相关论文: Homogenization of Enhancing Thin Layers

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory…

The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…

Diffusion models have been successfully applied to robotics problems such as manipulation and vehicle path planning. In this work, we explore their application to end-to-end navigation -- including both perception and planning -- by…

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical…

The light scattering problem for a confocal multilayered spheroid has been solved by the extended boundary condition method (EBCM) with a corresponding spheroidal basis. The solution preserves the advantages of the approach applied…

Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…

Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…

We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…

Two-scale homogenization limits of parabolic cross-diffusion systems in a heterogeneous medium with no-flux boundary conditions are proved. The heterogeneity of the medium is reflected in the diffusion coefficients or by the perforated…

We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…

In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic…

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a…

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…

We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling…

The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…

Imputing missing values in spatial-temporal traffic data is essential for intelligent transportation systems. Among advanced imputation methods, score-based diffusion models have demonstrated competitive performance. These models generate…

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…