8,487 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
references adde
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
Study of dopants for radiation-resistant silicon Final report
Radiation effects on electrical properties of both aluminum and lithium doped bulk silico
An explicit KO-degree map and applications
The goal of this note is to study the analog in unstable -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 for ,
which can be thought of as an extension of Matsumoto's celebrated theorem
describing of a field. These results provide the first step in a program
aimed at computing the sheaf for .Comment: 36 Pages, Final version, to appear Journal of Topolog
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Implementation issues in product line scoping
Often product line engineering is treated similar to the waterfall model in traditional software engineering, i.e., the different phases (scoping, analysis, architecting, implementation) are treated as if they could be clearly separated and would follow each other in an ordered fashion. However, in practice strong interactions between the individual phases become apparent. In particular, how implementation is done has a strong impact on economic aspects of the project and thus how to adequately plan it. Hence, assessing these relationships adequately in the beginning has a strong impact on performing a product line project right. In this paper we present a framework that helps in exactly this task. It captures on an abstract level the relationships between scoping information and implementation aspects and thus allows to provide rough guidance on implementation aspects of the project. We will also discuss the application of our framework to a specific industrial project
The Theories of Turbulence
The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum
Hybrid digital-analog computer parallel processor
Describes a hybrid digital-analog computer parallel processing apparatus wherein a template circuit, or multiplicity thereof, is connected to receive parallel digital inputs. Each template circuit has controlled current sources with control gates connected respectively to parallel digital inputs. Current subsources for each pixel normally have programmable current output and “0” or “1” responses. Each template circuit has a current summing device for algebraically adding the current outputs of current sources, while a greatest value is detected at a comparator which may have a ramp signal applied to another input thereby identifying which template produced a maximum indication from the same parallel inputs. A self-calibrating feedback controlled current generator supplies all current sources on a chip making it possible to generate a known comparator input independent of IC resistivity or other parameters. The value of the indication of other templates may also be determined by the time relation of comparator output signals. If templates of the apparatus represent printed character correlation data, the output of the processor would identify the template with maximum indication and character with highest probability from a set of pixel inputs. Similar apparatus can be cascaded to first identify details in a scene and then match such detail charts with second stage templates
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