Related papers: A note on the standard diffusion curve of TAP anal…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion…
We show that for low enough temperatures, but still above the AT line, the Jacobian of the TAP equations for the SK model has a macroscopic fraction of eigenvalues outside the unit interval. This provides a simple explanation for the…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…
The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
A Fokker Planck equation on fractal curves is obtained, starting from Chapmann-Kolmogorov equation on fractal curves. This is done using the recently developed calculus on fractals, which allows one to write differential equations on…
This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
The linear stability analysis of an optically thin plasma where a general reaction proceeds, including chemical relaxation time effects, is carried out . A fifth order dispersion equation (instead of the fourth order one resulting when such…
Diffusion models achieve strong generative performance but remain slow at inference due to the need for repeated full-model denoising passes. We present Token-Adaptive Predictor (TAP), a training-free, probe-driven framework that adaptively…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…
We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…