We study some questions related to general discrete velocity (with arbitrarily number of velocities) models (DVMs) of the Boltzmann equation. In the case of plane stationary problems the typical DVM reduces to a dynamical system (system of ODEs). Properties of such systems are studied in the most general case. In particular, a topological classification of their singular points is made and dimensions of the corresponding stable, unstable and center manifolds are computed. These results are applied to typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer. A classification of well-posed half-space problems for linearized DVMs is made. Exact solutions of a (simplified) linearized kinetic model of BGK type are found as a limiting case of the corresponding discrete models. Existence of solutions of weakly non-linear half-space problems for general DVMs are studied. The solutions are assumed to tend to an assigned Maxwellian at infinity, and the data for the outgoing particles at the boundary are assigned, possibly depending on the data for the incoming particles. The conditions, on the data at the boundary, needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated. Both implicit, in the non-degenerate cases, and sometimes, in both degenerate and non-degenerate cases, explicit conditions are found. Shock-waves can be seen as heteroclinic orbits connecting two singular points (Maxwellians) for DVMs. We give a constructive proof for the existence of solutions of the shock-wave problem for the general DVM. This is worked out for shock speeds close to a typical speed, corresponding to the sound speed in the continuous case. We clarify how close the shock speed must be for our theorem to hold, and present an iteration scheme for obtaining the solution. The main results of the paper can be used for DVMs for mixtures as well as for DVMs for one species.

As one category of energetic materials, impact-initiated reactive materials are able to release a high amount of stored chemical energy under high strain rate impact loading, and are used extensively in civil and military applications. In general, polymers are introduced as binder materials to trap the reactive metal powders inside, and also act as an oxidizing agent for the metal ingredient. Since critical attention has been paid on the metal / metal reaction, only a few types of polymer / reactive metal interactions have been studied in the literature. With the higher requirement of materials resistant to different thermal and mechanical environments, the understanding and characterization of polymer / reactive metal interactions are in great demand. In this study, PTFE (Polytetrafluoroethylene) 7A / Ti (Titanium) composites were studied under high strain rates by utilizing the Taylor impact and SHPB tests. Taylor impact tests with different impact velocities, sample dimensions and sample configurations were conducted on the composite, equipped with a high-speed camera for tracking transient images during the sudden process. SHPB and Instron tests were carried out to obtain the stress vs. strain curves of the composite under a wide range of strain rates, the result of which were also utilized for fitting the constitutive relations of the composite based on the modified Johnson-Cook strength model. Thermal analyses by DTA tests under different flow rates accompanied with XRD identification were conducted to study the reaction mechanism between PTFE 7A and Ti when only heat was provided. Numerical simulations on Taylor impact tests and microstructural deformations were also performed to validate the constitutive model built for the composite system, and to investigate the possible reaction mechanism between two components. The results obtained from the high strain rate tests, thermal analyses and numerical simulations were combined to provide a systematic study on the reaction mechanism between PTFE and Ti in the composite systems, which will be instructive for future energetic studies on other polymer / reactive metal systems.

Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

In the current research, a framework based on classical molecular dynamics (MD) is developed for computational mechanical analyses of complex nanoscale materials. The material system of focus is a combination of fcc-Al and and #945;-Fe₂O₃. The framework includes the development of an interatomic potential, a scalable parallel MD code, nanocrystalline composite structures, and methodologies for the quasistatic and dynamic strength analyses. The interatomic potential includes an embedded atom method (EAM) cluster functional, a Morse type pair function, and a second order electrostatic interaction function. The framework is applied to analyze the nanoscale mechanical behavior of the Al+Fe₂O₃ material system in two different settings. First, quasistatic strength analyses of nanocrystalline composites with average grain sizes varying from 3.9 nm to 7.2 nm are carried out. Second, shock wave propagation analyses are carried out in single crystalline Al, Fe₂O₃, and one of their interfaces. The quasistatic strength analyses reveal that the deformation mechanisms in the analyzed nanocrystalline structures are affected by a combination of factors including high fraction of grain boundary atoms and electrostatic forces. The slopes as well as the direct or inverse nature of observed Hall-Petch (H-P) relationships are strongly dependent upon the volume fraction of the Fe₂O₃ phase in the composites. The compressive strengths of single phase nanocrystalline structures are two to three times the tensile strengths owing to the differences in the movement of atoms in grain boundaries during compressive and tensile deformations. Analyses of shock wave propagation in single crystalline systems reveal that the shock wave velocity (US) and the particle velocity (UP) relationships as well as the type and the extent of shock-induced deformation in single crystals are strongly correlated with the choice of crystallographic orientation for the shock wave propagation. Analyses of shock wave propagation through an interface between Al and Fe2O3 point to a possible threshold UP value beyond which a shock-induced structural transformation that is reactive in nature in a region surrounding the interface may be taking place. Overall, the framework and the analyses establish an important computational approach for investigating the mechanical behavior of complex nanostructures at the atomic length- and time-scales.

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Understanding material behavior under extreme conditions is an important area of research in physics and material science. One method to study the behavior of materials under these conditions is to drive a strong shock wave through a material and watch its response. In many cases the material response is complicated by phase transitions such as lattice restructuring (Barker 1975; Mabire and Hereil 2000; Swift, Tierney et al. 2005) and melting (Asay 1975; Elias, Chapron et al. 1988; Werdiger, Eliezer et al. 1999; Mabire and Hereil 2000; Swift, Tierney et al. 2005). To study these dynamics we are using lasers in high time resolution pump-probe experiments to develop a real time diagnostic on the phase of a shocked material. This technique enables probing of the entire phase history of a material as it shock compresses and releases. In addition to linear reflectivity and ultra-fast 2D displacement interferometry, we developed a melting diagnostics based on the non-linear optical technique of third harmonic generation (THG) using a circularly polarized laser pulse. This diagnostic resolves the less than 300 fs melting transition of laser excited Si and GaAs, and it also detects a response in shock compressed silicon. Our results show that Si remains crystalline during compression of an elastic 100 kbar shock wave. Results from Si shocked to higher pressures (> 300 kbar) indicate a decrease in THG, suggesting some level of disordering or unexplained phase change. / text

Astrophysical flows have an enormous dynamic range of relevant length scales. The physics occurring on the smallest scales often influences the physics of the largest scales, and vice versa. I present a detailed study of the multiscale and multidimensional behavior of three high-energy astrophysical flows: jet-driven supernovae, massive black hole accretion, and current-driven instabilities in gamma-ray burst external shocks. Both theory and observations of core-collapse supernovae indicate these events are not spherically-symmetric; however, the observations are often modeled assuming a spherically-symmetric explosion. I present an in-depth exploration of the effects of aspherical explosions on the observational characteristics of supernovae. This is accomplished in large part by high-resolution, multidimensional numerical simulations of jet-driven supernovae. The existence of supermassive black holes in the centers of most large galaxies is a well-established fact in observational astronomy. How such black holes came to be so massive, however, is not well established. In this work, I discuss the implications of radiative feedback and multidimensional behavior on black hole accretion. I show that the accretion rate is drastically reduced relative to the Eddington rate, making it unlikely that stellar mass black holes could grow to supermassive black holes in less than a Hubble time. Finally, I discuss a mechanism by which magnetic field strength could be enhanced behind a gamma-ray burst external shock. This mechanism relies on a current-driven instability that would cause reorganization of the pre-shock plasma into clumps. Once shocked, these clumps generate vorticity in the post-shock plasma and ultimately enhance the magnetic energy via a relativistic dynamo process. / text

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Thèse (Sc.A.) -- Université du Québec à Chicoutimi, 2003. / Bibliogr.: f. [81]-84. Document électronique également accessible en format PDF. CaQCU

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.