Related papers: Accelerating solutions to the diffusion equation
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
Diffusion tensor coefficients play a central role in describing cosmic-ray transport in various astrophysical environments permeated with magnetic fields, which are usually modeled as a fluctuating field on top of a mean field. In this…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We present a complete description of the similarity solutions $u_{\alpha}(x,t)=t^{-\alpha/2}f(\Vert x \Vert/\sqrt{t};\alpha)$ for the following nonlinear diffusion equation $$ u_{t}+\gamma\vert u_{t} \vert =\Delta u\qquad(-1<\gamma<1) $$…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment containing the essential range of the limit profile the flux…
We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We derive equations of motion of hydrodynamic fluctuations performing perturbative expansion of the energy-momentum conservation equations around the boost invariant solution in one-dimensional expanding system. In the course of derivation,…
In this paper, we investigate generalized Carleman kinetic equation for n$\ge$2 and prove convergence towards the solution of equation with fast diffusion or porous medium type, $u_t=\Delta u^m$ ($0\le m\le2$), in its diffusive hydrodynamic…
We report experimental measurements of Lagrangian accelerations in the bulk of intense turbulent flows of dilute polymer solutions by following tracer particles with a high-speed optical tracking system. We observed a significant decrease…
In the presented paper known (up to the beginning of 2008) Lie- and non-Lie exact solutions of different $(1+1)$-dimensional diffusion-convection equations of form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$ are collected.
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…