Related papers: Self-Similar Modes of Coherent Diffusion
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for…
The gravitational evolution of scale free initial spectra $P(k)\propto k^n$ in an Einstein-de Sitter universe is widely believed to be self-similar for $-3<n<4$. However, for $-3<n<-1$ the existence of self-similar scaling has not been…
Properties of two equations describing the evolution of the probability density function (PDF) of the relative dispersion in turbulent flow are compared by investigating their solutions: the Richardson diffusion equation with the drift term…
In this paper we explore the theory of the anisotropic porous medium equation in the slow diffusion range. After revising the basic theory, we prove the existence of self-similar fundamental solutions (SSFS) of the equation posed in the…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a subcritical exponent. We show that separable solutions are stable in some suitable sense by finding a class…
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…
Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows…
Finite time extinction of any bounded solution to the fast diffusion equation with spatially inhomogeneous absorption $$ \partial_tu=\Delta u^m-|x|^{\sigma}u^p, \quad (x,t)\in\mathbb{R}^N\times(0,\infty), $$ with $N\geq1$ and exponents $$…
Coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. Theory of slow light propagation in atomic clouds is generalized to short pulse regime by taking into account group velocity dispersion. It is…
We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion…
I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…
We study the dynamic contraction a self-sustained glow discharge in air in a rectangular duct with convective cooling. A two dimensional numerical model of the plasma contraction was developed in a cylindrical frame. The process is…
Hot alkali metal vapors enclosed in sub-micron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at nanoscale. Here, we propose a novel approach for calculating the eigenmodes…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We consider a reaction-diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions,…