We study the phenomenon of diffusive radiative heat waves (Marshak waves) under general boundary conditions. In particular, we derive full analytic solutions for the subsonic case, that include both the ablation and the shock wave regions. Previous works in this regime, based on the work of [R. Pakula and R. Sigel, Phys. Fluids. 443, 28, 232 (1985)], present self-similar solutions for the ablation region alone, since in general, the shock region and the ablation region are not selfsimilar together. Analytic results for both regions were obtained only for the specific case in which the ratio between the ablation front velocity and the shock velocity is constant. In this work, we derive a full analytic solution for the whole problem in general boundary conditions. Our solution is composed of two different self-similar solutions, one for each region, that are patched at the heat front. The ablative region of the heat wave is solved in a manner similar to previous works. Then, the pressure at the front, which is derived from the ablative region solution, is taken as a boundary condition to the shock region, while the other boundary is described by Hugoniot relations. The solution is compared to full numerical simulations in several representative cases. The numerical and analytic results are found to agree within 1% in the ablation region, and within 2 − 5% in the shock region. This model allows better prediction of the physical behavior of radiation induced shock waves, and can be applied for high energy density physics experiments.

We study mode-I fracture in a viscoelastic lattice model with a nonlinear force law, with a focus on the velocity and linear stability of the steady-state propagating solution. This study is a continuation both of the study of the piecewise-linear model in mode I, and the study of more general nonlinear force laws in mode-III fracture. At small driving, there is a strong dependency of the velocity curve on the dissipation and a strong sensitivity to the smoothness of the force law at large dissipation. At large driving we calculate, via a linear stability analysis, the critical velocity for the onset of instability as a function of the smoothness, the dissipation and the ratio of lattice spacing to critical extension. This critical velocity is seen to be very sensitive to these parameters. We confirm our calculations via direct numerical simulations of the initial value problem.

This article studies the propagation of supersonic radiative Marshak waves. These waves are radiation dominated, and play an important role in inertial confinement fusion and in astrophysical and laboratory systems. For that reason, this phenomenon has attracted considerable experimental attention in recent decades in several different facilities. The present study integrates the various experimental results published in the literature, demonstrating a common physical base. A new simple semi-analytic model, is derived and presented along with advanced radiative hydrodynamic implicit Monte Carlo direct numerical simulations, which explain the experimental results. This study identifies the main physical effects dominating the experiments, notwithstanding their different apparatuses and different physical regimes. *

We study propagating mode-I fracture in two-dimensional amorphous materials using atomistic simulations. We use the continuous random network model of an amorphous material, creating samples using a two-dimensional analog of the Wooten-Winer-Weaire Monte Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which has not yet been achieved by other atomistic models for amorphous materials), the runs show microbranching, which increases with driving, transitioning to macrobranching for the largest drivings. In addition to the qualitative visual similarity of the simulated cracks to experiment, the simulation also succeeds in reproducing qualitatively the experimentally observed oscillations of the crack velocity.

No abstract