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Phonon relaxation and heat conduction in one-dimensional Fermi–Pasta–Ulam β lattices by molecular dynamics simulations |
| Hou Quan-Wen(侯泉文)a)b) and Cao Bing-Yang(曹炳阳)a)† |
a Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China; b Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072, China
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Abstract 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 autocorrelation 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 k1.688, which leads to a N0.41 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 N2/5 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.
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Received: 12 June 2011
Revised: 13 September 2011
Accepted manuscript online:
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PACS:
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44.10.+i
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(Heat conduction)
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63.22.-m
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(Phonons or vibrational states in low-dimensional structures and nanoscale materials)
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66.25.+g
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(Thermal conduction in nonmetallic liquids)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 50976052, 51136001, and 50730006), the Program for New Century Excellent Talents in University, China, the Tsinghua University Initiative Scientific Research Program, China, |
Cite this article:
Hou Quan-Wen(侯泉文) and Cao Bing-Yang(曹炳阳) Phonon relaxation and heat conduction in one-dimensional Fermi–Pasta–Ulam β lattices by molecular dynamics simulations 2012 Chin. Phys. B 21 014401
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