Numerical modeling of shock-sensitivity experiments

The Forest Fire rate model of shock initiation of heterogeneous explosives has been used to study several experiments commonly performed to measure the sensitivity of explosives to shock and to study initiation by explosive-formed jets. The minimum priming charge test, the gap test, the shotgun test, sympathetic detonation, and jet initiation have been modeled numerically using the Forest Fire rate in the reactive hydrodynamic codes SIN and 2DE

Quasilinear systems, semigroups, and nonlinear coupling

It is known that the semigroup S(t) corresponding to the sum A + B of two non-commuting generators, each having semigroups S/sub A/(t), respectively S/sub B/(t), is given by the Trotter product S/sub A/(t)*S/sub B/(t) = lim n..-->..infinity(S/sub A/(t/n)S/sub B/(t/n))/sup n/ provided the latter converges. We apply this principle in treating a quasilinear system with nonlinear coupling. The conjecture is that some hydrodynamic systems may have semigroups. 9 refs

Nonlinear semigroup theory for systems

The abstract Cauchy problem in a B-space is considered. Under certain conditions, and with use of the Generation Theorem of Crandall and Liggett (Am. J. Math., 93, 265-298 (1971)), the finite difference problem has a unique solution on (0,infinity). The author works here to extend the application of the Crandall-Liggett theorem to two conservation laws with linear coupling. (RWR

Using semigroups and the Trotter product formula to solve quasi-linear systems

A quasi-linear system with linear coupling terms is treated. An approximate system for which the Trotter product of constituent semigroups converges is solved. Then it is shown that the approximate solutions converge to a solution of the original system, and that the resulting solution operator is a semigroup. Remarks are made about a nonlinearly coupled system. 12 references