We solve the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critica...

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an i...

A procedure for constructing solutions to the Riemann problem for gas dynamics with a general convex equation of state is given. Approximate procedures, involving a local parametrization of the equation of state, are introduced in order to calculate numerical fluxes in conservative finite difference schemes. This leads to difference schemes which are as accurate and almost as fast as the analog...

Starting from the molliied version of the Enskog equation for a hard-sphere uid, a grid-free algorithm to obtain the solution is proposed. The algorithm is based on the nite pointset method. For illustration, it is applied to a Riemann problem. The shock-wave solution is compared to the results of Frezzotti and Sgarra where a good agreement is found.

We solve Burgers’ equation with random Riemann initial conditions. The closed solution allows simple expressions for its statistical moments. Using these ideas we design an efficient algorithm to calculate the statistical moments of the solution. Our methodology is an alternative to the Monte Carlo method. The present approach does not demand a random numbers generator as does the Monte Carlo m...

Note that the Cauchy and the Dirichlet datum are both constant vectors: we explain why it is meaningful considering this class of problems later on in the introduction. The self-similar viscous approximation (1.1) of an initial-boundary value problem was considered in Joseph and LeFloch [17]: they established compactness of the family Uε and provided an accurate description of a limit. Here we ...

The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence {g(un) dun} in the weak-⋆ topology of measures when {un} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u) du in a BV context. Several existing definitions ...

In the paper we are concerned with the large time behavior of solutions to the onedimensional Navier-Stokes-Poisson system in the case when the potential function of the self-consistent electric field may take distinct constant states at x = ±∞. Precisely, it is shown that if initial data are close to a constant state with asymptotic values at far fields chosen such that the Riemann problem on ...

We introduce a generalized solution of the Riemann problem for a general resonant nonlinear balance law, and we prove the convergence of the 2 2 Godunov numerical method based on these solutions. In particular, we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the Riemann problem, and an interesting multiplicity of time-asymptotic wave...

This talk will come in four parts. First, I will introduce the Riemann hypothesis (RH) as it was first introduced, using the Riemann zeta function, and discuss briefly its connection to number theory and prime numbers. Second, I will make this connection explicit by discussion a famous problem equivalent to RH. Third, I will examine the generalised Riemann hypothesis (GRH) and, finally, will li...