2,390 research outputs found
Collective behavior of heterogeneous neural networks
We investigate a network of integrate-and-fire neurons characterized by a
distribution of spiking frequencies. Upon increasing the coupling strength, the
model exhibits a transition from an asynchronous regime to a nontrivial
collective behavior. At variance with the Kuramoto model, (i) the macroscopic
dynamics is irregular even in the thermodynamic limit, and (ii) the microscopic
(single-neuron) evolution is linearly stable.Comment: 4 pages, 5 figure
From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
The evolution of infinitesimal, localized perturbations is investigated in a
one-dimensional diatomic gas of hard-point particles (HPG) and thereby
connected to energy diffusion. As a result, a Levy walk description, which was
so far invoked to explain anomalous heat conductivity in the context of
non-interacting particles is here shown to extend to the general case of truly
many-body systems. Our approach does not only provide a firm evidence that
energy diffusion is anomalous in the HPG, but proves definitely superior to
direct methods for estimating the divergence rate of heat conductivity which
turns out to be , in perfect agreement with the dynamical
renormalization--group prediction (1/3).Comment: 4 pages, 3 figure
Time evolution of wave-packets in quasi-1D disordered media
We have investigated numerically the quantum evolution of a wave-packet in a
quenched disordered medium described by a tight-binding Hamiltonian with
long-range hopping (band random matrix approach). We have obtained clean data
for the scaling properties in time and in the bandwidth b of the packet width
and its fluctuations with respect to disorder realizations. We confirm that the
fluctuations of the packet width in the steady-state show an anomalous scaling
and we give a new estimate of the anomalous scaling exponent. This anomalous
behaviour is related to the presence of non-Gaussian tails in the distribution
of the packet width. Finally, we have analysed the steady state probability
profile and we have found finite band corrections of order 1/b with respect to
the theoretical formula derived by Zhirov in the limit of infinite bandwidth.
In a neighbourhood of the origin, however, the corrections are .Comment: 19 pages, 9 Encapsulated Postscript figures; submitted to ``European
Physical Journal B'
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
Collective chaos in pulse-coupled neural networks
We study the dynamics of two symmetrically coupled populations of identical
leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon
varying the coupling strength, we find symmetry-breaking transitions that lead
to the onset of various chimera states as well as to a new regime, where the
two populations are characterized by a different degree of synchronization.
Symmetric collective states of increasing dynamical complexity are also
observed. The computation of the the finite-amplitude Lyapunov exponent allows
us to establish the chaoticity of the (collective) dynamics in a finite region
of the phase plane. The further numerical study of the standard Lyapunov
spectrum reveals the presence of several positive exponents, indicating that
the microscopic dynamics is high-dimensional.Comment: 6 pages, 5 eps figures, to appear on Europhysics Letters in 201
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
Dipolar ground state of planar spins on triangular lattices
An infinite triangular lattice of classical dipolar spins is usually
considered to have a ferromagnetic ground state. We examine the validity of
this statement for finite lattices and in the limit of large lattices. We find
that the ground state of rectangular arrays is strongly dependent on size and
aspect ratio. Three results emerge that are significant for understanding the
ground state properties: i) formation of domain walls is energetically favored
for aspect ratios below a critical valu e; ii) the vortex state is always
energetically favored in the thermodynamic limit of an infinite number of
spins, but nevertheless such a configuration may not be observed even in very
large lattices if the aspect ratio is large; iii) finite range approximations
to actual dipole sums may not provide the correct ground sta te configuration
because the ferromagnetic state is linearly unstable and the domain wall energy
is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as
a Rapid Communication in Phys. Rev.
Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation
We consider the growth of a vicinal crystal surface in the presence of a
step-edge barrier. For any value of the barrier strength, measured by the
length l_es, nucleation of islands on terraces is always able to destroy
asymptotically step-flow growth. The breakdown of the metastable step-flow
occurs through the formation of a mound of critical width proportional to
L_c=1/sqrt(l_es), the length associated to the linear instability of a
high-symmetry surface. The time required for the destabilization grows
exponentially with L_c. Thermal detachment from steps or islands, or a steeper
slope increase the instability time but do not modify the above picture, nor
change L_c significantly. Standard continuum theories cannot be used to
evaluate the activation energy of the critical mound and the instability time.
The dynamics of a mound can be described as a one dimensional random walk for
its height k: attaining the critical height (i.e. the critical size) means that
the probability to grow (k->k+1) becomes larger than the probability for the
mound to shrink (k->k-1). Thermal detachment induces correlations in the random
walk, otherwise absent.Comment: 10 pages. Minor changes. Accepted for publication in Phys. Rev.
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
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