相关论文: Solution of the Percus-Yevick equation for hard di…

A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure…

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…

High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…

This paper provides a methodology of verified computing for solutions to 1-dimensional advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic type. There are few…

A globally converging numerical method to solve coupled sets of non-linear integral equations is presented. Such systems occur e.g. in the study of Dyson-Schwinger equations of Yang-Mills theory and QCD. The method is based on the knowledge…

We study a two-dimensional fluid of dipolar hard disks by Monte Carlo simulations in a square with periodic boundary conditions and on the surface of a sphere. The theory of the dielectric constant and the asymptotic behaviour of the…

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…

We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical…

We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the…

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are…

We study the Cauchy problem for the Hamilton-Jacobi equation with a semiconcave initial condition. We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity…

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting…

The four-body bound state with two-body interactions is formulated in Three-Dimensional approach, a recently developed momentum space representation which greatly simplifies the numerical calculations of few-body systems without performing…

We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for…

We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…

An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can…

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…

An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded…

In this paper, we provide a systematic way of finding explicit solutions for a class of continuous fragmentation equations with growth or decay in the state space and derive explicit solutions in the cases of constant and linear…

We propose to solve polynomial hyperbolic partial differential equations (PDEs) with convex optimization. This approach is based on a very weak notion of solution of the nonlinear equation, namely the measure-valued (mv) solution,…