Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(\eps',k)>0, where \eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and $k\gg 1$ the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from communit

Recent advances in combustion modelling

vii, 231 p. : ill. ; 22 cm

Recent advances in combustion modelling

vii, 231 p. : ill. ; 22 cm

Recent advances in combustion modelling

vii, 231 p. : ill. ; 22 cm

On the Use of the HLL-Scheme or the Simulation of the Multi-Species Euler Equations

The HLL approximate Riemann solver is a reliable, fast and easy to implement tool for the under-resolved computation of inviscid flows. When applied to multi-species flows, it generates pressure oscillations at material interfaces. This is a well-known behaviour of conservative solvers and has been addressed as a problem by several authors before. We show that for this particular solver, the generation of pressure oscillations can be desired and is consistent with the underlying physics