We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials

A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows

Of the two-phase mixture models used to study deflagration-to-detonation transition in granular explosives, the Baer–Nunziato model is the most highly developed. It allows for unequal phase velocities and phase pressures, and includes source terms for drag and compaction that strive to erase velocity and pressure disequilibria. Since typical time scales associated with the equilibrating processes are small, source terms are stiff. This stiffness motivates the present work where we derive two reduced models in sequence, one with a single velocity and the other with both a single velocity and a single pressure. These reductions constitute outer solutions in the sense of matched asymptotic expansions, with the corresponding inner layers being just the partly dispersed shocks of the full model. The reduced models are hyperbolic and are mechanically as well as thermodynamically consistent with the parent model. However, they cannot be expressed in conservation form and hence require a regularization in order to fully specify the jump conditions across shock waves. Analysis of the inner layers of the full model provides one such regularization [Kapila et al., Phys. Fluids 9, 3885 (1997)], although other choices are also possible. Dissipation associated with degrees of freedom that have been eliminated is restricted to the thin layers and is accounted for by the jump conditions.

Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations

Quantum mechanically determined electrostatic potentials for isosurfaces of electron density of a variety of CHNO explosive molecules are analyzed to identify features that are indicative of sensit...

A quantum mechanical investigation of the relation between impact sensitivity and the charge distribution in energetic molecules

WOEB07 Presentation: Understanding Enhanced Blast Explosives: A Multi-Scale Challenge.

In this overview we present a reactive multiphase flow model to describe the physical processes associated with enhanced blast. This model is incorporated into CTH, a shock physics code, using a variant of the Baer and Nunziato nonequilibrium multiphase mixture to describe shock-driven reactive flow including the effects of interphase mass exchange, particulate drag, heat transfer and secondary combustion of multiphase mixtures. This approach is applied to address the various aspects of the reactive behavior of enhanced blast including detonation and the subsequent expansion of reactive products. The latter stage of reactive explosion involves shock-driven multiphase flow that produces instabilities which are the prelude to the generation of turbulence and subsequent mixing of surrounding air to cause secondary combustion. Turbulent flow is modeled in the context of Large Eddy Simulation (LES) with the formalism of multiphase PDF theory including a mechanistic model of metal combustion.

/pdf/modeling-enhanced-blast-explosives-usinga-multiphase-mixture-38vyb0ymf7.pdf

Modeling Enhanced Blast Explosives UsingA Multiphase Mixture Approach

Several HMX‐based explosive samples were subjected to shockless compression using Sandia’s Z magnetic compression accelerator. A multi‐panel ICE configuration containing various thicknesses of energetic composites PBX9501, PBXN9, LX‐10 was subjected to ramp loading up to 320 Kbar over 500 ns. A Velocity Interferometer System for Any Reflector (VISAR) was used to measure transmitted wave profile data of particle velocity and forward and backward procedures were used with an optimization method to determine appropriate EOS data.

Shockless compression studies of hmx‐based explosives

Isopropyl nitrate (IPN) is a liquid explosive of rather low energy. We have measured the sound speed and used it in the universal liquid Hugoniot to produce an estimated Hugoniot for this material. Gas‐gun‐driven, multiple‐magnetic‐gauge measurements were made to measure a Hugoniot state at 6 GPa; it was in good agreement with the prediction. Two similar experiments were conducted at higher pressure inputs to study the shock‐to‐detonation transition in IPN; the high inputs required for initiation necessitated the use of a two‐stage gun. One experiment with an input of 9.0 GPa into the IPN produced a run to detonation of about 3 mm and the in‐situ particle velocity profiles showed the expected homogeneous initiation behavior of a growing wave behind the shock front that overtakes the front and decays to a steady detonation. The reactive wave in the shocked IPN appears to have achieved a steady superdetonation in both of the initiation experiments. This is the first time a steady superdetonation has been measured with in‐situ gauges.

/pdf/hugoniot-and-shock-initiation-studies-of-isopropyl-nitrate-29ma7pdsgb.pdf

Hugoniot and shock initiation studies of isopropyl nitrate

A new approach to explosive sample preparation is described in which microelectronics-related processing techniques are utilized. Fused silica and alumina substrates were prepared utilizing laser machining. Films of PETN were deposited into channels within the substrates by physical vapor deposition. Four distinct explosive behaviors were observed with high-speed framing photography by driving the films with a donor explosive. Initiation at hot spots was directly observed, followed by either energy dissipation leading to failure, or growth to a detonation. Unsteady behavior in velocity and structure was observed as reactive waves failed due to decreasing channel width. Mesoscale simulations were performed to assist in experiment development and understanding. We have demonstrated the ability to pattern these films of explosives and preliminary mesoscale simulations of arrays of voids showed effects dependent on void size and that detonation would not develop with voids below a certain size. Future work involves experimentation on deposited films with regular patterned porosity to elucidate mesoscale explosive behavior.

Microenergetic research involving a coupled experimental and computational approach to evaluate microstructural effects on detonation and combustion at sub-millimeter geometries.

Melvin R. Baer

Papers

WOEB07 Presentation: Understanding Enhanced Blast Explosives: A Multi-Scale Challenge.

Modeling Enhanced Blast Explosives UsingA Multiphase Mixture Approach

Shockless compression studies of hmx‐based explosives

Hugoniot and shock initiation studies of isopropyl nitrate

Microenergetic research involving a coupled experimental and computational approach to evaluate microstructural effects on detonation and combustion at sub-millimeter geometries.