4,632 research outputs found
A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation
We show that the minimal speed for the existence of monotonic fronts of the
equation with , and in
derives from a variational principle. The variational principle allows
to calculate, in principle, the exact speed for arbitrary . The case
when is included as an extension of the results.Comment: Latex, postcript figure availabl
The effect of a cutoff on pushed and bistable fronts of the reaction diffusion equation
We give an explicit formula for the change of speed of pushed and bistable
fronts of the reaction diffusion equation when a small cutoff is applied at the
unstable or metastable equilibrium point. The results are valid for arbitrary
reaction terms and include the case of density dependent diffusion.Comment: 7 page
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model
In this paper, we investigated a density-dependent reaction-diffusion
equation, . This equation is known as the
extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is
widely used in the population dynamics, combustion theory and plasma physics.
By employing the suitable transformation, this equation was mapped to the
anomalous diffusion equation where the nonlinear reaction term was eliminated.
Due to its simpler form, some exact self-similar solutions with the compact
support have been obtained. The solutions, evolving from an initial state,
converge to the usual traveling wave at a certain transition time. Hence, it is
quite clear the connection between the self-similar solution and the traveling
wave solution from these results. Moreover, the solutions were found in the
manner that either propagates to the right or propagates to the left.
Furthermore, the two solutions form a symmetric solution, expanding in both
directions. The application on the spatiotemporal pattern formation in
biological population has been mainly focused.Comment: 5 pages, 2 figures, accepted by Phys. Rev.
Anomalous diffusion mediated by atom deposition into a porous substrate
Constant flux atom deposition into a porous medium is shown to generate a
dense overlayer and a diffusion profile. Scaling analysis shows that the
overlayer acts as a dynamic control for atomic diffusion in the porous
substrate. This is modeled by generalizing the porous diffusion equation with a
time-dependent diffusion coefficient equivalent to a nonlinear rescaling of
timeComment: 4 page
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