George H. Pimbley

Jet initiation and penetration of explosives

The two-dimensional Eulerian hydrodynamic code 2DE with the shock initiation of heterogeneous explosive burn model called Forest Fire, is used to model numerically the interaction of jets of steel, copper, tantalum, aluminum, and water with steel, water, and explosive targets. The calculated and experimental critical condition for propagating detonation may be described by the Held V/sup 2/d expression (jet velocity squared times the jet diameter). In PBX 9502, jets initiate an overdriven detonation smaller than the critical diameter, which either fails or enlarges to greater than the critical diameter while the overdriven detonation decays to the C-J state. In PBX 9404, the jet initiates a detonation that propagates only if it is maintained by the jet for an interval sufficient to establish a stable curved detonation front. The calculated penetration velocities into explosives, initiated by a low-velocity jet, are significantly less than for non-reactive solids of the same density. The detonation products near the jet tip have a pressure higher than that of nonreactive explosives, and thus slow the jet penetration. At high jet velocities, the calculated penetration velocities are similar for reactive and inert targets. 8 references, 17 figures, 1 table.

Three-dimensional modeling of inert metal-loaded explosives

Abstract The reactive three-dimensional hydrodynamic code 3DE has been used to investigate the reactive hydrodynamics of a matrix of tungsten particles in HMX. A propagating detonation proceeding through the matrix of tungsten particles gives calculated detonation velocities and pressures that are much higher than observed. If the heterogeneous shock initiation Forest Fire rate for HMX is used to describe the reactive kinetics, some of the individual detonation wavelets between the tungsten particles fail. The shocked explosive continues to decompose and release energy after shock passage. Equations of state are described for a tungsten and a leadloaded explosive that reproduce the observed performance of these nonideal explosives. The calibrated equations of state use a partial energy release suggested by the three-dimensional model. Evidence is presented that the explosives have a flat top Taylor wave characteristic of weak detonations.

Some conditions for weak convergence to equilibrium of nonlinear contraction semigroups

Let x(t) an element of D(A) be the solution of the following initial-value problem in a real Hilbert space H: x/sub t/ + Ax containing as an element 0, x(0) = f, f an element of D(A). A is a multivalued maximal monotone nonlinear operator. A semigroup T(t) of contractions on D(A)-bar solving the problem exists. What is of interest is whether x(t) = T(t)f converges to a fixed point as t ..-->.. infinity, and if so, how. The fixed points are exactly those points x/sup */ an element of D(A) such that 0 is an element of Ax/sup */. F is the (non-null) set of fixed points. With this assumption it has been shown that x(t) is bounded. Bruck (J. Funct. Anal., 18: 15-25(1975)) gives a sufficient condition on the operator A for weak convergence of x(t) to an element of x/sup */ is an element of F; this condition is called demipositivity. Demipositive operators as a class are examined, and three types of such operators that might, with benefit, receive special treatment are noted. (RWR)

ON A 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)

THE NONOCCURRENCE OF SECONDARY BIFURCATION WITH HAMMERSTEIN OPERATORS

We shall dwell on the superlinear case, with occasional remarks about the sublinear case. Otherwise we assume that K ( s , t ) is continuous symmetric and positive definite, that f ( s , -x ) = f ( s , x), and that f ( s , x) is continuous and differentiable in x as many times as needed. The term u ( t ) is monotonic increasing. Under these conditions it is known that problem ( I ) has a branch xA(-’)(s) of solutions, parametrized by X > 0, which bifurcates from the trivial solution a t the j t h eigenvalue p,” of the linearized problem: