1,486 research outputs found
Time-space fabric underlying anomalous diffusion
This study unveils the time-space transforms underlying anomalous diffusion
process. Based on this finding, we present the two hypotheses concerning the
effect of fractal time-space fabric on physical behaviors and accordingly
derive fractional quantum relationships between energy and frequency, momentum
and wavenumber which further give rise to fractional Schrodinger equation. As
an alternative modeling approach to the standard fractional derivatives, we
introduce the concept of the Hausdorff derivative underlying the Hausdorff
dimensions of metric spacetime. And in terms of the proposed hypotheses, the
Hausdorff derivative is used to derive a linear anomalous transport-diffusion
equation underlying anomalous diffusion process. Its Green's function solution
turns out to be a new type of stretched Gaussian distribution and is compared
with that from the Richardson's diffusion equation.Comment: Comments please go to [email protected]
Structural Derivative Model for Tissue Radiation Response
By means of a recently-proposed metric or structural derivative, called
scale-q-derivative approach, we formulate differential equation that models the
cell death by a radiation exposure in tumor treatments. The considered
independent variable here is the absorbed radiation dose D instead of usual
time. The survival factor, Fs, for radiation damaged cell obtained here is in
agreement with the literature on the maximum entropy principle, as it was
recently shown and also exhibits an excellent agreement with the experimental
data. Moreover, the well-known linear and quadratic models are obtained. With
this approach, we give a step forward and suggest other expressions for
survival factors that are dependent on the complex tumor structure.Comment: 6 pages, 2 collumn
A Spatial Structural Derivative Model for Ultraslow Diffusion
This study investigates the ultraslow diffusion by a spatial structural
derivative, in which the exponential function exp(x)is selected as the
structural function to construct the local structural derivative diffusion
equation model. The analytical solution of the diffusion equation is a form of
Biexponential distribution. Its corresponding mean squared displacement is
numerically calculated, and increases more slowly than the logarithmic function
of time. The local structural derivative diffusion equation with the structural
function exp(x)in space is an alternative physical and mathematical modeling
model to characterize a kind of ultraslow diffusion.Comment: 13 pages, 3 figure
Levy Anomalous Diffusion and Fractional Fokker--Planck Equation
We demonstrate that the Fokker-Planck equation can be generalized into a
'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional
space differentiations, in order to encompass the wide class of anomalous
diffusions due to a Levy stable stochastic forcing. A precise determination of
this equation is obtained by substituting a Levy stable source to the classical
gaussian one in the Langevin equation. This yields not only the anomalous
diffusion coefficient, but a non trivial fractional operator which corresponds
to the possible asymmetry of the Levy stable source. Both of them cannot be
obtained by scaling arguments. The (mono-) scaling behaviors of the Fractional
Fokker-Planck equation and of its solutions are analysed and a generalization
of the Einstein relation for the anomalous diffusion coefficient is obtained.
This generalization yields a straightforward physical interpretation of the
parameters of Levy stable distributions. Furthermore, with the help of
important examples, we show the applicability of the Fractional Fokker-Planck
equation in physics.Comment: 22 pages; To Appear in Physica
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