We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate vf in a shear flow increases with compressibility intensity ?, following the relation ?vf??2. Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case.

We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice. We derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the Bloch spectrum of the Schrodinger operator. Relying on the framework of the multibranch entropy solutions introduced by Brenier and Corrias, we compute efficiently multiphase solutions using well adapted and simple numerical schemes.

We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow theWell-Balanced approach's canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type Dt <= O(Dx^2) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.

We review some ideas about the physics of small-scale turbulent statistics, focusing on the scaling behavior of anisotropic fluctuations. We present results from direct numerical simulations of three-dimensional homogeneous, anisotropically forced, turbulent systems: the Rayleigh–Bénard system, the random-Kolmogorov-flow, and a third flow with constant anisotropic energy spectrum at low wave numbers. A comparison of the anisotropic scaling properties displays good similarity among these very different flows.

We present a computational approach for the WKB approximation of the wavefunction of an electron moving in a periodic one-dimensional crystal lattice by means of a nonstrictly hyperbolic system whose flux function stems from the Bloch spectrum of the Schrodinger operator. This second part focuses on the handling of the source terms which originate from adding a slowly varying exterior potential.

In this study we classify short echo-time brain magnetic resonance spectroscopic imaging (MRSI) data by applying a model-based canonical correlation analyses algorithm and by using, as prior knowledge, multimodal sources of information coming from high-resolution magic angle spinning (HR-MAS), MRSI and magnetic resonance imaging. The potential and limitations of fusing in vivo and ex vivo nuclear magnetic resonance sources to detect brain tumors is investigated.