9,698 research outputs found
Analysis of Relaxation Time in Random Walk with Jumps
We study the relaxation time in the random walk with jumps. The random walk
with jumps combines random walk based sampling with uniform node sampling and
improves the performance of network analysis and learning tasks. We derive
various conditions under which the relaxation time decreases with the
introduction of jumps.Comment: 13 page
Analysis of Relaxation Time in Random Walk with Jumps
International audienceWe study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various conditions under which the relaxation time decreases with the introduction of jumps
Particle jumps in structural glasses
Particles in structural glasses rattle around temporary equilibriumpositions,
that seldom change through a process which is much faster than the relaxation
time, known as particle jump. Since the relaxation of the system is due to the
accumulation of many such jumps, it could be possible to connect the single
particle short time motion to the macroscopic relaxation by understanding the
features of the jump dynamics. Here we review recent results in this research
direction, clarifying the features of particles jumps that have been understood
and those that are still under investigation, and examining the role of
particle jumps in different theories of the glass transition.Comment: 10 pages, 4 figures, Review articl
Levy flights from a continuous-time process
The Levy-flight dynamics can stem from simple random walks in a system whose
operational time (number of steps n) typically grows superlinearly with
physical time t. Thus, this processes is a kind of continuous-time random walks
(CTRW), dual to usual Scher-Montroll model, in which grows sublinearly with
t. The models in which Levy-flights emerge due to a temporal subordination let
easily discuss the response of a random walker to a weak outer force, which is
shown to be nonlinear. On the other hand, the relaxation of en ensemble of such
walkers in a harmonic potential follows a simple exponential pattern and leads
to a normal Boltzmann distribution. The mixed models, describing normal CTRW in
superlinear operational time and Levy-flights under the operational time of
subdiffusive CTRW lead to paradoxical diffusive behavior, similar to the one
found in transport on polymer chains. The relaxation to the Boltzmann
distribution in such models is slow and asymptotically follows a power-law
Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
A detailed study is presented for a large class of uncoupled continuous-time
random walks (CTRWs). The master equation is solved for the Mittag-Leffler
survival probability. The properly scaled diffusive limit of the master
equation is taken and its relation with the fractional diffusion equation is
discussed. Finally, some common objections found in the literature are
thoroughly reviewed.Comment: Preprint version of an already published paper. 8 page
A random walk description of the heterogeneous glassy dynamics of attracting colloids
We study the heterogeneous dynamics of attractive colloidal particles close
to the gel transition using confocal microscopy experiments combined with a
theoretical statistical analysis. We focus on single particle dynamics and show
that the self part of the van Hove distribution function is not the Gaussian
expected for a Fickian process, but that it reflects instead the existence, at
any given time, of colloids with widely different mobilities. Our confocal
microscopy measurements can be described well by a simple analytical model
based on a conventional continuous time random walk picture, as already found
in several other glassy materials. In particular, the theory successfully
accounts for the presence of broad tails in the van Hove distributions that
exhibit exponential, rather than Gaussian, decay at large distance.Comment: 13 pages, 5 figs. Submitted to special issue "Classical and Quantum
Glasses" of J. Phys.: Condens. Matter; v2: response to refere
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