1,788 research outputs found
Cooling nonlinear lattices toward localisation
We describe the energy relaxation process produced by surface damping on
lattices of classical anharmonic oscillators. Spontaneous emergence of
localised vibrations dramatically slows down dissipation and gives rise to
quasi-stationary states where energy is trapped in the form of a gas of weakly
interacting discrete breathers. In one dimension (1D), strong enough on--site
coupling may yield stretched--exponential relaxation which is reminiscent of
glassy dynamics. We illustrate the mechanism generating localised structures
and discuss the crucial role of the boundary conditions. For two--dimensional
(2D) lattices, the existence of a gap in the breather spectrum causes the
localisation process to become activated. A statistical analysis of the
resulting quasi-stationary state through the distribution of breathers'
energies yield information on their effective interactions.Comment: 10 pages, 11 figure
Slow energy relaxation and localization in 1D lattices
We investigate the energy relaxation process produced by thermal baths at
zero temperature acting on the boundary atoms of chains of classical anharmonic
oscillators. Time-dependent perturbation theory allows us to obtain an explicit
solution of the harmonic problem: even in such a simple system nontrivial
features emerge from the interplay of the different decay rates of Fourier
modes. In particular, a crossover from an exponential to an inverse-square-root
law occurs on a time scale proportional to the system size . A further
crossover back to an exponential law is observed only at much longer times (of
the order ). In the nonlinear chain, the relaxation process is initially
equivalent to the harmonic case over a wide time span, as illustrated by
simulations of the Fermi-Pasta-Ulam model. The distinctive feature is
that the second crossover is not observed due to the spontaneous appearance of
breathers, i.e. space-localized time-periodic solutions, that keep a finite
residual energy in the lattice. We discuss the mechanism yielding such
solutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure
Coupled transport in rotor models
Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.Peer reviewedPublisher PD
Energy diffusion in hard-point systems
We investigate the diffusive properties of energy fluctuations in a
one-dimensional diatomic chain of hard-point particles interacting through a
square--well potential. The evolution of initially localized infinitesimal and
finite perturbations is numerically investigated for different density values.
All cases belong to the same universality class which can be also interpreted
as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit
is nevertheless exceptional in that normal diffusion is found in tangent space
and yet anomalous diffusion with a different rate for perturbations of finite
amplitude. The different behaviour of the two classes of perturbations is
traced back to the "stable chaos" type of dynamics exhibited by this model.
Finally, the effect of an additional internal degree of freedom is
investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure
Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
We explore the statistical behavior of the discrete nonlinear Schroedinger
equation. We find a parameter region where the system evolves towards a state
characterized by a finite density of breathers and a negative temperature. Such
a state is metastable but the convergence to equilibrium occurs on astronomical
time scales and becomes increasingly slower as a result of a coarsening
processes. Stationary negative-temperature states can be experimentally
generated via boundary dissipation or from free expansions of wave packets
initially at positive temperature equilibrium.Comment: 4 pages, 5 figure
Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
We study heat transport in a chain of harmonic oscillators with random
elastic collisions between nearest-neighbours. The equations of motion of the
covariance matrix are numerically solved for free and fixed boundary
conditions. In the thermodynamic limit, the shape of the temperature profile
and the value of the stationary heat flux depend on the choice of boundary
conditions. For free boundary conditions, they also depend on the coupling
strength with the heat baths. Moreover, we find a strong violation of local
equilibrium at the chain edges that determine two boundary layers of size
(where is the chain length), that are characterized by a
different scaling behaviour from the bulk. Finally, we investigate the
relaxation towards the stationary state, finding two long time scales: the
first corresponds to the relaxation of the hydrodynamic modes; the second is a
manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
Looking for a simple Big Five factorial structure in the domain of adjectives.
The Big Five factors structure is currently the benchmark for personality dimensions. In the domain of adjectives, various instruments have been developed to measure the Big Five. In this contribution the authors propose a methodology to find a simple factorial structure and apply this methodology to the domain of Big Five as measured by adjectives. Using data collected on a sample of 337 Ss (mean age 21.69 yrs), a five-factor benchmark structure is proposed derived from the 50 best marker adjectives selected among the adjectives contained in three instruments specifically developed to measure the Big Five (i.e., L. R. Goldberg's 100 adjectives list, IASR-B5, and SACBIF (1992)). They use this common factor structure (or benchmark structure) to investigate the differences and the similarities between the three operationalizations of the Big Five, and to investigate the placements of the full set of adjectives contained in the three instruments. The main features of the proposed methodology and the generalizability of the obtained results are discussed
Geometric dynamical observables in rare gas crystals
We present a detailed description of how a differential geometric approach to
Hamiltonian dynamics can be used for determining the existence of a crossover
between different dynamical regimes in a realistic system, a model of a rare
gas solid. Such a geometric approach allows to locate the energy threshold
between weakly and strongly chaotic regimes, and to estimate the largest
Lyapunov exponent. We show how standard mehods of classical statistical
mechanics, i.e. Monte Carlo simulations, can be used for our computational
purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The
value of the energy threshold turns out to be in excellent agreement with the
numerical estimate based on the crossover between slow and fast relaxation to
equilibrium obtained in a previous work by molecular dynamics simulations.Comment: RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev.
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.
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