Related papers: Effective numerical treatment of sub-diffusion equ…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
This paper aims to address the unsupervised video anomaly detection (VAD) problem, which involves classifying each frame in a video as normal or abnormal, without any access to labels. To accomplish this, the proposed method employs…
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…
The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
Anomaly detection is a critical task in industrial manufacturing, aiming to identify defective parts of products. Most industrial anomaly detection methods assume the availability of sufficient normal data for training. This assumption may…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
In this paper, we propose a unified framework of inexact stochastic Alternating Direction Method of Multipliers (ADMM) for solving nonconvex problems subject to linear constraints, whose objective comprises an average of finite-sum smooth…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…
This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…