Sonic Hyperbolic Phase Transitions and Chapman-Jouguet Detonations

Detonations and deflagrations in cosmological phase transitions

We study the steady state motion of bubble walls in cosmological phase transitions. Taking into account the boundary and continuity conditions for the fluid variables, we calculate numerically the wall velocity as a function of the nucleation temperature, the latent heat, and a friction parameter. We determine regions in the space of these parameters in which detonations and/or deflagrations ar...

Existence of Chapman-Jouguet Detonation and Deflagration Waves

We study the existence of profiles for Chapman-Jouguet detonation and deflagration waves in the Navier-Stokes equations for a reacting gas. In the limit of small viscosity, heat conductivity, and diffusion, the profiles correspond to heteroclinic orbits of a system of singularly perturbed ordinary differential equations. The burned end state of the waves, however, is a nonhyperbolic equilibrium...

Stability of cosmological detonation fronts.

We present results of a linear stability analysis of relativistic detonation fronts, which have been considered as representing phase interfaces in cosmological first order phase transitions. After discussing general stability conditions for detonation fronts, we concentrate on the properties of the fronts with respect to corrugation instabilities and discuss separately the cases of Chapman-Jou...

Phase Transitions and Minimal Hypersurfaces in Hyperbolic Space

The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behaviour at infinity. Then, we study the limit as the length scale tends to zero through a Γ-convergence analysis, obta...

Modeling of Solid Phase Detonations