856 research outputs found
Rare events and scaling properties in field-induced anomalous dynamics
We show that, in a broad class of continuous time random walks (CTRW), a
small external field can turn diffusion from standard into anomalous. We
illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in
disordered and glassy materials, and in the L\'evy walk process, which
describes superdiffusion within inhomogeneous media. For both models, in the
presence of an external field, rare events induce a singular behavior in the
originally Gaussian displacements distribution, giving rise to power-law tails.
Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating
waiting times and of a drift yields a non-Gaussian distribution characterized
by long spatial tails and strong anomalous superdiffusion.Comment: 11 pages, 3 figure
Scaling properties of field-induced superdiffusion in Continous Time Random Walks
We consider a broad class of Continuous Time Random Walks with large
fluctuations effects in space and time distributions: a random walk with
trapping, describing subdiffusion in disordered and glassy materials, and a
L\'evy walk process, often used to model superdiffusive effects in
inhomogeneous materials. We derive the scaling form of the probability
distributions and the asymptotic properties of all its moments in the presence
of a field by two powerful techniques, based on matching conditions and on the
estimate of the contribution of rare events to power-law tails in a field.Comment: 17 pages, 8 figures, Proceedings of the Conference "Small system
nonequilibrium fluctuations, dynamics and stochastics, and anomalous
behavior", KITPC, Beijing, Chin
Earthworm populations in Eucalyptus spp plantation at Embrapa Forestry, Brazil (Oligochaeta).
Presented at the 6th International Oligochaete Taxonomy Meeting, Palmeira de Faro, Portugal, 2013
Transport and Scaling in Quenched 2D and 3D L\'evy Quasicrystals
We consider correlated L\'evy walks on a class of two- and three-dimensional
deterministic self-similar structures, with correlation between steps induced
by the geometrical distribution of regions, featuring different diffusion
properties. We introduce a geometric parameter , playing a role
analogous to the exponent characterizing the step-length distribution in random
systems. By a {\it single-long jump} approximation, we analytically determine
the long-time asymptotic behavior of the moments of the probability
distribution, as a function of and of the dynamic exponent
associated to the scaling length of the process. We show that our scaling
analysis also applies to experimentally relevant quantities such as escape-time
and transmission probabilities.
Extensive numerical simulations corroborate our results which, in general,
are different from those pertaining to uncorrelated L\'evy-walks models.Comment: 10 pages, 11 figures; some concepts rephrased to improve on clarity;
a few references added; symbols and line styles in some figures changed to
improve on visibilit
L\'evy walks and scaling in quenched disordered media
We study L\'evy walks in quenched disordered one-dimensional media, with
scatterers spaced according to a long-tailed distribution. By analyzing the
scaling relations for the random-walk probability and for the resistivity in
the equivalent electric problem, we obtain the asymptotic behavior of the mean
square displacement as a function of the exponent characterizing the scatterers
distribution. We demonstrate that in quenched media different average
procedures can display different asymptotic behavior. In particular, we
estimate the moments of the displacement averaged over processes starting from
scattering sites, in analogy with recent experiments. Our results are compared
with numerical simulations, with excellent agreement.Comment: Phys. Rev. E 81, 060101(R) (2010
Ground-state Properties of Small-Size Nonlinear Dynamical Lattices
We investigate the ground state of a system of interacting particles in small
nonlinear lattices with M > 2 sites, using as a prototypical example the
discrete nonlinear Schroedinger equation that has been recently used
extensively in the contexts of nonlinear optics of waveguide arrays, and
Bose-Einstein condensates in optical lattices. We find that, in the presence of
attractive interactions, the dynamical scenario relevant to the ground state
and the lowest-energy modes of such few-site nonlinear lattices reveals a
variety of nontrivial features that are absent in the large/infinite lattice
limits: the single-pulse solution and the uniform solution are found to coexist
in a finite range of the lattice intersite coupling where, depending on the
latter, one of them represents the ground state; in addition, the single-pulse
mode does not even exist beyond a critical parametric threshold. Finally, the
onset of the ground state (modulational) instability appears to be intimately
connected with a non-standard (``double transcritical'') type of bifurcation
that, to the best of our knowledge, has not been reported previously in other
physical systems.Comment: 7 pages, 4 figures; submitted to PR
L\'evy-type diffusion on one-dimensional directed Cantor Graphs
L\'evy-type walks with correlated jumps, induced by the topology of the
medium, are studied on a class of one-dimensional deterministic graphs built
from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a
standard random walk on the sets but is also allowed to move ballistically
throughout the empty regions. Using scaling relations and the mapping onto the
electric network problem, we obtain the exact values of the scaling exponents
for the asymptotic return probability, the resistivity and the mean square
displacement as a function of the topological parameters of the sets.
Interestingly, the systems undergoes a transition from superdiffusive to
diffusive behavior as a function of the filling of the fractal. The
deterministic topology also allows us to discuss the importance of the choice
of the initial condition. In particular, we demonstrate that local and average
measurements can display different asymptotic behavior. The analytic results
are compared with the numerical solution of the master equation of the process.Comment: 9 pages, 9 figure
Shot, scene and keyframe ordering for interactive video re-use
This paper presents a complete system for shot and scene detection in broadcast videos, as well as a method to select the best representative key-frames, which could be used in new interactive interfaces for accessing large collections of edited videos. The final goal is to enable an improved access to video footage and the re-use of video content with the direct management of user-selected video-clips
Microscopic energy flows in disordered Ising spin systems
An efficient microcanonical dynamics has been recently introduced for Ising
spin models embedded in a generic connected graph even in the presence of
disorder i.e. with the spin couplings chosen from a random distribution. Such a
dynamics allows a coherent definition of local temperatures also when open
boundaries are coupled to thermostats, imposing an energy flow. Within this
framework, here we introduce a consistent definition for local energy currents
and we study their dependence on the disorder. In the linear response regime,
when the global gradient between thermostats is small, we also define local
conductivities following a Fourier dicretized picture. Then, we work out a
linearized "mean-field approximation", where local conductivities are supposed
to depend on local couplings and temperatures only. We compare the approximated
currents with the exact results of the nonlinear system, showing the
reliability range of the mean-field approach, which proves very good at high
temperatures and not so efficient in the critical region. In the numerical
studies we focus on the disordered cylinder but our results could be extended
to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure
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