Paper information

# Numerical experiments on noisy chains: From collective transitions to nucleation-diffusion

## M. Castro, G. Lythe

We consider chains of particles with nearest-neighbor coupling, independently subjected to noise, all initially in the same well of a symmetric double-well potential. If there are sufficiently few particles, transitions from one well to another are “collective”; i.e., all particles remain close together as they make the passage from one well to the other. In longer chains, only a fraction of the particles make an initial transition, creating a nucleated region that may grow or collapse by diffusion of its boundaries. Numerical experiments are used to explore the change of the scaling of the passage time as a function of the length of the chain, which distinguishes the two regimes. A suitable relationship between the noise amplitude, coupling, and number of particles in the chain yields convergence to the continuum $\\phi^4$ or Allen–Cahn stochastic partial differential equations in one space dimension. We estimate the characteristic width of newly nucleated regions and construct a numerical effective potential describing the dynamics in the nucleation-diffusion regime.

Keywords: Stochastics, nucleation, passage time

### SIAM Journal on Applied Dynamical Systems Volume: 7 Issue: 1 Pages: 207-219

JCR Impact Factor and WoS quartile: 1.211 (2008); 1.956 - Q1 (2019)

DOI reference: 10.1137/070695514

Published on paper: .

Citation:
M. Castro, G. Lythe. Numerical experiments on noisy chains: From collective transitions to nucleation-diffusion. SIAM Journal on Applied Dynamical Systems. January 2008.