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- W1880453088 abstract "Motivated by the problem of modeling nucleation in non-isothermal systems,we consider the stochastic evolution of a coupled system of a lattice spinvariable $sigma$ and a continuous variable $e$ (corresponding to the phase andthe energy density of a continuum system). The spin variables flip with ratesdepending both on a Kac potential type interaction with the spins and on aninteraction with the $e$-field, which plays the role of the external field inferromagnetics but evolves by a diffusion equation with a forcing depending onthe spins. We analyze the mesoscopic limit, where space scales like the diverginginteraction range of the Kac potential, $gamma^{-1},$ while time is not rescaled.By writing $sigma$ as random time change of a family of independent spins,and thus reducing the problem to investigating integral equations parametrizedby independent random variables, we show that as $gammato 0$ the average ofthe spins over small cubes and the field $e$ converge in probability to thesolution of a system of nonlocal evolution equations which is similar to thephase field equations. In some cases the convergence holds until times of order${log(gamma^{-1})}.$" @default.
- W1880453088 created "2016-06-24" @default.
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- W1880453088 date "2000-11-06" @default.
- W1880453088 modified "2023-09-24" @default.
- W1880453088 title "Mesoscopic limit for non-isothermal phase transition" @default.
- W1880453088 hasPublicationYear "2000" @default.
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