Quadratic and rate-independent limits for a large-deviations functional

G.A. Bonaschi, M.A. Peletier

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6 Citaten (Scopus)
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Samenvatting

We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth–death process on a lattice, with rates derived from Kramers’ law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ‘L log L’ gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process. Keywords: Large deviations Gamma convergence Gradient flows Markov chains Rate-independent systems
Originele taal-2Engels
Pagina's (van-tot)1191-1219
Aantal pagina's29
TijdschriftContinuum Mechanics and Thermodynamics
Volume28
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - jul 2016

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