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: 2.013 - Q1 (2018)
DOI reference: 10.1137/070695514
Published on paper: January 2008.
M. Castro, G. Lythe. Numerical experiments on noisy chains: From collective transitions to nucleation-diffusion. SIAM Journal on Applied Dynamical Systems. vol. 7, no. 1, pp. 207-219, January 2008.