55 research outputs found
Scaling dependence on time and distance in nonlinear fractional diffusion equations and possible applications to the water transport in soils
Recently, fractional derivatives have been employed to analyze various
systems in engineering, physics, finance and hidrology. For instance, they have
been used to investigate anomalous diffusion processes which are present in
different physical systems like: amorphous semicondutors, polymers, composite
heterogeneous films and porous media. They have also been used to calculate the
heat load intensity change in blast furnace walls, to solve problems of control
theory \ and dynamic problems of linear and nonlinear hereditary mechanics of
solids. In this work, we investigate the scaling properties related to the
nonlinear fractional diffusion equations and indicate the possibilities to the
applications of these equations to simulate the water transport in unsaturated
soils. Usually, the water transport in soils with anomalous diffusion, the
dependence of concentration on time and distance may be expressed in term of a
single variable given by In particular, for the
systems obey Fick's law and Richards' equation for water transport. We show
that a generalization of Richards' equation via fractional approach can
incorporate the above property.Comment: 9 page
Integro-differential diffusion equation for continuous time random walk
In this paper we present an integro-differential diffusion equation for
continuous time random walk that is valid for a generic waiting time
probability density function. Using this equation we also study diffusion
behaviors for a couple of specific waiting time probability density functions
such as exponential, and a combination of power law and generalized
Mittag-Leffler function. We show that for the case of the exponential waiting
time probability density function a normal diffusion is generated and the
probability density function is Gaussian distribution. In the case of the
combination of a power-law and generalized Mittag-Leffler waiting probability
density function we obtain the subdiffusive behavior for all the time regions
from small to large times, and probability density function is non-Gaussian
distribution.Comment: 12 page
Tsallis distribution and luminescence decays
Usually, the Kohlrausch (stretched exponential) function is employed to fit
the luminescence decays. In this work we propose to use the Tsallis
distribution as an alternative to describe them. We show that the curves of the
luminescence decay obtained from the Tsallis distribution are close to those
ones obtained from the stretched exponential. Further, we show that our result
can fit well the data of porous silicon at low temperature and simulation
result of the trapping controlled luminescence model.Comment: 8 pages and 4 figure
Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach
We consider the Langevin equation with multiplicative noise term which
depends on time and space. The corresponding Fokker-Planck equation in
Stratonovich approach is investigated. Its formal solution is obtained for an
arbitrary multiplicative noise term given by , and the
behaviors of probability distributions, for some specific functions of %
, are analyzed. In particular, for , the physical
solutions for the probability distribution in the Ito, Stratonovich and
postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod
Entropic Upper Bound on Gravitational Binding Energy
We prove that the gravitational binding energy {\Omega} of a self gravitating
system described by a mass density distribution {\rho}(x) admits an upper bound
B[{\rho}(x)] given by a simple function of an appropriate, non-additive
Tsallis' power-law entropic functional Sq evaluated on the density {\rho}. The
density distributions that saturate the entropic bound have the form of
isotropic q-Gaussian distributions. These maximizer distributions correspond to
the Plummer density profile, well known in astrophysics. A heuristic scaling
argument is advanced suggesting that the entropic bound B[{\rho}(x)] is unique,
in the sense that it is unlikely that exhaustive entropic upper bounds not
based on the alluded Sq entropic measure exit. The present findings provide a
new link between the physics of self gravitating systems, on the one hand, and
the statistical formalism associated with non-additive, power-law entropic
measures, on the other hand
Stretched-Gaussian asymptotics of the truncated L\'evy flights for the diffusion in nonhomogeneous media
The L\'evy, jumping process, defined in terms of the jumping size
distribution and the waiting time distribution, is considered. The jumping rate
depends on the process value. The fractional diffusion equation, which contains
the variable diffusion coefficient, is solved in the diffusion limit. That
solution resolves itself to the stretched Gaussian when the order parameter
. The truncation of the L\'evy flights, in the exponential and
power-law form, is introduced and the corresponding random walk process is
simulated by the Monte Carlo method. The stretched Gaussian tails are found in
both cases. The time which is needed to reach the limiting distribution
strongly depends on the jumping rate parameter. When the cutoff function falls
slowly, the tail of the distribution appears to be algebraic.Comment: 19 pages, 5 figure
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