We study in what sense one can determine the flux functions k = k(x) and f = f(u), k piecewise constant, in the scalar hyperbolic conservation law u(t) + (k(x)f (u))(x) = 0 by observing the solution u(t, center dot) of the Cauchy problem with suitable piecewise constant initial data u vertical bar(t=0) = u(o).

We consider stochastic differential games with N players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of N Hamilton-Jacobi-Bellman (HJB) and N Kolmogorov-Fokker-Planck (KFP) partial differential equations.

We present the results of a computational study of coronary trees obtained from CT acquisition at resolution of 0.35mm x 0.35mm x 0.4mm and presenting significant stenotic plaques. We analyze the cardiovascular implications of stenotic plaques for a sizeable number of patients and show that the standard clinical criterion for surgical or percutaneous intervention, based on the Fractional Flow Reserve (FFR), is well reproduced by simulations in a range of inflow conditions that can be finely controlled.

A Godunov scheme is derived for two-dimensional scalar conservation laws without or with source terms following ideas originally proposed by Boukadida and LeRoux [Math. Comput., 63 (1994), pp. 541-553] in the context of a staggered Lax-Friedrichs scheme. In both situations, the numerical fluxes are obtained at each interface of a uniform Cartesian computational grid just by means of the "external waves" involved in the entropy solution of the elementary two-dimensional (2D) Riemann problems; in particular, all the wave-interaction phenomena are overlooked.

When numerically simulating a kinetic model of an n+nn+ semiconductor device, obtaining a constant macroscopic current at steady state is still a challenging task. Part of the difficulty comes from the multiscale, discontinuous nature of both p|n junctions, which create spikes in the electric field and enclose a channel where corresponding depletion layers glue together. The kinetic formalism furnishes a model holding inside the whole domain, but at the price of strongly varying parameters.

The numerical approximation of one-dimensional relativistic Dirac wave equations is considered within the recent framework consisting in deriving local scattering matrices at each interface of the uniform Cartesian computational grid. For a Courant number equal to unity, it is rigorously shown that such a discretization preserves exactly the (Formula presented.) norm despite being explicit in time. This construction is well-suited for particles for which the reference velocity is of the order of (Formula presented.), the speed of light.

Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme-mass-ratio binary systems, to the computation of several tidal invariants.