292 research outputs found
From a kinetic equation to a diffusion under an anomalous scaling
A linear Boltzmann equation is interpreted as the forward equation for the
probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t))
is an autonomous reversible jump process, with waiting times between two jumps
with finite expectation value but infinite variance, and Y(t) is an additive
functional of K(t). We prove that under an anomalous rescaling Y converges in
distribution to a two-dimensional Brownian motion. As a consequence, the
appropriately rescaled solution of the Boltzmann equation converges to a
diffusion equation
On the universality of anomalous one-dimensional heat conductivity
In one and two dimensions, transport coefficients may diverge in the
thermodynamic limit due to long--time correlation of the corresponding
currents. The effective asymptotic behaviour is addressed with reference to the
problem of heat transport in 1d crystals, modeled by chains of classical
nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium
numerical simulations confirm that the finite-size thermal conductivity
diverges with the system size as . However, the
exponent deviates systematically from the theoretical prediction
proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev.
Lett. {\bf 89}, 200601 (2002)].Comment: 4 pages, submitted to Phys.Rev.
Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices
Heat conduction in three-dimensional nonlinear lattices is investigated using
a particle dynamics simulation. The system is a simple three-dimensional
extension of the Fermi-Pasta-Ulam (FPU-) nonlinear lattices, in
which the interparticle potential has a biquadratic term together with a
harmonic term. The system size is , and the heat is made to
flow in the direction the Nose-Hoover method. Although a linear
temperature profile is realized, the ratio of enerfy flux to temperature
gradient shows logarithmic divergence with . The autocorrelation function of
energy flux is observed to show power-law decay as ,
which is slower than the decay in conventional momentum-cnserving
three-dimensional systems (). Similar behavior is also observed in
the four dimensional system.Comment: 4 pages, 5 figures. Accepted for publication in J. Phys. Soc. Japan
Letter
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
A simple one-dimensional model of heat conduction which obeys Fourier's law
We present the computer simulation results of a chain of hard point particles
with alternating masses interacting on its extremes with two thermal baths at
different temperatures. We found that the system obeys Fourier's law at the
thermodynamic limit. This result is against the actual belief that one
dimensional systems with momentum conservative dynamics and nonzero pressure
have infinite thermal conductivity. It seems that thermal resistivity occurs in
our system due to a cooperative behavior in which light particles tend to
absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR
Thermal conductivity of the Toda lattice with conservative noise
We study the thermal conductivity of the one dimensional Toda lattice
perturbed by a stochastic dynamics preserving energy and momentum. The strength
of the stochastic noise is controlled by a parameter . We show that
heat transport is anomalous, and that the thermal conductivity diverges with
the length of the chain according to , with . In particular, the ballistic heat conduction of the
unperturbed Toda chain is destroyed. Besides, the exponent of the
divergence depends on
Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier
We address the problem of heat conduction in 1-D nonlinear chains; we show
that, acting on the parameter which controls the strength of the on site
potential inside a segment of the chain, we induce a transition from conducting
to insulating behavior in the whole system. Quite remarkably, the same
transition can be observed by increasing the temperatures of the thermal baths
at both ends of the chain by the same amount. The control of heat conduction by
nonlinearity opens the possibility to propose new devices such as a thermal
rectifier.Comment: 4 pages with figures included. Phys. Rev. Lett., to be published
(Ref. [10] corrected
Correlations and scaling in one-dimensional heat conduction
We examine numerically the full spatio-temporal correlation functions for all
hydrodynamic quantities for the random collision model introduced recently. The
autocorrelation function of the heat current, through the Kubo formula, gives a
thermal conductivity exponent of 1/3 in agreement with the analytical
prediction and previous numerical work. Remarkably, this result depends
crucially on the choice of boundary conditions: for periodic boundary
conditions (as opposed to open boundary conditions with heat baths) the
exponent is approximately 1/2. This is expected to be a generic feature of
systems with singular transport coefficients. All primitive hydrodynamic
quantities scale with the dynamic critical exponent predicted analytically.Comment: 7 pages, 11 figure
Fermi-Pasta-Ulam lattice: Peierls equation and anomalous heat conductivity
The Peierls equation is considered for the Fermi-Pasta-Ulam lattice.
Explicit form of the linearized collision operator is obtained. Using this form
the decay rate of the normal mode energy as a function of wave vector is
estimated to be proportional to . This leads to the long
time behavior of the current correlation function, and, therefore, to the
divergent coefficient of heat conductivity. These results are in good agreement
with the results of recent computer simulations. Compared to the results
obtained though the mode coupling theory our estimations give the same
dependence of the decay rate but a different temperature dependence. Using our
estimations we argue that adding a harmonic on-site potential to the
Fermi-Pasta-Ulam lattice may lead to finite heat conductivity in this
model.Comment: 6 pages, revised manuscript, to appear in Phys.Rev.
Heat conduction in 1D lattices with on-site potential
The process of heat conduction in one-dimensional lattice with on-site
potential is studied by means of numerical simulation. Using discrete
Frenkel-Kontorova, --4 and sinh-Gordon we demonstrate that contrary to
previously expressed opinions the sole anharmonicity of the on-site potential
is insufficient to ensure the normal heat conductivity in these systems. The
character of the heat conduction is determined by the spectrum of nonlinear
excitations peculiar for every given model and therefore depends on the
concrete potential shape and temperature of the lattice. The reason is that the
peculiarities of the nonlinear excitations and their interactions prescribe the
energy scattering mechanism in each model. For models sin-Gordon and --4
phonons are scattered at thermalized lattice of topological solitons; for
sinh-Gordon and --4 - models the phonons are scattered at localized
high-frequency breathers (in the case of --4 the scattering mechanism
switches with the growth of the temperature).Comment: 26 pages, 18 figure
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