相关论文: Advection-Diffusion in Lagrangian Coordinates

We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…

Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…

We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, $H^s$-in-space stochastic forcing in a periodic box. We prove that in many circumstances, these flows are…

We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…

An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. For a given stirring velocity field, the mixing efficiency is measured in terms of an equivalent…

We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in…

We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratifed layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced…

We consider the advection-diffusion equation \[ \phi_t + Au \cdot \nabla \phi = \Delta \phi, \qquad \phi(0,x)=\phi_0(x) \] on $\bbR^2$, with $u$ a periodic incompressible flow and $A\gg 1$ its amplitude. We provide a sharp characterization…

This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…

We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward…

Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a…

The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…

We study the effect of advection and small diffusion on passive tracers. The advecting velocity field is assumed to have mean zero and to possess time-periodic stream lines. Using a canonical transform to action-angle variables followed by…

We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular…

Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…

In this paper, we present a second-order accurate finite-difference method for solving convectiondiffusion equations with interfacial jumps on a moving interface. The proposed method is constructed under a semi-Lagrangian framework for…

The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…