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

Mesoscale Modeling of Shocks in Heterogeneous Reactive Materials

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1129&context=usdoepub

A reaction progress variable modeling approach for non-ideal multiphase explosives

A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS This database can be used with the CHEETAH 140 or CHEETAH 20 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition

/pdf/exponential-6-parameterization-for-the-jcz3-eos-501xjthgp0.pdf

Exponential 6 parameterization for the JCZ3-EOS

This work presents statistically-based models to describe reactive behaviour in heterogeneous energetic materials. Mesoscale effects are incorporated in continuum-level reactive flow descriptions using probability density functions (pdfs) that are associated with thermodynamic and mechanical states. A generalised approach is presented that includes multimaterial behaviour by treating the volume fraction as a random kinematic variable. Model simplifications are then sought to reduce the complexity of the description without compromising the statistical approach. Reactive behaviour is first considered for non-deformable media having a random temperature field as an initial state. A pdf transport relationship is derived and an approximate moment approach is incorporated in finite element analysis to model an example application whereby a heated fragment impacts a reactive heterogeneous material which leads to a delayed cook-off event. Modelling is then extended to include deformation effects associated with ...

Probabilistic models for reactive behaviour in heterogeneous condensed phase media

Two-phase shock-driven reacting flow simulations are conducted to determine the post-detonation shock-focusing ignition and burning of aluminum particle mixtures. A model for aluminum particles that accounts for material compressibility from shock heating and expansion is presented. The Lagrangian description of the particles is incorporated into an Eulerian description of the gas phase resulting in a fully compressible, two-way coupled simulation. Simulations are conducted of an isolated explosive located near a corner to promote ignition of the particles from shock focusing. Parametric studies are conducted to determine the effects of equivalence ratio, particle size, and charge placement, on the post-detonation pressure and impulse. Results highlight the importance of the timing and position of the shock focusing event relative to the local mixture equivalence ratio that results in an optimal equivalence ratio which maximizes impulse for the geometry considered.

Melvin R. Baer

Papers

Mesoscale Modeling of Shocks in Heterogeneous Reactive Materials

A reaction progress variable modeling approach for non-ideal multiphase explosives

Exponential 6 parameterization for the JCZ3-EOS

Probabilistic models for reactive behaviour in heterogeneous condensed phase media

Modeling of particle compressibility and ignition from shock focusing