Pattern Formation in Chemical Systems: The Effect of Convection

Abstract

The spontaneous nucleation of spatial patterns far from thermal equilibrium has long been a puzzling phenomenon both from experimental and theoretical point of views. Numerous questions related to pattern formation and pattern selection in physical, chemical and biological systems remain still unanswered. However, great progress in the understanding of these phenomena have been achieved in the framework of reaction-diffusion equations which are believed to accurately describe many nonequilibrium systems (I). It has also been suggested that, like in equilibrium phase transitions and hydrodynamic instabilities, when chemical spatial or temporal structures appear through the breaking of a continuous symmetry(e.g. translational or rotational symmetry for spatial structures, phase or gauge symmetry for temporal oscillations) they are particularly sensitive to small external fields or to Internal fluctuations (2). Effectively, in this case, long range fluctuations may spontaneously develop, leading to topological defects In the structure (e.g. dislocations in hydrodynamical patterhs (3), chemical waves in oscillating or excitable media (4)). A stochastic analysis leads to the evaluation of the probability of such fluctuations and consequently to their statistics.