Wave Profile for Breakdown Waves with a Large Current Behind the Wave Front

For analytical solution of breakdown waves with a large current behind the wave front, we employ a one-dimensional, steady-state, three-component (electrons, ions, and neutral particles) fluid model. This project involves breakdown waves propagating in the opposite direction of the electric field force on electrons, anti-force waves (return stroke in lightning); and the electron gas partial pressure is considered to provide the driving force for the propagation of the wave. The basic set of equations consists of the equation of conservation of mass flux, equation of conservation of momentum, equation of conservation of energy, plus Poisson’s equation. The waves are considered to have a shock front. In this study, we examine the possibility and validity of large currents measured and reported by few investigators. Existence of a relationship between wave speed and peak current values is investigated as well. Existence of a large current behind the wave front alters the equation of conservation of energy and Poisson’s equation, as well as the shock boundary condition on electron temperature. Considering a current behind the shock front, we have made appropriate modifications in our set of electron fluid dynamical equations. Using the modified set of equations and the shock condition on electron temperature, we have been able to integrate the set of electron fluid dynamical equations for current bearing anti-force waves. For a range of wave speeds and with the largest current possible for a specific wave speed, we present the wave profile for electric field, electron velocity, and the ionization rate within the dynamical transition region of the wave for anti-force waves

VIBRA: An interactive computer program for steady-state vibration response analysis of linear damped structures

An interactive steady state frequency response computer program with graphics is documented. Single or multiple forces may be applied to the structure using a modal superposition approach to calculate response. The method can be reapplied to linear, proportionally damped structures in which the damping may be viscous or structural. The theoretical approach and program organization are described. Example problems, user instructions, and a sample interactive session are given to demonstate the program's capability in solving a variety of problems

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.Comment: 21 pages, To appear in Compositio Mathematic

Chemistry: Space resources for teachers including suggestions for classroom activities and laboratory experiments

Curriculum supplement to assist general chemistry teachers in updating instruction materials with aerospace development

TEA: A Code for Calculating Thermochemical Equilibrium Abundances

We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. (1958) and Eriksson (1971). It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. We tested the code against the method of Burrows & Sharp (1999), the free thermochemical equilibrium code CEA (Chemical Equilibrium with Applications), and the example given by White et al. (1958). Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.Comment: 14 pages, 8 figures, article is submitted to ApJS, posted on arXiv for public commentary, please send comments to the lead autho