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• W2003042174 abstract "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." @default.
• W2003042174 created "2016-06-24" @default.
• W2003042174 creator A5002816287 @default.
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• W2003042174 date "2008-01-01" @default.
• W2003042174 modified "2023-10-18" @default.
• W2003042174 title "Numerical Experiments on Noisy Chains: From Collective Transitions to Nucleation-Diffusion" @default.
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• W2003042174 doi "https://doi.org/10.1137/070695514" @default.
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