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We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an…
This paper examines the mathematical properties of the relativistic diffusion equation. The peculiar solution which Hiscock and Lindblom identified as an instability is shown to emerge from an ill-posed initial value problem. These do not…
In inhomogeneous environments, the correct expression of the diffusive flux is often not given by the Fick's law $\Gamma = - D \nabla n $. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
Considering turbulence is crucial to understanding clouds. However, covering all scales involved in the turbulent mixing of clouds with their environment is computationally challenging, urging the development of simpler models to represent…
The diffusion, "explosion" and "evaporation" of dimers and the subsequent coalescence are treated in a formal way by identifying and solving the differential equations deduced from the respective behaviors of dimers in the different cases.…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This…
We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…
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…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Due to its parabolic character, the diffusion equation exhibits instantaneous spatial spreading, and becomes unstable when Lorentz-boosted. According to the conventional interpretation, these features reflect a fundamental incompatibility…
We propose a mathematical model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…