Penetration of Boundary Perturbations in Unstable Chemical Systems

Abstract

The effects of boundary perturbations of chemical species are investigated in a linear analysis for systems of coupled chemical reactions, with diffusion, which have instabilities. At marginal stability of one of the harmonic modes of such a system the penetration depth of the chemical boundary perturbation coupled to that mode approaches infinity at resonance, that is, at the frequency of boundary perturbation equal to the marginal oscillatory frequency of the mode. For the case of equal and diagonal diffusion coefficients for all chemical species the penetration of the perturbation is homogeneous at resonance. In general inhomogeneous penetration occurs in association with symmetry-breaking instabilities of the system. The propagation of an impulse boundary perturbation is derived. Some possible applications of the theory are suggested but not demonstrated: (1) analysis of chemical instabilities; (2) analogies of electronic devices such as tuned amplifiers, transmitters, and receivers (chemical radio); (3) communication in aggregates of biological systems; and (4) mechanism of pheromone emission and reception.