Differential equations of electrodiffusion: constant field solutions, uniqueness, and new formulas of Goldman-Hodgkin-Katz type

The equations governing one-dimensional, steady-state electrodiffusion are considered when there are arbitrarily many mobile ionic species present, in any number of valence classes, possibly also with a uniform distribution of fixed charges. Exact constant field solutions and new formulas of Goldman-Hodgkin-Katz type are found. All of these formulas are exact, unlike the usual approximate ones. Corresponding boundary conditions on the ionic concentrations are identified. The question of uniqueness of constant field solutions with such boundary conditions is considered, and is re-posed in terms of an autonomous ordinary differential equation of order $n+1$ for the electric field, where $n$ is the number of valence classes. When there are no fixed charges, the equation can be integrated once to give the non-autonomous equation of order $n$ considered previously in the literature including, in the case $n=2$, the form of Painlev\'e's second equation considered first in the context of electrodiffusion by one of us. When $n=1$, the new equation is a form of Li\'enard's equation. Uniqueness of the constant field solution is established in this case.Comment: 29 pages, 5 figure

Airy series solution of Painlev\'e II in electrodiffusion: conjectured convergence

A perturbation series solution is constructed in terms of Airy functions for a nonlinear two-point boundary-value problem arising in an established model of steady electrodiffusion in one dimension, for two ionic species carrying equal and opposite charges. The solution includes a formal determination of the associated electric field, which is known to satisfy a form of the Painlev\'e II differential equation. Comparisons with the numerical solution of the boundary-value problem show excellent agreement following termination of the series after a sufficient number of terms, for a much wider range of values of the parameters in the model than suggested by previously presented analysis, or admitted by previously presented approximation schemes. These surprising results suggest that for a wide variety of cases, a convergent series expansion is obtained in terms of Airy functions for the Painlev\'e transcendent describing the electric field. A suitable weighting of error measures for the approximations to the field and its first derivative provides a monotonically decreasing overall measure of the error in a subset of these cases. It is conjectured that the series does converge for this subset.Comment: 30 pages, 9 figures. Typos corrected, figures modified, extra references adde

Low energy electron attachment to condensed formic acid

Dissociative electron attachment to formic acid in the condensed phase is studied using improved mass spectrometric detection of the negative ion fragments. The desorbed yields are measured as a function of incident electron energy in the range between 3 to 20 eV. Unlike previous work, the formation of the dehydrogenated anion HCOO? is observed and the signal to noise ratio is much higher for all other ions detected, i.e. OH?, O? and H?. Resonant structure seen in all anion yield functions, is attributed to dissociative electron attachment (DEA), whereas above 14 eV nonresonant dipolar dissociation (DD) dominates the desorption yields

Hempstead Union Free School District and United Public Service Employees Union

In the matter of the fact-finding between the Hempstead Union Free School District, employer, and the United Public Service Employees Union, union. PERB case no. M2009-300. Before: Stuart L. Bass, fact finder

Ultraviolet effects on conductive coated coverglasses

Experiments on the International Sun-Earth Explorer required that the outer surface of the spacecraft be conductive. For the solar panels this was accomplished by using solar cell coverglasses coated with indium-oxide and interconnected to ground. This paper presents results of ultraviolet tests performed as part of the overall qualification program for cell assemblies using these coverglasses. The samples were exposed under vacuum at a controlled temperature to 5000 equivalent sun hours. Coverglass transmission curves and cell assembly current-voltage curves were measured before and after the test. Observed degradations were of the order of 1 percent more for conductively coated coverglasses than for coverglasses without conductive coatings

A Game of Attribute Decomposition for Software Architecture Design

Attribute-driven software architecture design aims to provide decision support by taking into account the quality attributes of softwares. A central question in this process is: What architecture design best fulfills the desirable software requirements? To answer this question, a system designer needs to make tradeoffs among several potentially conflicting quality attributes. Such decisions are normally ad-hoc and rely heavily on experiences. We propose a mathematical approach to tackle this problem. Game theory naturally provides the basic language: Players represent requirements, and strategies involve setting up coalitions among the players. In this way we propose a novel model, called decomposition game, for attribute-driven design. We present its solution concept based on the notion of cohesion and expansion-freedom and prove that a solution always exists. We then investigate the computational complexity of obtaining a solution. The game model and the algorithms may serve as a general framework for providing useful guidance for software architecture design. We present our results through running examples and a case study on a real-life software project.Comment: 23 pages, 5 figures, a shorter version to appear at 12th International Colloquium on Theoretical Aspects of Computing (ICTAC 2015

Ion-tracer anemometer

Gas velocity measuring instrument measures transport time of ion-trace traveling fixed distance between ionization probe and detector probe. Electric field superimposes drift velocity onto flow velocity so travel times can be reduced to minimize ion diffusion effects

An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin matrices", which are explicit maps from odd dimensional split smooth affine quadrics to geometric models of the spaces appearing in Bott periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit map. As applications, we deduce that $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.Comment: 36 Pages, Final version, to appear Journal of Topolog

Direct photons in Pb+Pb at CERN-SPS from microscopic transport theory

Direct photon production in central Pb+Pb collisions at CERN-SPS energy is calculated within the relativistic microscopic transport model UrQMD, and within distinctly different versions of relativistic hydrodynamics. We find that in UrQMD the local momentum distributions of the secondaries are strongly elongated along the beam axis initially. Therefore, the pre-equilibrium contribution dominates the photon spectrum at transverse momenta above $\approx 1.5$ GeV. The hydrodynamics prediction of a strong correlation between the temperature and radial expansion velocities on the one hand and the slope of the transverse momentum distribution of direct photons on the other hand thus is not recovered in UrQMD. The rapidity distribution of direct photons in UrQMD reveals that the initial conditions for the longitudinal expansion of the photon source (the meson ``fluid'') resemble rather boostinvariance than Landau-like flow.Comment: 14 pages, RevTex, 5 Encapsulated-PostScript Figure