Direct Numeric Simulation of Shock Wave Structures without the Use of Artificial Viscosity

The purpose of this work is to directly simulate shock wave structures without the use of artificial viscosity. The commonly used artificial viscosity model is replaced with an irreversibility model. Irreversibilities are not typically taken into account when modeling the shock processes because shocks are resolved in a large domain where the thickness of the shock is thin compared to the numeric grid resolution. The result is the shock is poorly resolved. In addition processes other than shock processes are adiabatic and reversible. The result is artificial viscosity, a form of irreversibility, is added to the numeric cells near the shock in order to account for the irreversibilities generated within the shock structure. In this work the shocks are resolved and the physical sources of irreversibilities, namely viscous dissipation and localized heat transfer, are directly incorporated within the shock process. The resulting simulations yield a more realistic shock structure, the shape of which can be integrated to determine the resulting increase in entropy of the shocked material. Metrics such as shock thickness and wave structure compare favorably to experimental results. Irreversibility is traditionally accounted for by inserting artificial viscosity into the energy balance. Artificial viscosity reduces numerical overshoot, diminishes the total energy, and smears out the shock front over several cells thereby eliminating the need for nanoscale grid resolution necessary to resolve the shock front and numerically resolve the gradients. This approach fails to correctly model the shock wave structure of distended materials because their dynamic loading is a highly dissipative process and completely irreversible. Thus, the work described herein models on a bulk scale a thermodynamically consistent representation of the irreversibilities associated with shock wave formation such as viscous dissipation and heat conduction and seeks to determine if these sources of irreversibility are comparable to artificial viscosity

Selected Flexibility Exercises and Baseball Hitting Proficiency

There appears to be an increasing interest among baseball coaches n the development of a flexibility program to improve hitting consistency. Through an analysis of the form used for hitting a baseball, fisher revealed that a full powered swing is dependent of the range of motion in the body’s joints and that a subsequent amount of force is lost when flexion in the hips is decreased. The identification of selected flexibility exercises related to the success of hitting and implementation into training programs would be of significant value to coaches and players alike. The purpose of this study was to determine whether a relationship existed between the use of selected flexibility exercises and hitting proficiency

Self-Improving Algorithms

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we need to process a sequence I_1, I_2, ... of inputs I = (x_1, x_2, ..., x_n) of some fixed length n, where each x_i is drawn independently from some arbitrary, unknown distribution D_i. The goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution D = D_1 * D_2 * ... * D_n. We give such self-improving algorithms for two problems: (i) sorting a sequence of numbers and (ii) computing the Delaunay triangulation of a planar point set. Both algorithms achieve optimal expected limiting complexity. The algorithms begin with a training phase during which they collect information about the input distribution, followed by a stationary regime in which the algorithms settle to their optimized incarnations.Comment: 26 pages, 8 figures, preliminary versions appeared at SODA 2006 and SoCG 2008. Thorough revision to improve the presentation of the pape