相关论文: A general numerical solution of dispersion relatio…

A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…

The nucleus-nucleus potential and energy dissipation in fusion reactions are obtained from microscopic mean-field dynamics. The deduced potentials nicely reproduce the one extracted from experimental data. Energy dissipation shows a…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Speckle is an intrinsic pattern in optical coherence tomography (OCT) that obscures fine image features and degrades effective resolution. In this study, we propose a numerical speckle reduction method based on the dispersed scatterer model…

In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…

In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension…

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find…

Modern problems in magnetization dynamics require more and more the numerical determination of the spin-wave spectra and -dispersion in magnetic systems where analytic theories are not yet available. Micromagnetic simulations can be used to…

An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. The system of nuclear fragments exhibits a 1-st order liquid-gas phase transition. The peculiar thermodynamic properties of the model…

A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…

Let $\{x_1, x_2, ..., x_n\}$ be a vector of real numbers. An integer relation algorithm is a computational scheme to find the $n$ integers $a_k$, if they exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years,…

The global observable distributions of nucleus-nucleus collisions at high energy are studied. It is shown that these distributions are sensitive to interaction dynamics and can be used to investigate the evolution of dense nuclear matter.…

We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral light beams, and other important families of…

State-of-the-art models for aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method to numerically solve particle growth kinetics. In this method, particles that are smaller than the critical size are…

We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate $x$ and time $t$) Laplace transform of self-consistent plasma electric field $E(x,t) \to…

The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current.…