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Phonon relaxation and heat conduction in one-dimensional Fermi Pasta Ulam β lattices by molecular dynamics simulations

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Chinese Physics B 2012年第1期21卷 279-283页

作者： Hou Quan-Wen Cao Bing-Yang Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Engineering MechanicsTsinghua UniversityBeijing 100084China Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education Department of Applied PhysicsNorthwestern Polytechnical UniversityXi’an 710072China

The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.

关键词： thermal conductivity phonon relaxation low-dimensional heat conduction FermiPasta Ulam (FPU) Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education Department of Applied Physics Northwestern Polytechnical University Xi'an 710072 China lattice

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Propagation dynamics on the Fermi-Pasta-Ulam lattices

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Frontiers of physics 2013年第3期8卷 349-355页

作者： Zong-Qiang Yuan Zhi-Gang Zheng Department of Physics and the Beijing Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing) Beijing Normal University Beijing 100875 China

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate co- herently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta Ulam lattice.

关键词： Fermi-Past-Ulam model solitary wave low-dimensional heat conduction

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