10,767 research outputs found
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 for the electric
field, where 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 considered previously in the literature including, in the
case , the form of Painlev\'e's second equation considered first in the
context of electrodiffusion by one of us. When , 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
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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
Cation mono- and co-doped anatase TiO nanotubes: An {\em ab initio} investigation of electronic and optical properties
The structural, electronic, and optical properties of metal (Si, Ge, Sn, and
Pb) mono- and co-doped anatase TiO nanotubes are investigated, in order
to elucidate their potential for photocatalytic applications. It is found that
Si doped TiO nanotubes are more stable than those doped with Ge, Sn, or
Pb. All dopants lower the band gap, except the (Ge, Sn) co-doped structure, the
decrease depending on the concentration and the type of dopant.
Correspondingly, a redshift in the optical properties for all kinds of dopings
is obtained. Even though a Pb mono- and co-doped TiO nanotube has the
lowest band gap, these systems are not suitable for water splitting, due to the
location of the conduction band edges, in contrast to Si, Ge, and Sn mono-doped
TiO nanotubes. On the other hand, co-doping of TiO does not improve
its photocatalytic properties. Our findings are consistent with recent
experiments which show an enhancement of light absorption for Si and Sn doped
TiO nanotubes.Comment: revised and updated, 23 pages (preprint style), 7 figures, 5 table
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
A gas flow indicator for portable life support systems
A three-part program was conducted to develop a gas flow indicator (GFI) to monitor ventilation flow in a portable life support system. The first program phase identified concepts which could potentially meet the GFI requirements. In the second phase, a working breadboard GFI, based on the concept of a pressure sensing diaphragm-aneroid assembly connected to a venturi, was constructed and tested. Extensive testing of the breadboard GFI indicated that the design would meet all NASA requirements including eliminating problems experienced with the ventilation flow sensor used in the Apollo program. In the third program phase, an optimized GFI was designed by utilizing test data obtained on the breadboard unit. A prototype unit was constructed using prototype materials and fabrication techniques, and performance tests indicated that the prototype GFI met or exceeded all requirements
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
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