Recently, Nagel and Stein studied the b-heat equation, where b is the Kohn Laplacian on the boundary of a weakly-pseudoconvex domain of finite type in C. They showed that the Schwartz kernel of e b satisfies good “off-diagonal” estimates, while that of e b −π satisfies good “on-diagonal” estimates, where π denotes the Szegö projection. We offer a simple proof of these results, which easily gene...

The system of shock wave-induced vapor condensation in uids of large heat capacity has been investigated theoretically. The wave structure is governed by diierences in the time scales associated with various relaxation mechanisms and their coupling to the macroscopic ow. In the low to moderate Mach number range, the viscous and heat-conducting forces are localized within a discontinuous forerun...

A new discrete velocity scheme for solving the Boltzmann equation is described. Directly solving the Boltzmann equation is computationally expensive because, in addition to working in physical space, the nonlinear collision integral must also be evaluated in a velocity space. Collisions between each point in velocity space with all other points in velocity space must be considered in order to c...

We study the evolution of supernova core from the beginning of gravitational collapse of a 15M⊙ star up to 1 second after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic ν-radiation-hydrodynamics in the implicit time-differencing. We aim to explore the evolution of shock wave in a long term and investigate the form...

Two optical techniques are experimentally investigated to measure the shock wave velocity and particle velocity in metals subjected to hyper velocity impacts. Fabry-Perot interferometer based optical system has been developed and used to measure the interface velocity profile of impacted Tantalum-Glass and Aluminum-Glass targets. Optical fibers coupled to fast photodiodes are implemented to mea...

a considerable amount of energy is released in the form of shock wave from explosive charge detonation. shock wave energy is responsible for the creation of crushing and fracture zone around the blast hole. the rest of the shock wave energy is transferred to rock mass as ground vibration. ground vibration is conveyed to the adjacent structures by body and surface waves. geological structures li...

In these notes we analyze some problems related to the controllability and observability of partial differential equations and its space semidiscretizations. First we present the problems under consideration in the classical examples of the wave and heat equations and recall some well known results. Then we analyze the 1−d wave equation with rapidly oscillating coefficients, a classical problem...

Abstract. Exact one-dimensional steady flow equations for viscous, heat conducting calorically perfect gases were derived in terms of a velocity potential. These nonlinear differential equations were integrated numerically thus predicting detailed variation of thermodynamic and flow properties through the normal steady compression shock waves for an entire range of ratios of secondary and prima...