Vacuum polarization, a key prediction of quantum theory, can cause variety intriguing phenomena that be triggered by high-intensity laser pulses. The Heisenberg-Euler theory the vacuum supplements Maxwell's electromagnetism with nonlinear photon-photon interactions mediated fluctuations. This work presents numerical solver for leading weak-field corrections. present code implementation reaches ...

The generalized Riemann problem (GRP) scheme for the Euler equations and gaskinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity be...

Pharmacotherapy is a major treatment method in healthcare centers, and the injection of powdered drugs is among common pharmacotherapy techniques. Medication errors and nosocomial infections are among major health issues in the world. On the other hand, powdered drugs are widely used in hospitals; however, drug mixture is a very time-consuming process. The objective of this invention was to acc...

This paper consists of two parts. In the rst part we give a review of a good multigrid method for solving the steady Euler equations of gas dynamics on a locally reened mesh. The method is self-adaptive and makes use of unstructured grids that can be considered as parts of a nested sequence of structured grids. It is brieey described and applied to some steady Euler-ow problems. The method appe...

We present a highly robust second order accurate scheme for the Euler equations and the ideal MHD equations. The scheme is of predictor-corrector type, with a MUSCL scheme following as a special case. The crucial ingredients are an entropy stable approximate Riemann solver and a new spatial reconstruction that ensures positivity of mass density and pressure. For multidimensional MHD, a new disc...

Highorder extensions of the classical Godunov scheme offer computationally attractive features including inherent conservation, geometric flexibility, and accuracy for solving hyperbolic conservation laws. The Godunov-type methods typically do not rely on staggered grids, and the cellaveraged solution is not assumed to be continuous across the cell (control volume) edges. The discontinuity of t...

Considering n fluids, which are homogeneous, inviscid, incompressible and without surface tension, the 3D Euler equations with long wave assumptions provide the multi-layer shallow-water model with free surface. Since salinity is assumed discontinuous, these equations can be used to describe the oceans. The study of the hyperbolicity of this quasi-linear PDEs system is divided in two parts. Fir...

In this paper, we address the numerical solution of optimal transport problem on undirected weighted graphs, taking shortest path distance as cost. The is obtained from long-time limit gradient descent dynamics. Among different time stepping procedures for discretization dynamics, a backward Euler scheme combined with inexact Newton--Raphson method results in robust and accurate approach graphs...