Reaction–diffusion systems with fluctuating diffusivity; spatio-temporal chaos and phase separation

Abstract

The homogeneous stable state of a one-component reaction–diffusion system with positive diffusivity always remains stable by diffusion. We have shown that dichotomously fluctuating diffusivity leads to an instability of the stable state for an optimal range of correlation times of dichotomous noise. The instability condition corresponds to the rare event of instantaneous diffusivity remaining negative for typical realizations of dichotomous fluctuations over a finite correlation time. Detailed numerical simulations reveal that, depending on the characteristic non-linearity of the reaction term, this fluctuating diffusivity-driven instability results in irregular non-stationary patterns in the form of spatio-temporal chaos or phase-separation.

Itô-distribution from Gibbs measure and a comparison with experiment

“…The method presented here is general enough to find application in other problems where local characteristics of fluctuating diffusion is important. Diffusing diffusion is an idea of contemporary interest [29][30][31][32][33] particularly in the context of some non-ergodic, transient diffusion processes [34][35][36][37] and the present work could be of relevance there.…”

It\^o--distribution from Gibbs measure and a comparison with experiment

“…The method presented here is general enough to find application in other problems where local characteristics of fluctuating diffusion is important. Diffusing diffusion is an idea of contemporary interest [29][30][31][32][33] particularly in the context of some non-ergodic, transient diffusion processes [34][35][36][37] and the present work could be of relevance there.…”

Motion of an active particle with dynamical disorder

“…35,54 Apart from the Brownian dynamics, applications of the switching model in describing several biochemical processes such as cellular signalling, chemotaxis, synaptic dynamics, growth of cell population, and pattern formation are noteworthy in relation to the present topic. [55][56][57][58][59] In addition to the AYB diffusion of Brownian particles, stochasticity in diffusivity naturally arises in the dynamics of macromolecules such as conformational fluctuations of proteins 60,61 and the motion of the center of mass of (de)polymerising or shapeshifting molecules. 61,62 The non-Gaussian behavior can also be observed for sub-diffusing particles moving in gels or viscoelastic media such as the cytoplasmic environment due to heterogeneity.…”