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Bunimovich, Leonid; Khlabystova, Milena A.

doi:10.1023/a:1024623827182

Cited by 6 publications

(1 citation statement)

References 5 publications

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“…The analytic solution in Ref. 29 presents a similar conclusion in one-dimensional Lorentz gas with rotating scatterers. It is helpful to illustrate the dynamical characteristics determined by the dimensionless moment of inertia η by plotting the Poincaré surface of the section.…”

Section: The Dynamics Of the Systemsupporting

confidence: 54%

Heat Conduction in Homogeneous and Heterogeneous Billiard Systems

Mao

Deng

2008

Int. J. Mod. Phys. B

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We investigate the heat conduction in a modified Lorentz gas with freely rotating disks periodically placed along one-dimensional channel. The heat conductivity is dependent on the moment of inertia η of the disks, with a power-law decay when η > 1. By plotting the Poincaré surface of the section, we observe a contraction of phase space over the range of η > 1, which is sensitive to the initial condition. We find that the power-law decay of the heat conductivity is relevant to the mixing phase space. As a possible application, we model the heterostructure by connecting the segments of different η, and predict the analytical results of the temperature profiles and the heat conductivity, which are in good agreement with the numerical ones.

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Section: The Dynamics Of the Systemsupporting

confidence: 54%

Heat Conduction in Homogeneous and Heterogeneous Billiard Systems

Mao

Deng

2008

Int. J. Mod. Phys. B

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Rotor Interaction in the Annulus Billiard

Bálint¹,

Troubetzkoy²

2004

Journal of Statistical Physics

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Superdiffusive Heat Transport in a Class of Deterministic One-dimensional Many-Particle Lorentz Gases

2009

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We study heat transport in a one-dimensional chain of a finite number N of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper, [1], a spatially continuous version of this model was derived in a scaling regime where the scattering probability of the tracers is γ ∼ 1/N , corresponding to the Grad limit. A Boltzmann type equation describing the transport of heat was obtained. In this paper, we show numerically that the Boltzmann description obtained in [1] is indeed a bona fide limit of the particle model. Furthermore, we also study the heat transport of the model when the scattering probability is one, corresponding to deterministic dynamics. At a coarse grained level the model behaves as a persistent random walker with a broad waiting time distribution and strong correlations associated to the deterministic scattering. We show, that, in spite of the absence of global conserved quantities, the model leads to a superdiffusive heat transport.

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Cited by 6 publications

References 5 publications

Heat Conduction in Homogeneous and Heterogeneous Billiard Systems

Heat Conduction in Homogeneous and Heterogeneous Billiard Systems

Rotor Interaction in the Annulus Billiard

Superdiffusive Heat Transport in a Class of Deterministic One-dimensional Many-Particle Lorentz Gases

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