Rotation number of the overdamped Frenkel–Kontorova model with ac-driving

Bambi Hu; Wen-Xin Qin; Zhigang Zheng

doi:10.1016/j.physd.2005.06.022

Rotation number of the overdamped Frenkel–Kontorova model with ac-driving

Bambi Hu, Wen-Xin Qin^*, Zhigang Zheng

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

17 Citations (Scopus)

Abstract

The dynamical behavior of the overdamped and overdamped limit cases of the Frenkel–Kontorova model with ac-driving is studied. The relationship is established between the average velocity of the particles and the rotation number of the orientation preserving homeomorphism on the circle induced from the Poincaré map. The dynamical behavior for both cases is determined completely by the rotation number. Numerical results are also provided for the second order system to support the theoretical conclusions.

Original language	English
Pages (from-to)	172-190
Number of pages	19
Journal	Physica D: Nonlinear Phenomena
Volume	208
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physd.2005.06.022
Publication status	Published - 1 Sept 2005

Scopus Subject Areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

User-Defined Keywords

Average velocity
Mode-locking
Orientation preserving homeomorphism
Overdamped Frenkel-Kontorova model
Rotation number

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10.1016/j.physd.2005.06.022

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@article{405c64a825af4e55bd6e9d093c250dce,

title = "Rotation number of the overdamped Frenkel–Kontorova model with ac-driving",

abstract = "The dynamical behavior of the overdamped and overdamped limit cases of the Frenkel–Kontorova model with ac-driving is studied. The relationship is established between the average velocity of the particles and the rotation number of the orientation preserving homeomorphism on the circle induced from the Poincar{\'e} map. The dynamical behavior for both cases is determined completely by the rotation number. Numerical results are also provided for the second order system to support the theoretical conclusions.",

keywords = "Average velocity, Mode-locking, Orientation preserving homeomorphism, Overdamped Frenkel-Kontorova model, Rotation number",

author = "Bambi Hu and Wen-Xin Qin and Zhigang Zheng",

note = "Funding Information: This work is supported in part by grants from the Hong Kong Research Grants Council (RGC)and the Hong Kong Baptist University Faculty Research Grant (FRG), and in part by the Special Funds for Major State Basic Research Projects, National Natural Science Foundation of China and Natural Science Foundation of Jiangsu Province. WXQ is indebted to Prof. Oleg Braun, Dr. Lei Yang and Dr. Jasmina Teksi{\'c} for helpful discussions. ZHENG is also supported by Foundation for the Author of National Excellent Doctoral Dissertation of PR China, the TRAPOYT in Higher Education Institutions of MOE, the Fund for Doctoral Training of MOE, the Huo-Ying-Dong Educational Funds for Excellent Young Teachers, and the Hong Kong Croucher Foundation. Publisher copyright: {\textcopyright} 2005 Elsevier B.V.",

year = "2005",

month = sep,

day = "1",

doi = "10.1016/j.physd.2005.06.022",

language = "English",

volume = "208",

pages = "172--190",

journal = "Physica D: Nonlinear Phenomena",

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}

TY - JOUR

T1 - Rotation number of the overdamped Frenkel–Kontorova model with ac-driving

AU - Hu, Bambi

AU - Qin, Wen-Xin

AU - Zheng, Zhigang

N1 - Funding Information: This work is supported in part by grants from the Hong Kong Research Grants Council (RGC)and the Hong Kong Baptist University Faculty Research Grant (FRG), and in part by the Special Funds for Major State Basic Research Projects, National Natural Science Foundation of China and Natural Science Foundation of Jiangsu Province. WXQ is indebted to Prof. Oleg Braun, Dr. Lei Yang and Dr. Jasmina Teksić for helpful discussions. ZHENG is also supported by Foundation for the Author of National Excellent Doctoral Dissertation of PR China, the TRAPOYT in Higher Education Institutions of MOE, the Fund for Doctoral Training of MOE, the Huo-Ying-Dong Educational Funds for Excellent Young Teachers, and the Hong Kong Croucher Foundation. Publisher copyright: © 2005 Elsevier B.V.

PY - 2005/9/1

Y1 - 2005/9/1

N2 - The dynamical behavior of the overdamped and overdamped limit cases of the Frenkel–Kontorova model with ac-driving is studied. The relationship is established between the average velocity of the particles and the rotation number of the orientation preserving homeomorphism on the circle induced from the Poincaré map. The dynamical behavior for both cases is determined completely by the rotation number. Numerical results are also provided for the second order system to support the theoretical conclusions.

AB - The dynamical behavior of the overdamped and overdamped limit cases of the Frenkel–Kontorova model with ac-driving is studied. The relationship is established between the average velocity of the particles and the rotation number of the orientation preserving homeomorphism on the circle induced from the Poincaré map. The dynamical behavior for both cases is determined completely by the rotation number. Numerical results are also provided for the second order system to support the theoretical conclusions.

KW - Average velocity

KW - Mode-locking

KW - Orientation preserving homeomorphism

KW - Overdamped Frenkel-Kontorova model

KW - Rotation number

UR - http://www.scopus.com/inward/record.url?scp=23144444560&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.06.022

DO - 10.1016/j.physd.2005.06.022

M3 - Journal article

AN - SCOPUS:23144444560

SN - 0167-2789

VL - 208

SP - 172

EP - 190

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -

Rotation number of the overdamped Frenkel–Kontorova model with ac-driving

Abstract

Scopus Subject Areas

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