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Scaling and the thermal conductivity of the Frenkel-Kontorova model
Zhi-Gang Shao1, Lei Yang, Wei-Rong Zhong
1Department of Physics, Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
Abstract:
We have studied the dependence of the thermal conductivity kappa on the strength of the interparticle potential lambda and the strength of the external potential beta in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, kappa proportional, variantlambda;{32}/beta;{2} . This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity kappa is therefore a decreasing functon of beta and an increasing function of lambda.
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