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The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a time- dependent constraint.
Brownian motion in a field of force and the diffusion model of chemical reactions
Hendrik Anthony Kramers · 1940
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Stochastic differential equations and applications. Vol. 1
Avner Friedman · 1975
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The Fokker-Planck equation
Hannes Risken · 1989
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Reaction-rate theory: fifty years after Kramers
Peter Hanggi, Peter Talkner, and Michal Borkovec · 1990
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Free energy and the Fokker-Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1996
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The variational formulation of the Fokker-Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Real analysis
Emmanuele DiBenedetto · 2002
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Gradient flows in metric spaces and in the space of probability measures
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2005
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Spectral gap for log-concave probability measures on the real line
Pierre Fougères · 2005
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Thermodynamics of rate-independent plasticity
Giuseppe Puglisi and Lev Truskinovsky · 2005
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Existence and stability for Fokker-Planck equations with log-concave reference measure
Luigi Ambrosio, Giuseppe Savaré, and Lorenzo Zambotti · 2009
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The thermodynamic origin of hysteresis in insertion batteries
Wolfgang Dreyer, Janko Jamnik, Clemens Guhlke, Robert Huth, Jože Moškon, and Miran Gaberšček · 2010
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From diffusion to reaction via Γ \Gamma -convergence
Mark A. Peletier, Giuseppe Savaré, and Marco Veneroni · 2010
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Hysteresis and phase transition in many-particle storage systems
Wolfgang Dreyer, Clemens Guhlke, and Michael Herrmann · 2011
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Kramers’ formula for chemical reactions in the context of a Wasserstein gradient flow
Michael Herrmann and Barbara Niethammer · 2011
Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction
Steffen Arnrich, Alexander Mielke, Mark A. Peletier, Giuseppe Savaré, and Marco Veneroni · 2012
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Kramers and non-kramers phase transitions in many-particle systems with dynamical constraint
Michael Herrmann, Barbara Niethammer, and Juan J.L. Velázquez · 2012
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On a Fokker-Planck equation coupled with a constraint – analysis of a lithium-ion battery model
Robert Huth · 2012
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From discrete visco-elasticity to continuum rate-independent plasticity: Rigorous results
Alexander Mielke and Lev Truskinovsky · 2012
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Eyring-Kramers formula for Poincaré and logarithmic Sobolev inequalities
André Schlichting · 2012
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Differential, energetic, and metric formulations for rate-independent processes
Alexander Mielke · 2011
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Emergence of rate-independent dissipation from viscous systems with wiggly energies
Alexander Mielke · 2011
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Kramers’ law: validity, derivations and generalisations
Nils Berglund · 2013
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Well-posedness of a nonlocal Fokker-Planck equation
Simon Eberle · 2013
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Global existence for a nonlocal and nonlinear Fokker-Planck equation
Wolfgang Dreyer, Robert Huth, Alexander Mielke, Joachim Rehberg, and Michael Winkler · 2014
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