Resistive Magnetohydrodynamic Equilibria in a Torus

It was recently demonstrated that static, resistive, magnetohydrodynamic equilibria, in the presence of spatially-uniform electrical conductivity, do not exist in a torus under a standard set of assumed symmetries and boundary conditions. The difficulty, which goes away in the ``periodic straight cylinder approximation,'' is associated with the necessarily non-vanishing character of the curl of the Lorentz force, j x B. Here, we ask if there exists a spatial profile of electrical conductivity that permits the existence of zero-flow, axisymmetric r esistive equilibria in a torus, and answer the question in the affirmative. However, the physical properties of the conductivity profile are unusual (the conductivity cannot be constant on a magnetic surface, for example) and whether such equilibria are to be considered physically possible remains an open question.Comment: 17 pages, 4 figure

Political Institutions and Greenhouse Gas Controls

Research and insights taken from the field of political economy suggest that institutions limit the extent to which efficient policies to reduce greenhouse gas emissions are likely to be adopted. High transaction costs among nations, as well as domestic constraints like voter xenophobia and distrust of markets in the U.S. and ineffective legal and economic institutions in China, discourage international agreement. The U.S. must focus upon limiting economic harm from adopting poorly designed policies and developing strategies for adaptation or technology-driven geoengineering. Most importantly, the lessons of political economy must become central to the study of climate policy, including a healthy exchange of views between political economists and climate modelers.

Cost Escalation in Nuclear Power

This report is concerned with the escalation of capital costs of nuclear central station power plants between the early 1960s and the present. The report presents an historical overview of the development of the nuclear power industry and cost escalation in the industry, using existing data on orders and capital costs. New data are presented on regulatory delays in the licensing process, derived from a concurrent study being carried on in the Social Science group at Caltech. The conclusions of the study are that nuclear capital costs have escalated more rapidly than the GNP deflator or the construction industry price index. Prior to 1970, cost increases are related to bottleneck problems in the nuclear construction and supplying industries and the regulatory process; intervenors play only a minor role in cost escalation. After 1970, generic changes introduced into the licensing process by intervenors (including environmental impact reviews, antitrust reviews, more stringent safety standards) dominate the cost escalation picture, with bottlenecks of secondary importance. Recent increases in the time from application for a construction permit to commercial operation are related not only to intervenor actions, but also to suspensions, cancellations or postponements of construction by utilities due to unfavorable demand or financing conditions

Elliptic curves with a given number of points over finite fields

Given an elliptic curve $E$ and a positive integer $N$, we consider the problem of counting the number of primes $p$ for which the reduction of $E$ modulo $p$ possesses exactly $N$ points over $\mathbb F_p$. On average (over a family of elliptic curves), we show bounds that are significantly better than what is trivially obtained by the Hasse bound. Under some additional hypotheses, including a conjecture concerning the short interval distribution of primes in arithmetic progressions, we obtain an asymptotic formula for the average.Comment: A mistake was discovered in the derivation of the product formula for K(N). The included corrigendum corrects this mistake. All page numbers in the corrigendum refer to the journal version of the manuscrip

Toroidal Vortices in Resistive Magnetohydrodynamic Equilibria

Resistive steady states in toroidal magnetohydrodynamics (MHD), where Ohm's law must be taken into account, differ considerably from ideal ones. Only for special (and probably unphysical) resistivity profiles can the Lorentz force, in the static force-balance equation, be expressed as the gradient of a scalar and thus cancel the gradient of a scalar pressure. In general, the Lorentz force has a curl directed so as to generate toroidal vorticity. Here, we calculate, for a collisional, highly viscous magnetofluid, the flows that are required for an axisymmetric toroidal steady state, assuming uniform scalar resistivity and viscosity. The flows originate from paired toroidal vortices (in what might be called a ``double smoke ring'' configuration), and are thought likely to be ubiquitous in the interior of toroidally driven magnetofluids of this type. The existence of such vortices is conjectured to characterize magnetofluids beyond the high-viscosity limit in which they are readily calculable.Comment: 17 pages, 4 figure

Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field

Numerical studies of the effect of a dc magnetic field on dynamo action (development of magnetic fields with large spatial scales), due to helically-driven magnetohydrodynamic turbulence, are reported. The apparent effect of the dc magnetic field is to suppress the dynamo action, above a relatively low threshold. However, the possibility that the suppression results from an improper combination of rectangular triply spatially-periodic boundary conditions and a uniform dc magnetic field is addressed: heretofore a common and convenient computational convention in turbulence investigations. Physical reasons for the observed suppression are suggested. Other geometries and boundary conditions are offered for which the dynamo action is expected not to be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma

Mendelssohn in Performance by Siegwart Reichwald

Montgomery reviews and critiques Reichwald\u27s work

A Comparative Study of Barren County Schools 1938-1950

This study shows that the school census is dropping rapidly in rural areas. It must be remembered that with the introduction of more labor saving farm machinery and the consolidation of small farms that the end is not in sight. A greater percentage of children are enrolled in our schools. The percentage of attendance is higher and will continue to slowly improve. As consolidation of small schools progresses, school plants and physical equipment will improve. Over one-half of the children in average daily attendance are transported. Percentage of enrollment and percentage of attendance are much better in the transported group. The average number of college hours of teachers is less but a greater number have degrees. More children are taught by teachers of more training and experience. More teachers use modern teaching aids and devices than those a decade ago. Illiteracy of parents is less due to compulsory school attendance, increased subscription to newspapers and the almost universal presence of radios in the homes. Administration of our schools is not all corrupt; teachers are not all incompetent; children are being taught the same things by newer and improved methods and our school systems are doing excellent jobs despite many difficulties