Nonequilibrium Shear Viscosity Computations with Langevin Dynamics

Joubaud, Rémi; Stoltz, Gabriel

doi:10.1137/110836237

Cited by 13 publications

(15 citation statements)

References 34 publications

(37 reference statements)

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“…Recall that, unless otherwise mentioned, all operators are defined on S , and that formal adjoint operators are by default considered on L 2 (µ). Recall also that Joubaud & Stoltz (2013) or the updated preprint version Joubaud & Stoltz (2012b)). We provide a simplified version of it for completeness.…”

Section: Proofs Of the Resultsmentioning

confidence: 99%

The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics

Leimkuhler¹,

Matthews²,

2015

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We consider numerical methods for thermodynamic sampling, i.e. computing sequences of points distributed according to the Gibbs-Boltzmann distribution, using Langevin dynamics and overdamped Langevin dynamics (Brownian dynamics). A wide variety of numerical methods for Langevin dynamics may be constructed based on splitting the stochastic differential equations into various component parts, each of which may be propagated exactly in the sense of distributions. Each such method may be viewed as generating samples according to an associated invariant measure that differs from the exact canonical invariant measure by a stepsize-dependent perturbation. We provide error estimatesà la Talay-Tubaro on the invariant distribution for small stepsize, and compare the sampling bias obtained for various choices of splitting method. We further investigate the overdamped limit and apply the methods in the context of driven systems where the goal is sampling with respect to a nonequilibrium steady state. Our analyses are illustrated by numerical experiments.

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Section: Proofs Of the Resultsmentioning

confidence: 99%

The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics

Leimkuhler¹,

Matthews²,

2015

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“…A closely related dynamics, differing in the choice of boundary conditions (we detail our choice below) and how the external forcing is handled, is considered in [12] where the authors perform rigorous asymptotic analysis on the invariant measure as well as numerical viscosity experiments.…”

Section: Simple Lennard-jones Fluidmentioning

confidence: 99%

Derivation of Langevin dynamics in a nonzero background flow field

et al. 2013

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Abstract.We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of Mathematics Subject Classification. 82C05, 82C31.

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“…In fact, the uniform coercivity property is true only for functions whose average with respect to the Gibbs distribution in the velocity variable p y (for Theorem 2) or p x (for Theorem 3) vanishes. We show here how to correct the proof of [3,Theorem 2], the corrections in the proof of Theorem 3 being similar. We refer to [4] for a full corrected proof.…”

Section: −1mentioning

confidence: 98%

“…We show here how to correct the proof of [3,Theorem 2], the corrections in the proof of Theorem 3 being similar. We refer to [4] for a full corrected proof.…”

Section: −1mentioning

confidence: 98%