10,749 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
A polarised QCD condensate: nu p elastic scattering as a probe of U_A(1) dynamics
U_A(1) dynamics have the potential to induce a polarised condensate inside a
nucleon. The formation of this condensate is related to the realisation of
U_A(1) symmetry breaking by tunneling processes such as instantons. If it is
present, the polarised condensate induces a term in g_1 which has support only
at x=0. Tunneling processes then induce a net transfer of ``spin'' from finite
x to x=0. The polarised condensate may be measured by comparing the
flavour-singlet axial charges which are extracted from polarised deep inelastic
and nu p elastic scattering experiments.Comment: 13 pages LaTeX, Section 3 improved to include discussion of the 3
flavour quark instanton interaction; to appear in Mod. Phys. Lett.
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