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Heat conduction in the nonlinear response regime: Negative differential thermal resistance

Heat conduction in the nonlinear response regime: Negative differential thermal resistance. Dahai HE. Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University. TIENCS @Singapore 2010.

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Heat conduction in the nonlinear response regime: Negative differential thermal resistance

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  1. Heat conduction in the nonlinear response regime: Negative differential thermal resistance Dahai HE Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University TIENCS @Singapore 2010

  2. Transport processes: Linear response j – generalized flux F – generalized force μ– transport coefficient e.g., Fick’s law for mass transport, Newton’s law for shear stress transport, Fourier’s law for heat transport, Ohm’s law for electronic transport. Onsager Kubo

  3. Transport processes: Nonlinear response Heat conduction in nonlinear response regime: • Temperature profile: non-uniform local temperature gradient. • Deviation from the linear law: Negative differential thermal resistance (NDTR) may occur. NDTR:heat flux decreases as the temperature difference increases

  4. Negative Differential Resistance in Electronic Transport Typical I/V curve of the tunneling diode L. Esaki, Phys. Rev. 109, 603 (1958) http://en.wikipedia.org/wiki/File:Negative_differential_resistance.png

  5. NDTR in Thermal Diode TL TR B. Hu et al., PRE 74, 060101 (2006) B. Li et al., PRL 93, 184301 (2004) Negative differential thermal resistance (NDTR)

  6. NDTR in Thermal transistor B. Li et al., APL 88, 143501 (2006)

  7. As decreases, increases but decreases. The origin of NDTR is from the competition between the growing external thermal force and the decreasing thermal boundary conductance. Mechanism of NDTR in Weakly-Coupled Chains D. He, et al, Phys. Rev. B 80, 104302 (2009) Thermal boundary conductance

  8. T+ T- Model D. He, et al, Phys. Rev. E 81, 041131 (2010)

  9. A. FK model

  10. FK model: NDTR NDTR http://en.wikipedia.org/wiki/File:Negative_differential_resistance.png

  11. FK model: Nonlinearity effect

  12. FK model: Size effect Shrinkage of the NDTR regime for increasing N

  13. B. Φ4 model

  14. Φ4model: Nonlinearity effect

  15. Φ4model: Size effect

  16. Φ4 model: Saturation of heat current Heat current Scaled temperature profile

  17. Question • Why does heat current saturate at large temperature difference for the Ф4 model? • How to characterize the disappearing of NDTR as the system size increases?

  18. Continuum limit K. Aoki and D. Kusnezov, Phys.Lett. A265,250 (2000) Assume:

  19. Phenomenological analysis

  20. Phenomenological analysis NDTR: N<N*

  21. C. FPU-βmodel

  22. FPU-β model: Nonlinearity effect Z. Rieder, et al, J. Math. Phys. 8, 1073 (1967)

  23. FPU-βmodel: Size effect

  24. Conclusion • NDTR can occur in a structurally homogeneous system, which shows that spatial asymmetry is not a necessary condition for NDTR. • Nonlinearityof the onsite potential is imperative to the occurrence of NDTR. A threshold of the nonlinearity for the exhibition of NDTR is numerically shown. • Occurrence of NDTR: FK and Φ4 (  ); FPU-β() • NDTR regime generally becomes smaller as the system size increases. • Phenomenological analysis is provided to characterize the size-induced crossover from NDTR to PDTR.

  25. Thank You 

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