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Comparative Study of Simulation of Temperature Rise in Ring Main Unit
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Published on: July 5, 2024

Heat conduction in two-dimensional disk models.

Daxing Xiong1, Jiao Wang, Yong Zhang

  • 1Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study explores heat conduction in 2D disk models. For momentum-conserving systems, thermal conductivity shows logarithmic dependence on system size, while non-conserving systems reach a finite value.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Heat conduction in low-dimensional systems is crucial for understanding thermal transport.
  • Previous studies often used rectangular models, lacking unambiguous 2D dimensionality.
  • Disk models offer a clear two-dimensional geometry for heat conduction studies.

Purpose of the Study:

  • Investigate heat conduction in 2D disk lattice models with concentric heat baths.
  • Analyze thermal conductivity in both momentum-conserving and non-conserving systems.
  • Compare disk models to previous rectangular models for heat conduction analysis.

Main Methods:

  • Utilized two-dimensional (2D) lattice models of disk shape.
  • Incorporated two concentric circular heat baths with radii r1 and r2.
  • Considered Fermi-Pasta-Ulam (FPU) beta model (momentum conserving) and the phi4 system (nonconserving).

Main Results:

  • In FPU beta systems, thermal conductivity (κ) exhibits a logarithmic dependence on system size (L), κ∼(ln L)α, where α is a function of r1/r2.
  • For r1/r2 approaching 1, α approaches 1, indicating a pure logarithmic dependence.
  • In the phi4 system, thermal conductivity converges to a finite value as system size increases.

Conclusions:

  • Disk models provide a clear 2D framework for studying heat conduction.
  • Momentum conservation significantly influences thermal transport behavior in these models.
  • The observed logarithmic dependence in FPU systems aligns with theoretical predictions.