [1]. Many fundamental physiological processes are driven by excitable behaviour, including propagation of information through nerve cell complexes and functioning of cardiac muscle, and excitability is important in biological morphology and some examples of population dynamics [2].
In appropriate circumstances, a distributed excitable system can support a travelling wave of excitation followed by a return to the equilibrium state, and the characteristic spiral, target pattern or scroll wave forms have attracted enormous attention. In virtually all this work, the supporting medium has been assumed to be at rest, or in uniform motion. However, the effects of medium movement on the excitation wave dynamics have been studied for slight deformations [3]; and effects of nonuniform advection onto chemical reactions, but without excitable properties were studied in [4, 5]. Little or no attention has been given to the situation where the excitable medium with recovery undergoes relative straining motion, as in a shear flow or even a non-uniform elastic deformation -- though experiments with the Belousov-Zhabotinsky reaction have demonstrated that sufficiently strong convective motion of the chemically reacting medium can break the excitation waves [6].
In this letter we identify and analyse the influence on excitation waves of one of the simplest examples of relative motion of the medium, a constant linear shear. Though the model is very simple, shearing strain is a key component of all more complex deformations of the medium, and we demonstrate and explain its effectiveness in breaking individual waves and wave patterns.