Tortuosity of lightning return stroke channels

Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data

Crossing the Boundary: a study of the nature and extent of racism in local league cricket

Since the start of the 1993/4 football season the 'Let's Kick Racism Out of Football’ has had some success in persuading clubs and players to recognise racism in the game and act to counter it. This summer, following our own research (Long et al, 1995) the Rugby Football League and the Commission for Racial Equality launched a 13-point Action Plan for professional clubs to adopt. Within cricket 'Hit Racism for Six' (HR46) was set-up last year to act as a pressure group to stimulate discussion about racism in cricket. Issues of race and racism in sport have recently attracted considerable media attention and stimulated popular debate. Emotion has run high over the articles by Robert Henderson (1995) and Roger Bannister (Connor 1995), the continuing confrontation between Raymond Illingworth and Devon Malcolm, the Botham/Lamb v Khan court case and the trouble on the terraces at Headingley during the summer of 1996. The balance attempted by programmes in the Radio 5 series on ‘Race around the UK’ represented one attempt to encourage a more considered approach, but throughout it has been clear that there is still a shortage of substantive research on race in sport. The Carnegie National Sports Development Centre conducted a study of black and ethnic minorities in cricket in Yorkshire that focused on issues of participation and sports development. Following the success of our rugby league project, Leeds City Council were keen for us to try to explore the more sensitive issues around race and racism. While the study of rugby league had been on the professional game this study of cricket was to be of local league cricket. Within the region this is how most people experience their cricket with some 1,300 teams affiliated to the Yorkshire Cricket Association. To establish views on race and racism we sought responses from: a) the secretaries of local league clubs b) Asian, black and white players in the leagues c) league umpire

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Logarithmic behavior of degradation dynamics in metal--oxide semiconductor devices

In this paper the authors describe a theoretical simple statistical modelling of relaxation process in metal-oxide semiconductor devices that governs its degradation. Basically, starting from an initial state where a given number of traps are occupied, the dynamics of the relaxation process is measured calculating the density of occupied traps and its fluctuations (second moment) as function of time. Our theoretical results show a universal logarithmic law for the density of occupied traps $\bar{} \sim \phi (T,E_{F}) (A+B \ln t)$, i.e., the degradation is logarithmic and its amplitude depends on the temperature and Fermi Level of device. Our approach reduces the work to the averages determined by simple binomial sums that are corroborated by our Monte Carlo simulations and by experimental results from literature, which bear in mind enlightening elucidations about the physics of degradation of semiconductor devices of our modern life

Minimum-error discrimination between three mirror-symmetric states

We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested.Comment: 4 pages, 2 figure

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Irradiation of Materials with Short, Intense Ion pulses at NDCX-II

We present an overview of the performance of the Neutralized Drift Compression Experiment-II (NDCX-II) accelerator at Berkeley Lab, and report on recent target experiments on beam driven melting and transmission ion energy loss measurements with nanosecond and millimeter-scale ion beam pulses and thin tin foils. Bunches with around 10^11 ions, 1-mm radius, and 2-30 ns FWHM duration have been created with corresponding fluences in the range of 0.1 to 0.7 J/cm^2. To achieve these short pulse durations and mm-scale focal spot radii, the 1.1 MeV He+ ion beam is neutralized in a drift compression section, which removes the space charge defocusing effect during final compression and focusing. The beam space charge and drift compression techniques resemble necessary beam conditions and manipulations in heavy ion inertial fusion accelerators. Quantitative comparison of detailed particle-in-cell simulations with the experiment play an important role in optimizing accelerator performance.Comment: 15 pages, 7 figures. revised manuscript submitted to Laser and Particle Beam

Brief of Corporate Law Professors as Amici Curie in Support of Respondents

The Supreme Court has looked to the rights of corporate shareholders in determining the rights of union members and non-members to control political spending, and vice versa. The Court sometimes assumes that if shareholders disapprove of corporate political expression, they can easily sell their shares or exercise control over corporate spending. This assumption is mistaken. Because of how capital is saved and invested, most individual shareholders cannot obtain full information about corporate political activities, even after the fact, nor can they prevent their savings from being used to speak in ways with which they disagree. Individual shareholders have no “opt out” rights or practical ability to avoid subsidizing corporate political expression with which they disagree. Nor do individuals have the practical option to refrain from putting their savings into equity investments, as doing so would impose damaging economic penalties and ignore conventional financial guidance for individual investors