1,101 research outputs found
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
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
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
Asymmetric Wave Propagation in Nonlinear Systems
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As
a reference system, we consider a layered nonlinear, non mirror-symmetric model
described by the one-dimensional Discrete Nonlinear Schreodinger equation with
spatially varying coefficients embedded in an otherwise linear lattice. We
construct a class of exact extended solutions such that waves with the same
frequency and incident amplitude impinging from left and right directions have
very different transmission coefficients. This effect arises already for the
simplest case of two nonlinear layers and is associated with the shift of
nonlinear resonances. Increasing the number of layers considerably increases
the complexity of the family of solutions. Finally, numerical simulations of
asymmetric wavepacket transmission are presented which beautifully display the
rectifying effect
Relaxation of classical many-body hamiltonians in one dimension
The relaxation of Fourier modes of hamiltonian chains close to equilibrium is
studied in the framework of a simple mode-coupling theory. Explicit estimates
of the dependence of relevant time scales on the energy density (or
temperature) and on the wavenumber of the initial excitation are given. They
are in agreement with previous numerical findings on the approach to
equilibrium and turn out to be also useful in the qualitative interpretation of
them. The theory is compared with molecular dynamics results in the case of the
quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.
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.
The rate of CD4 decline as a determinant of progression to AIDS independent of the most recent CD4 count
The data of two cohort studies of HIV-infected individuals were used to examine whether the rate of CD4 decline is a determinant of HIV progression, independent of the most recent CD4 count. Time from seroconversion to clinical AIDS was the main outcome measure. Rates of CD4 decline were estimated using the ordinary least squares regression method. AIDS incidences were compared in individuals who had previously experienced either a steeper or a less steep rate of CD4 decline. Cox proportional hazards model including a time-dependent covariate for the rate of CD4 decline was performed. The rate of prior CD4 decline was significantly associated with the risk of developing AIDS independently from the most recent CD4 count, with a 2 % increase in hazard of AIDS (P < 0.01) for a difference of 10 cells/mm(3) in the estimated yearly drop in CD4 count. This finding gives scientific credit to the belief that individuals with a prior steeper CD4 decline consistently have a higher subsequent risk of developing AIDS than those with a less steep prior decline
Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension
We consider the long time, large scale behavior of the Wigner transform
W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation
on a 1-d integer lattice, with a weak multiplicative noise. This model has been
introduced in Basile, Bernardin, and Olla to describe a system of interacting
linear oscillators with a weak noise that conserves locally the kinetic energy
and the momentum. The kinetic limit for the Wigner transform has been shown in
Basile, Olla, and Spohn. In the present paper we prove that in the unpinned
case there exists such that for any the
weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1,
satisfies a one dimensional fractional heat equation with . In the pinned case an analogous
result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the
limit satisfies then the usual heat equation
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