Anomalous diffusion for a class of systems with two conserved quantities

Cédric Bernardin; Gabriel Stoltz

doi:10.1088/0951-7715/25/4/1099

Anomalous diffusion for a class of systems with two conserved quantities

Cédric Bernardin
, Gabriel Stoltz

CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

We introduce a class of one-dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. A system of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows that these models are still super-diffusive. This is proven rigorously for harmonic potentials.

Original language	English
Pages (from-to)	1099-1133
Number of pages	35
Journal	Nonlinearity
Volume	25
Issue number	4
DOIs	https://doi.org/10.1088/0951-7715/25/4/1099
Publication status	Published - 1 Apr 2012

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abstract = "We introduce a class of one-dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. A system of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows that these models are still super-diffusive. This is proven rigorously for harmonic potentials.",

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AB - We introduce a class of one-dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. A system of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows that these models are still super-diffusive. This is proven rigorously for harmonic potentials.

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Anomalous diffusion for a class of systems with two conserved quantities

Abstract

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