Error Analysis of Modified Langevin Dynamics
| Autor: | Stephane Redon, Gabriel Stoltz, Zofia Trstanova |
|---|---|
| Přispěvatelé: | Algorithms for Modeling and Simulation of Nanosystems (NANO-D), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), MATHematics for MatERIALS (MATHERIALS), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC), ANR-14-CE23-0012,COSMOS,Statistique numérique et simulation moléculaire(2014), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Work (thermodynamics) Statistical Mechanics (cond-mat.stat-mech) Monte Carlo method Ergodicity FOS: Physical sciences Statistical and Nonlinear Physics Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Hypoelliptic operator 0103 physical sciences FOS: Mathematics Ergodic theory Variance reduction Mathematics - Numerical Analysis Statistical physics [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 0101 mathematics 010306 general physics Galerkin method Langevin dynamics Condensed Matter - Statistical Mechanics Mathematical Physics |
| Zdroj: | Journal of Statistical Physics Journal of Statistical Physics, Springer Verlag, 2016, 164 (4), pp.735-771. ⟨10.1007/s10955-016-1544-6⟩ Journal of Statistical Physics, 2016, 164 (4), pp.735-771. ⟨10.1007/s10955-016-1544-6⟩ |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-016-1544-6 |
| Popis: | International audience; We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations. |
| Databáze: | OpenAIRE |
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