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arXiv · 1708.09018

Turing instability in a model with two interacting Ising lines: linear stability and non-equilibrium fluctuations

M. Capanna·N. Soprano-Loto
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Abstract

This is the second of two articles on the study of a particle system model that exhibits a Turing instability type effect. About the hydrodynamic quations obtained in \cite{CSL17a}, we find conditions under which Turing instability occurs around the null equilibrium solution. In this instability regime: for long times at which the process is of infinitesimal order, we prove that the non-equilibrium fluctuations around the hydrodynamic limit are Gaussian; for times converging to the critical one at which the process is of finite order, we prove that the $\pm 1$-Fourier modes are uniformly away from zero.

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M. Capanna, N. Soprano-Loto. 2017-08-29. Turing instability in a model with two interacting Ising lines: linear stability and non-equilibrium fluctuations. https://doi.org/10.1007/s10955-018-2206-7

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