منابع مشابه
Generalized Stochastic Fokker-Planck Equations
We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case of complex systems experiencing small-scale constraints. In the limit of short-r...
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We present new Φ-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.
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The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numeri...
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This is the second paper in a series concerning the study of steady states, including stationary solutions and measures, of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, we obtain some non-existence results of stationary measures under conditions involving anti-Lyapunov type of functions associated with the sta...
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This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker–Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth conve...
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ژورنال
عنوان ژورنال: The European Physical Journal Special Topics
سال: 2017
ISSN: 1951-6355,1951-6401
DOI: 10.1140/epjst/e2016-60215-1