Bulletin of the American Physical Society
77th Annual Meeting of the Southeastern Section of the APS
Volume 55, Number 10
Wednesday–Saturday, October 20–23, 2010; Baton Rouge, Louisiana
Session FC: Explosions, Momentum, and Mathematical Physics |
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Chair: David Ernst, Vanderbilt University Room: Nicholson Hall 118 |
Friday, October 22, 2010 8:30AM - 8:42AM |
FC.00001: Formulation of Macroscale Compaction Dynamics based on Mesoscale Simulations of Uniaxial Waves in Granular Explosive Sunada Chakravarthy, Keith A. Gonthier A macroscale continuum theory for Deflagration-to-Detonation Transition (DDT) in granular explosive is generalized to account for the simultaneous existence of an arbitrary number of condensed phases. The theory assumes phase separation, and allows for flexible partitioning of dissipation between phases in a thermodynamically consistent manner. The constitutive theory is complex and requires descriptions for dissipation partition functions, relaxation rate functions, and phase-specific parameters that are not well-characterized, particularly for dynamic loading. A key focus of this study is to formulate expressions for phase-specific intergranular stresses and compaction potential energies based on mesoscale simulations of uniaxial compaction waves because of their importance to compaction induced heating and combustion. Predictions will be compared to quasi-static compaction data for granular HMX. [Preview Abstract] |
Friday, October 22, 2010 8:42AM - 8:54AM |
FC.00002: Low-Order Modeling for the Impact Energetics of Laser-Driven Micro-Flyers with Thin Stationary Targets Mark Fry, Keith Gonthier The impact of high-speed (500-1500~m/s), laser driven micro-flyers (thickness $\sim$ 5~$\mu$m) with thin energetic targets (thickness $\sim$ 10~$\mu$s) is being examined to characterize deformation induced heating and combustion of these materials. To guide development of experiments, a low-order (zero-dimensional) model is formulated that can accurately and efficiently estimate ballistics maps for a large dimensional parameter space. The model accounts for the energetics of early time wave interactions and longer time shearing of the target during penetration and perforation. The model is validated against data for the impact of larger flyer and target configurations, and is used to predict ballistic maps for micro-scale configurations. Preliminary predictions for the impact of aluminum micro-flyers with thin steel targets indicate that the ballistic behavior is sensitive to micro-flyer mass and geometry. Model limitations are highlighted, and improvements are suggested. [Preview Abstract] |
Friday, October 22, 2010 8:54AM - 9:06AM |
FC.00003: Wave Structures and Energetics of Compaction-Induced Particle Dispersal in a Gas Michael Crochet, Keith Gonthier Shock wave propagation in gas/solid particle systems has been analyzed in the study of dust explosion suppression, as well as the post-detonation dispersal of metal particles in explosive mixtures. The predicted flow regimes exhibit considerable changes in the solid volume fraction; however, drag and heat transfer laws used in present models are restricted to either the dilute or dense flow regimes. Furthermore, the mechanisms primarily responsible for solid heating and possible ignition within each region are currently not well-characterized. Here, a multiphase continuum model is used to predict flow structures arising from compaction wave interactions, using empirical relations valid for all volume fractions. The results of a parametric study examining the effects of wave strength, initial solid volume fraction, and particle diameter on the wave profiles are examined, for both planar piston impact and spherical particle dispersal simulations. The relative contributions of compression, compaction and drag to the gas and solid energetics are analyzed to assess the likelihood of combustion initiation. [Preview Abstract] |
Friday, October 22, 2010 9:06AM - 9:18AM |
FC.00004: Design of a spin-down experiment for measuring momentum accommodation on planar surfaces Tathagata Acharya, Michael Martin A mathematical model has been developed to quantify momentum accommodation coefficient as a function of ambient pressure, gas density, ambient temperature, mass of the gas molecule, and the angular velocity of a disk. An experimental method is proposed for the measurement of momentum accommodation coefficient. The experimental method involves accelerating a disk to a given angular velocity and then allowing it to spin down over a measured time interval. Numerical simulations have been performed to evaluate the correct size of experimental chamber in order to avoid wall effects, and to determine the limiting pressure that will help achieve free molecular flow in the experimental chamber. Simulations indicate that the transition between the continuum and free molecular regimes starts below 10$^{-4}$ atmospheric pressure. [Preview Abstract] |
Friday, October 22, 2010 9:18AM - 9:30AM |
FC.00005: Frame Indifferent (Truly Covariant) Formulation of Electrodynamics Christo Christov The Electromagnetic field is considered from the point of view of mechanics of continuum. It is shown that Maxwell's equations are mathematically strict corollaries form the equation of motions of an elastic incompressible liquid. If the concept of frame-indifference (material invariance) is applied to the model of elastic liquid, then the partial time derivatives have to be replaced by the convective time derivative in the momentum equations, and by the Oldroyd upper-convected derivative in the constitutive relation. The convective/convected terms involve the velocity at a point of the field, and as a result, when deriving the Maxwell form of the equations, one arrives at equations which contain both the terms of Maxwell's equation and the so-called laws of motional EMF: Faraday's, Oersted--Ampere's, and the Lorentz-force law. Thus a unification of the electromagnetism is achieved. Since the new model is frame indifferent, it is truly covariant in the sense that the governing system is invariant when changing to a coordinate frame that can accelerate or even deform in time. [Preview Abstract] |
Friday, October 22, 2010 9:30AM - 9:42AM |
FC.00006: Linear and Nonlinear Effects in Freak Wave Formation Jessica Graber Freak (or rogue) waves are waves of great height that appear out of nowhere from otherwise ordinary, if rough, seas. The steepness of these waves can cause an enormous amount of damage to ships and oil platforms. The number of these waves physically occurring appears to be larger than predicted by the Gaussian statistics often used to model sea states. Understanding the cause of freak waves will help us to predict dangerous conditions, and engineer structures better able to withstand such waves. A number of mechanisms have been studied as the source of freak waves, including linear focusing, refraction of waves through a current field, and nonlinear effects. The Benjamin-Feir instability is a promising candidate with ``breather'' solutions of the nonlinear Schrodinger equation. Two of these breather solutions are the Ma soliton solution with large waves appear periodically in space at a given time, and the Akhmediev soliton solution, which is a wave forming periodically in time at a specific position. The relationship between linear and nonlinear effects has not been well-studied. Comparing the time scales on which the linear and nonlinear effects act gives us an idea of the regime in which various input parameters cause one effect or the other to be negligible, and when they act together to create a heightened response. [Preview Abstract] |
Friday, October 22, 2010 9:42AM - 9:54AM |
FC.00007: Approximate Solutions to d$^{2}$x/dt$^{2}$ + [1+( dx/dt)$^{2}$]x = 0 Using a Polar Representation 'Kale Oyedeji, Ronald E. Mickens It can be shown that the following nonlinear differential equation \begin{center} d$^{2}$x/dt$^{2}$ + [1+( dx/dt)$^{2}$]x = 0 \end{center} has only periodic solutions. The application of standard perturbation methods, harmonic balance, and other approximation techniques all reach the conclusion that the angular frequency has a singularity for a finite value of the initial amplitude A, where the initial conditions are x(0) = A and dx(0)/dt = 0. Since a phase-space analysis demonstrates that such a singularity does not exist, we must seek other methods to give the required valid behavior for the angular frequency as a function or the initial amplitude. This presentation reports our work using a method based on a polar representation for the periodic solutions. We compare these results with a priori calculations and give an explanation as to why the earlier calculations were ``interpreted'' as being incorrect. [Preview Abstract] |
Friday, October 22, 2010 9:54AM - 10:06AM |
FC.00008: Polar Representations of Solutions to Nonlinear Oscillator Differential Equations Ronald E. Mickens A fundamental issue in the theory of nonlinear oscillations is how to construct valid analytical approximations for the oscillatory solutions of the associated second-order differential equations. If such equations have a harmonic oscillator limiting form, then, in general, these equations may be reformulated such that a small parameter can be created and the standard perturbation methods can then be applied to determine approximations to the required solutions. Other ``global'' methods, e.g., harmonic balance, can also be used to obtain estimates for periodic solutions. Our purpose in this presentation is to construct a new technique which may then be used to calculate approximations to the oscillatory solutions of nonlinear oscillatory systems. This method begins with an exact polar mathematical representation for the solution. These equations are then converted to an iteration scheme which can be used to determine approximate solutions to the original problem. An advantage of this procedure is that all of the iterations may be solved (at least to first-order in the iteration variable) exactly. [Preview Abstract] |
Friday, October 22, 2010 10:06AM - 10:18AM |
FC.00009: The mass, energy, space and time systemic theory- MEST Dayong Cao The solar system is mass-energy center, and the wave (space-time) and planet are around. Sun absorb the matter (mass-energy) and radiate the light (space-time). It's space-time has a space time structure. It has a positive curvature and a sphericalstructure. The dark hole system is the space-time center, and the dark mass-energy and dark planet (dark comet) are around. Dark hole absorb the light (space-time), and radiate the dark mass-energy (mass-energy). The dark mass-energy main make up of the negative proton and the negative neutron who can take negative density and negative pressure. The dark mass-energy has a dark mass-energy structure. It is a negative curvature and a inverse sphericalstructure. The general relativity equation, $R_{ik}-\frac{1}{2}g_{ik}R=-{\kappa}T_{ik}$. The left of the equation is the metric tensor of the space-time structure; the right of the equation is the energy-momentum tensor. The dark hole has the below equation, $R'_{i'k'}-\frac{1}{2}g'_{i'k'}R'=-{\kappa}'T'_{i'k'}$. The left of the equation is the metric tensor of the dark mass-energy structure; the right of the equation is the dark space-time (field) tensor. $(R_{ik}-\frac{1}{2}g_{ik}R)+(R'_{i'k'}-\frac{1}{2}g'_{i'k'}R')=-({\kappa}T_{ik}+{\kappa}'T'_{i'k'})=0$. The above equation show that the cosmological model is a balance system. The star system and the dark hole system are the uniform distribution. There is the transmutation and the interaction between the dark hole system and star system. [Preview Abstract] |
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