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

Smoke and Shadows: Rendering and Light Interaction of Smoke in Real-Time Rendered Virtual Environments

Realism in computer graphics depends upon digitally representing what we see in the world with careful attention to detail, which usually requires a high degree of complexity in modelling the scene. The inevitable trade-off between realism and performance means that new techniques that aim to improve the visual fidelity of a scene must do so without compromising the real-time rendering performance. We describe and discuss a simple method for realistically casting shadows from an opaque solid object through a GPU (graphics processing unit) based particle system representing natural phenomena, such as smoke

A follow-up study of the 1949 and 1950 graduates of Chandler School for Women, Boston, Massachusetts, and a survey of the employers of the Chandler graduates, with implications for curriculum revision.

Thesis (Ed.M.)--Boston Universityb1466393

Gauge symmetry and the EMC spin effect

We emphasise the EMC spin effect as a problem of symmetry and discuss the renormalisation of the $C=+1$ axial tensor operators. This involves the generalisation of the Adler-Bell-Jackiw anomaly to each of these operators. We find that the contribution of the axial anomaly to the spin dependent structure function $g_1 (x, Q^2)$ scales at $O(\alpha_s)$. This means that the anomaly can be a large $x$ effect in $g_1$. Finally we discuss the jet signature of the anomaly.Comment: 17 pages, Latex, Cavendish preprint HEP 93/

The Impact of a Clinical Faculty Institute on Participants\u27 Skills for Mentoring Novice Teachers, Grades K-8

A seven-day Clinical Faculty Institute was implemented to increase the skills of mentor teachers and to develop a cadre of Clinical Faculty for the four participating colleges and universities. The 128 participants entered with some confidence in their ability to mentor novice teachers in areas typically taught in methods courses; whereas, they displayed minimal confidence in skills typically taught in supervisory courses. By the end of the Institute, participants showed significant changes in their self-perceptions of skills in twenty areas, with post-scores clustering between 3.5 and 3.9 on a four-point scale. Future institutes should focus on supervisory skills and then emphasize more reflection upon the congruence of teaching, with the best practices articulated in national standards

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.

A neural network version of the measure correlate predict algorithm for estimating wind energy yield.

A neural network version of the measure correlate predict algorithm for estimating wind energy yiel