760 research outputs found
On the anomalous thermal conductivity of one-dimensional lattices
The divergence of the thermal conductivity in the thermodynamic limit is
thoroughly investigated. The divergence law is consistently determined with two
different numerical approaches based on equilibrium and non-equilibrium
simulations. A possible explanation in the framework of linear-response theory
is also presented, which traces back the physical origin of this anomaly to the
slow diffusion of the energy of long-wavelength Fourier modes. Finally, the
results of dynamical simulations are compared with the predictions of
mode-coupling theory.Comment: 5 pages, 3 figures, to appear in Europhysics 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
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
Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs
We consider a d-dimensional crystal with an arbitrary harmonic interaction
and an anharmonic on-site potential, with stochastic Langevin heat bath at each
site. We develop an integral formalism for the correlation functions that is
suitable for the study of their relaxation (time decay) as well as their
behavior in space. Furthermore, in a perturbative analysis, for the
one-dimensional system with weak coupling between the sites and small quartic
anharmonicity, we investigate the steady state and show that the Fourier's law
holds. We also obtain an expression for the thermal conductivity (for arbitrary
next-neighbor interactions) and give the temperature profile in the steady
state
Finite thermal conductivity in 1d lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing
that it is the first example of a 1d nonlinear lattice exhibiting normal
transport properties in the absence of an on-site potential. Numerical
estimates obtained by simulating a chain in contact with two thermal baths at
different temperatures are found to be consistent with those ones based on
linear response theory. The dynamics of the Fourier modes provides direct
evidence of energy diffusion. The finiteness of the conductivity is traced back
to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis
of two variants of this model.Comment: 4 pages, 3 postscript figure
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 one-dimensional lattices with self-consistent heat baths: a heuristic derivation
We derive the thermal conductivities of one-dimensional harmonic and
anharmonic lattices with self-consistent heat baths (BRV lattice) from the
Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we
obtain the same result as previous works. However, our approach is heuristic
and reveals phonon picture explicitly within the heat transport process. The
results for harmonic and anharmonic lattices are compared with numerical
calculations from Green-Kubo formula. The consistency between derivation and
simulation strongly supports that effective (renormalized) phonons are energy
carriers in anharmonic lattices although there exist some other excitations
such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS
A Framework for Verifiable and Auditable Collaborative Anomaly Detection
Collaborative and Federated Leaning are emerging approaches to manage cooperation between a group of agents for the solution of Machine Learning tasks, with the goal of improving each agent's performance without disclosing any data. In this paper we present a novel algorithmic architecture that tackle this problem in the particular case of Anomaly Detection (or classification of rare events), a setting where typical applications often comprise data with sensible information, but where the scarcity of anomalous examples encourages collaboration. We show how Random Forests can be used as a tool for the development of accurate classifiers with an effective insight-sharing mechanism that does not break the data integrity. Moreover, we explain how the new architecture can be readily integrated in a blockchain infrastructure to ensure the verifiable and auditable execution of the algorithm. Furthermore, we discuss how this work may set the basis for a more general approach for the design of collaborative ensemble-learning methods beyond the specific task and architecture discussed in this paper
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