Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

High intensity x-ray diffraction in transmission mode employing an analog of Poisson's spot

Poisson’s spot is a diffraction phenomenon producing an intensity maximum at the center of the geometric shadow of circular opaque objects. In an analog of the Poisson spot experiment, we show that a tubular cone of x-rays incident upon a crystalline sample produces diffraction spots or foci, corresponding to Bragg maxima within a transmission shadow. We discuss the beam geometry and the intensity gain recorded at the foci in transmission mode. We describe the geometric growth and decay of the foci over a linear axis with the aid of a movie sequence synchronized with the plotting of a diffractogram. The mean signal of a small central area in each successive camera image provides the intensity data for the diffractogram

Central Charge and the Andrews-Bailey Construction

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have constructed a `generalized' character formula depending on two parameters \ra and $\r2$, using the Bailey pairs of the unitary model $M(p-1,p)$. By taking appropriate limits of these parameters, they were able to obtain the characters of model $M(p,p+1)$, $N=1$ model $SM(p,p+2)$, and the unitary $N=2$ model with central charge $c=3(1-{\frac{2}{p}})$. In this letter we computed the effective central charge associated with this `generalized' character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.Comment: Latex2e, requires cite.sty package, 13 pages. Additional footnote, citation and reference

A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

Numerical Algorithm for Detecting Ion Diffusion Regions in the Geomagnetic Tail with Applications to MMS Tail Season May 1 -- September 30, 2017

We present a numerical algorithm aimed at identifying ion diffusion regions (IDRs) in the geomagnetic tail, and test its applicability. We use 5 criteria applied in three stages. (i) Correlated reversals (within 90 s) of Vx and Bz (at least 2 nT about zero; GSM coordinates); (ii) Detection of Hall electric and magnetic field signatures; and (iii) strong (>10 mV/m) electric fields. While no criterion alone is necessary and sufficient, the approach does provide a robust, if conservative, list of IDRs. We use data from the Magnetospheric Multiscale Mission (MMS) spacecraft during a 5-month period (May 1 to September 30, 2017) of near-tail orbits during the declining phase of the solar cycle. We find 148 events satisfying step 1, 37 satisfying steps 1 and 2, and 17 satisfying all three, of which 12 are confirmed as IDRs. All IDRs were within the X-range [-24, -15] RE mainly on the dusk sector and the majority occurred during traversals of a tailward-moving X-line. 11 of 12 IDRs were on the dusk-side despite approximately equal residence time in both the pre- and post-midnight sectors (56.5% dusk vs 43.5% dawn). MMS could identify signatures of 4 quadrants of the Hall B-structure in 3 events and 3 quadrants in 7 of the remaining 12 confirmed IDRs identified. The events we report commonly display Vx reversals greater than 400 km/s in magnitude, normal magnetic field reversals often >10 nT in magnitude, maximum DC |E| which are often well in excess of the threshold for stage 3. Our results are then compared with the set of IDRs identified by visual examination from Cluster in the years 2000-2005.Comment: In Submission at JGR:Space Physic

Research Factsheet: Woodfuel experiment - North Thurlbar, Newton Rigg

An experiment has been set up to assess the economic viability and environmental impacts of woodfuel harvesting in North Thurlbar, a small wood land on the University of Cumbria Newton Rigg campus estate. This factsheet describes the aim of the study and the experiment design

Shock tube instrumentation techniques for study of hypervelocity entry problems

Shock tube instrumentation methods for convective heat transfer study and radiative properties of high temperature gas at conditions simulating hypervelocity entr