Related papers: Effective diffusion in the region between two surf…
We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the…
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
In this presentation, we analytically derive the dispersion equation for surface waves traveling along reactive boundaries which are periodically modulated in time. In addition, we show numerical results for the dispersion curves and…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We consider the Fisher-KPP equation on a three-dimensional domain surrounded by a thin layer whose diffusion rates are drastically different from that in the bulk. The bulk is isotropic, while the layer is considered to be anisotropic and…
Diffusion models have shown remarkable capabilities in generating high-fidelity data across modalities such as images, audio, and video. However, their computational intensity makes deployment on edge devices a significant challenge. This…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…
The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a…
After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…
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…
For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…
This paper deals with a challenging, frequently encountered, yet not properly investigated problem in two-frame optical flow estimation. That is, the input frames are compounds of two imaging layers -- one desired background layer of the…
A grand challenge in fundamental physics and practical applications is overcoming wave diffusion to deposit energy into a target region deep inside a diffusive system. While it is known that coherently controlling the incident wavefront…
We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…