704 research outputs found
Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
The pioneering computer simulations of the energy relaxation mechanisms
performed by Fermi, Pasta and Ulam can be considered as the first attempt of
understanding energy relaxation and thus heat conduction in lattices of
nonlinear oscillators. In this paper we describe the most recent achievements
about the divergence of heat conductivity with the system size in 1d and 2d
FPU-like lattices. The anomalous behavior is particularly evident at low
energies, where it is enhanced by the quasi-harmonic character of the lattice
dynamics. Remakably, anomalies persist also in the strongly chaotic region
where long--time tails develop in the current autocorrelation function. A modal
analysis of the 1d case is also presented in order to gain further insight
about the role played by boundary conditions.Comment: Invited article to appear in the Chaos focus issue on "Studies of
Nonlinear Problems. I" by Enrico Fermi, John Pasta, and Stanislaw Ulam
Desynchronization in diluted neural networks
The dynamical behaviour of a weakly diluted fully-inhibitory network of
pulse-coupled spiking neurons is investigated. Upon increasing the coupling
strength, a transition from regular to stochastic-like regime is observed. In
the weak-coupling phase, a periodic dynamics is rapidly approached, with all
neurons firing with the same rate and mutually phase-locked. The
strong-coupling phase is characterized by an irregular pattern, even though the
maximum Lyapunov exponent is negative. The paradox is solved by drawing an
analogy with the phenomenon of ``stable chaos'', i.e. by observing that the
stochastic-like behaviour is "limited" to a an exponentially long (with the
system size) transient. Remarkably, the transient dynamics turns out to be
stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.
Self-Consistent Mode-Coupling Approach to 1D Heat Transport
In the present Letter we present an analytical and numerical solution of the
self-consistent mode-coupling equations for the problem of heat conductivity in
one-dimensional systems. Such a solution leads us to propose a different
scenario to accomodate the known results obtained so far for this problem. More
precisely, we conjecture that the universality class is determined by the
leading order of the nonlinear interaction potential. Moreover, our analysis
allows us determining the memory kernel, whose expression puts on a more firm
basis the previously conjectured connection between anomalous heat conductivity
and anomalous diffusion.Comment: Submitted to Physical Review
Structure factor and dynamics of the helix-coil transition
Thermodynamical properties of the helix-coil transition were successfully
described in the past by the model of Lifson, Poland and Sheraga. Here we
compute the corresponding structure factor and show that it possesses a
universal scaling behavior near the transition point, even when the transition
is of first order. Moreover, we introduce a dynamical version of this model,
that we solve numerically. A Langevin equation is also proposed to describe the
dynamics of the density of hydrogen bonds. Analytical solution of this equation
shows dynamical scaling near the critical temperature and predicts a gelation
phenomenon above the critical temperature. In the case when comparison of the
two dynamical approaches is possible, the predictions of our phenomenological
theory agree with the results of the Monte Carlo simulations.Comment: 11 pages, 7 figure
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
Anomalous kinetics and transport from 1D self--consistent mode--coupling theory
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D)
many-particle systems as described by self-consistent mode-coupling theory. The
corresponding nonlinear integro-differential equations for the relevant
correlators are solved analytically and checked numerically. In particular, we
find that the memory functions exhibit a power-law decay accompanied by
relatively fast oscillations. Furthermore, the scaling behaviour and,
correspondingly, the universality class depends on the order of the leading
nonlinear term. In the cubic case, both viscosity and thermal conductivity
diverge in the thermodynamic limit. In the quartic case, a faster decay of the
memory functions leads to a finite viscosity, while thermal conductivity
exhibits an even faster divergence. Finally, our analysis puts on a more firm
basis the previously conjectured connection between anomalous heat conductivity
and anomalous diffusion
Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators
The largest Lyapunov exponent of a system composed by a heavy impurity
embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators
is numerically computed for various values of the impurity mass . A
crossover between weak and strong chaos is obtained at the same value
of the energy density (energy per degree of freedom)
for all the considered values of the impurity mass . The threshold \epsi
lon_{_T} coincides with the value of the energy density at which a
change of scaling of the relaxation time of the momentum autocorrelation
function of the impurity ocurrs and that was obtained in a previous work ~[M.
Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete
Lyapunov spectrum does not depend significantly on the impurity mass . These
results suggest that the impurity does not contribute significantly to the
dynamical instability (chaos) of the chain and can be considered as a probe for
the dynamics of the system to which the impurity is coupled. Finally, it is
shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak
to strong chaos at the same value of the energy density that the crossover
value of largest Lyapunov exponent. Implications of this result
are discussed.Comment: 6 pages, 5 figures, revtex4 styl
Large Deviation Approach to the Randomly Forced Navier-Stokes Equation
The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. By virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. Moreover, an explicit
expression of the prefactor of the scaling law is obtained.Comment: 24 page
Dimension dependent energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. We study the existence of energy thresholds for discrete breathers,
i.e., the question whether, in a certain system, discrete breathers of
arbitrarily low energy exist, or a threshold has to be overcome in order to
excite a discrete breather. Breather energies are found to have a positive
lower bound if the lattice dimension d is greater than or equal to a certain
critical value d_c, whereas no energy threshold is observed for d<d_c. The
critical dimension d_c is system dependent and can be computed explicitly,
taking on values between zero and infinity. Three classes of Hamiltonian
systems are distinguished, being characterized by different mechanisms
effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure
Breathers on lattices with long range interaction
We analyze the properties of breathers (time periodic spatially localized
solutions) on chains in the presence of algebraically decaying interactions
. We find that the spatial decay of a breather shows a crossover from
exponential (short distances) to algebraic (large distances) decay. We
calculate the crossover distance as a function of and the energy of the
breather. Next we show that the results on energy thresholds obtained for short
range interactions remain valid for and that for (anomalous
dispersion at the band edge) nonzero thresholds occur for cases where the short
range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199
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