Homogenization of fully overdamped Frenkel-Kontorova models

被引：31

作者：

Forcadel, N. ^{[2
,3
,4
]}

Imbert, C. ^{[1
]}

Monneau, R. ^{[2
]}

机构：

[1] Univ Paris 09, CNRS, CEREMADE, UMR 7534, F-75775 Paris 16, France

[2] Paris Est ENPC, CERMICS, F-77455 Marne La Vallee 2, France

[3] Ecole Polytech, CMAP INRIA Futurs, Projet Commands, F-91128 Palaiseau, France

[4] UMA, ENSTA, F-75739 Paris 15, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 03期

关键词：

Particle systems; Periodic homogenization; Frenkel-Kontorova models; Hamilton-Jacobi equations; Hull function; Cumulative distribution function; Slepcev formulation; HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS; DEVILS STAIRCASE;

D O I：

10.1016/j.jde.2008.06.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the fully overdamped Frenkel-Kontorova model. This is an infinite system of coupled first-order ODEs. Each ODE represents the microscopic evolution of one particle interacting with its neighbors and Submitted to a fixed periodic potential. After a proper rescaling, a macroscopic model describing the evolution of densities of particles is obtained. We get this homogenization result for a general class of Frenkel-Kontorova models. The proof is based on the construction of suitable hull functions in the framework of viscosity solutions. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1057 / 1097

页数：41

共 50 条

[41] Farey fractions and the Frenkel-Kontorova model
Kao, HC
Lee, SC
Tzeng, WJ
PHYSICAL REVIEW E, 1997, 55 (03): : 2628 - 2631
[42] Synchronization in the Frenkel-Kontorova type system
Yang, Yang
Wang, Cang-Long
Jiang, Hong
Chen, Jian-Min
Duan, Wen-Shan
PHYSICA SCRIPTA, 2012, 86 (01)
[43] SOLUTION TO FRENKEL-KONTOROVA DISLOCATION MODEL
HOBART, R
CELLI, V
JOURNAL OF APPLIED PHYSICS, 1962, 33 (01) : 60 - &
[44] GLOBAL UNIVERSALITY IN THE FRENKEL-KONTOROVA MODEL
BIHAM, O
MUKAMEL, D
PHYSICAL REVIEW A, 1989, 39 (10): : 5326 - 5335
[45] The ground state of the Frenkel-Kontorova model
Babushkin, A. Yu.
Abkaryan, A. K.
Dobronets, B. S.
Krasikov, V. S.
Filonov, A. N.
PHYSICS OF THE SOLID STATE, 2016, 58 (09) : 1834 - 1845
[46] Heat conduction in the Frenkel-Kontorova model
Hu, BB
Yang, L
CHAOS, 2005, 15 (01)
[47] Nonlinear dynamics of the Frenkel-Kontorova model
Braun, OM
Kivshar, YS
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1998, 306 (1-2): : 1 - 108
[48] Farey fractions and the Frenkel-Kontorova model
Phys Rev E., 3-A (2628):
[49] Entanglement of solitons in the Frenkel-Kontorova model
Marcovitch, S.
Reznik, B.
PHYSICAL REVIEW A, 2008, 78 (05):
[50] PROPERTIES OF SOLITONS IN THE FRENKEL-KONTOROVA MODEL
JOOS, B
SOLID STATE COMMUNICATIONS, 1982, 42 (10) : 709 - 713

← 1 2 3 4 5 →