Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combina...

Coarse-Grained Numerical Bifurcation Analysis of Lattice Boltzmann Models

In this paper we study the coarse-grained bifurcation analysis approach proposed by I.G. Kevrekidis and collaborators in PNAS 97(18):9840–9843. We extend the results obtained in that paper for a one-dimensional FitzhHugh-Nagumo lattice Boltzmann model in several ways. First, we extend the coarse-grained time stepper concept to enable the computation of periodic solutions and we use the more ver...

Coarse Grained Molecular Dynamics

Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles.

We derive and study two different formalisms used for nonequilibrium processes: the coherent-state path integral, and an effective, coarse-grained stochastic equation of motion. We first study the coherent-state path integral and the corresponding field theory, using the annihilation process A+A→A as an example. The field theory contains counterintuitive quartic vertices. We show how they can b...

A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular Dynamics

Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and a liquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooled liquid is determined by diffusion and convection of heat, on the mac...