530 research outputs found
Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment and deposition
Monolayer cluster growth in far-from-equilibrium systems is investigated by
applying simulation and analytic techniques to minimal hard core particle
(exclusion) models. The first model (I), for post-deposition coarsening
dynamics, contains mechanisms of diffusion, attachment, and slow activated
detachment (at rate epsilon<<1) of particles on a line. Simulation shows three
successive regimes of cluster growth: fast attachment of isolated particles;
detachment allowing further (epsilon t)^(1/3) coarsening of average cluster
size; and t^(-1/2) approach to a saturation size going like epsilon^(-1/2).
Model II generalizes the first one in having an additional mechanism of
particle deposition into cluster gaps, suppressed for the smallest gaps. This
model exhibits early rapid filling, leading to slowing deposition due to the
increasing scarcity of deposition sites, and then continued power law (epsilon
t)^(1/2) cluster size coarsening through the redistribution allowed by slow
detachment. The basic (epsilon t)^(1/3) domain growth laws and epsilon^(-1/2)
saturation in model I are explained by a simple scaling picture. A second,
fuller approach is presented which employs a mapping of cluster configurations
to a column picture and an approximate factorization of the cluster
configuration probability within the resulting master equation. This allows
quantitative results for the saturation of model I in excellent agreement with
the simulation results. For model II, it provides a one-variable scaling
function solution for the coarsening probability distribution, and in
particular quantitative agreement with the cluster length scaling and its
amplitude.Comment: Accepted in Phys. Rev. E; 9 pages with figure
Migration and proliferation dichotomy in tumor cell invasion
We propose a two-component reaction-transport model for the
migration-proliferation dichotomy in the spreading of tumor cells. By using a
continuous time random walk (CTRW) we formulate a system of the balance
equations for the cancer cells of two phenotypes with random switching between
cell proliferation and migration. The transport process is formulated in terms
of the CTRW with an arbitrary waiting time distribution law. Proliferation is
modeled by a standard logistic growth. We apply hyperbolic scaling and
Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion.
In particular, we take into account both normal diffusion and anomalous
transport (subdiffusion) in order to show that the standard diffusion
approximation for migration leads to overestimation of the overall cancer
spreading rate.Comment: 9 page
Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach
We investigate equilibrium properties of two very different stochastic
collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas.
For both models the equilibrium velocity distribution is a L\'evy distribution,
the Maxwell distribution being a special case. We show how these models are
related to fractional kinetic equations. Our work demonstrates that a stable
power-law equilibrium, which is independent of details of the underlying
models, is a natural generalization of Maxwell's velocity distribution.Comment: PRE Rapid Communication (in press
Rates of convergence of nonextensive statistical distributions to Levy distributions in full and half spaces
The Levy-type distributions are derived using the principle of maximum
Tsallis nonextensive entropy both in the full and half spaces. The rates of
convergence to the exact Levy stable distributions are determined by taking the
N-fold convolutions of these distributions. The marked difference between the
problems in the full and half spaces is elucidated analytically. It is found
that the rates of convergence depend on the ranges of the Levy indices. An
important result emerging from the present analysis is deduced if interpreted
in terms of random walks, implying the dependence of the asymptotic long-time
behaviors of the walks on the ranges of the Levy indices if N is identified
with the total time of the walks.Comment: 20 page
Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
The role of external forces in systems exhibiting anomalous diffusion is
discussed on the basis of the describing Langevin equations. Since there exist
different possibilities to include the effect of an external field the concept
of {\it biasing} and {\it decoupled} external fields is introduced.
Complementary to the recently established Langevin equations for anomalous
diffusion in a time-dependent external force-field [{\it Magdziarz et al.,
Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of
anomalous diffusion in a decoupled time-dependent force-field is derived
Microtubules: Montroll's kink and Morse vibrations
Using a version of Witten's supersymmetric quantum mechanics proposed by
Caticha, we relate Montroll's kink to a traveling, asymmetric Morse double-well
potential suggesting in this way a connection between kink modes and
vibrational degrees of freedom along microtubulesComment: 2pp, twocolum
Parrondo-like behavior in continuous-time random walks with memory
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass
stochastic processes with memory. In this article we will show how the random
combination of two different unbiased CTRWs can give raise to a process with
clear drift, if one of them is a CTRW with memory. If one identifies the other
one as noise, the effect can be thought as a kind of stochastic resonance. The
ultimate origin of this phenomenon is the same of the Parrondo's paradox in
game theoryComment: 8 pages, 3 figures, revtex; enlarged and revised versio
Superfast front propagation in reactive systems with anomalous diffusion
We study a reaction diffusion system where we consider a non-gaussian process
instead of a standard diffusion. If the process increments follow a probability
distribution with tails approaching to zero faster than a power law, the usual
qualitative behaviours of the standard reaction diffusion system, i.e.,
exponential tails for the reacting field and a constant front speed, are
recovered. On the contrary if the process has power law tails, also the
reacting field shows power law tail and the front speed increases exponentially
with time. The comparison with other reaction-transport systems which exhibit
anomalous diffusion shows that, not only the presence of anomalous diffusion,
but also the detailed mechanism, is relevant for the front propagation.Comment: 4 pages and 4 figure
The delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation
It has been alleged in several papers that the so called delayed
continuous-time random walks (DCTRWs) provide a model for the one-dimensional
telegraph equation at microscopic level. This conclusion, being widespread now,
is strange, since the telegraph equation describes phenomena with finite
propagation speed, while the velocity of the motion of particles in the DCTRWs
is infinite. In this paper we investigate how accurate are the approximations
to the DCTRWs provided by the telegraph equation. We show that the diffusion
equation, being the correct limit of the DCTRWs, gives better approximations in
norm to the DCTRWs than the telegraph equation. We conclude therefore
that, first, the DCTRWs do not provide any correct microscopic interpretation
of the one-dimensional telegraph equation, and second, the kinetic (exact)
model of the telegraph equation is different from the model based on the
DCTRWs.Comment: 12 pages, 9 figure
The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure
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