428 research outputs found
Entropy potential and Lyapunov exponents
According to a previous conjecture, spatial and temporal Lyapunov exponents
of chaotic extended systems can be obtained from derivatives of a suitable
function: the entropy potential. The validity and the consequences of this
hypothesis are explored in detail. The numerical investigation of a
continuous-time model provides a further confirmation to the existence of the
entropy potential. Furthermore, it is shown that the knowledge of the entropy
potential allows determining also Lyapunov spectra in general reference frames
where the time-like and space-like axes point along generic directions in the
space-time plane. Finally, the existence of an entropy potential implies that
the integrated density of positive exponents (Kolmogorov-Sinai entropy) is
independent of the chosen reference frame.Comment: 20 pages, latex, 8 figures, submitted to CHAO
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-size effects on the Hamiltonian dynamics of the XY-model
The dynamical properties of the finite-size magnetization M in the critical
region T<T_{KTB} of the planar rotor model on a L x L square lattice are
analyzed by means of microcanonical simulations . The behavior of the q=0
structure factor at high frequencies is consistent with field-theoretical
results, but new additional features occur at lower frequencies. The motion of
M determines a region of spectral lines and the presence of a central peak,
which we attribute to phase diffusion. Near T_{KTB} the diffusion constant
scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter
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
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
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 simulation study of energy transport in the Hamiltonian XY-model
The transport properties of the planar rotator model on a square lattice are
analyzed by means of microcanonical and non--equilibrium simulations. Well
below the Kosterlitz--Thouless--Berezinskii transition temperature, both
approaches consistently indicate that the energy current autocorrelation
displays a long--time tail decaying as t^{-1}. This yields a thermal
conductivity coefficient which diverges logarithmically with the lattice size.
Conversely, conductivity is found to be finite in the high--temperature
disordered phase. Simulations close to the transition temperature are insted
limited by slow convergence that is presumably due to the slow kinetics of
vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen
A stochastic model of anomalous heat transport: analytical solution of the steady state
We consider a one-dimensional harmonic crystal with conservative noise, in
contact with two stochastic Langevin heat baths at different temperatures. The
noise term consists of collisions between neighbouring oscillators that
exchange their momenta, with a rate . The stationary equations for the
covariance matrix are exactly solved in the thermodynamic limit ().
In particular, we derive an analytical expression for the temperature profile,
which turns out to be independent of . Moreover, we obtain an exact
expression for the leading term of the energy current, which scales as
. Our theoretical results are finally found to be consistent
with the numerical solutions of the covariance matrix for finite .Comment: Minor changes in the text. To appear in Journal of Physics
Nonequilibrium Invariant Measure under Heat Flow
We provide an explicit representation of the nonequilibrium invariant measure
for a chain of harmonic oscillators with conservative noise in the presence of
stationary heat flow. By first determining the covariance matrix, we are able
to express the measure as the product of Gaussian distributions aligned along
some collective modes that are spatially localized with power-law tails.
Numerical studies show that such a representation applies also to a purely
deterministic model, the quartic Fermi-Pasta-Ulam chain
Spatial Relationship of Signatures of Interplanetary Coronal Mass Ejections
Interplanetary coronal mass ejections (ICMEs) are characterized by a number of signatures. In particular, we examine the relationship between Fe charge states and other signatures during ICMEs in solar cycle 23. Though enhanced Fe charge states characterize many ICMEs, average charge states vary from event to event, are more likely to be enhanced in faster or flare‐related ICMEs, and do not appear to depend on whether the ICME is a magnetic cloud. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87650/2/681_1.pd
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