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

Separable Externalities in Cost and Production Functions

The characterization of external effects as “separable” has played an important role in the development of the theory of externalities. The separable case is particularly well behaved when procedures for achieving an optimum allocation of resources in the presence of externalities are examined. Davis and Whinston (1962) find that separability assures the existence of a certain kind of equilibrium in bargaining between firms which create externalities, and that equilibrium does not exist without separability. Kneese and Bower (1968) argue that with separability the computation of Pigovian taxes to remedy externalities is particularly simple. Marchand and Russell (1974) demonstrate that certain liability rules regarding external effects lead to Pareto optimal outcomes if and only if externalities are separable. In each of these cases the problem is posed in terms of two firms related by technological externalities, and separability is defined in terms of a cost function. In this paper, we will characterize that class of production functions which give rise to separable cost functions, and show that the relation between production functions and separable cost functions is by no means as trivial as has been claimed

A Case Study of Regulatory Programs of the Federal Energy Administration

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Stability of Pure Trade Equilibrium with Externalities

Sufficient conditions for the stability of competitive equilibrium in a pure trade economy with externalities are developed in this paper. Externalities are introduced through the assumption that each individual's utility depends on the consumption of every other individual. A two-level adjustment process is postulated. At fixed prices, individual strategies must be made mutually consistent. Each individual's strategy is stated as a relation which maps prices and the demands of all other individuals into the demand of that individual. The equilibrium of the externality adjustment process is a demand allocation, depending on price, which is feasible and maximizes utility for each individual at given prices. Sufficient conditions for stability of the externality adjustment process are proved and interpreted. The equilibrium demand functions are then used in a tatonnement process to investigate the stability of competitive equilibrium. All the standard theorems on excess demand functions which give sufficient conditions for stability apply to the equilibrium demand functions of an economy with externalities. It is established that the stability properties of an economy without externalities possess a certain type of continuity. Any sequence of economies with externalities which converges in the proper sense to an economy without externalities characterized by gross substitutability has the property that for all t > T the competitive equilibrium of the economy with externalities is stable. Weaker stability conditions on the limit economy can make this theorem fail

Separability and vanishing externalities

In one of the most influential papers written on the subject of externalities, Otto Davis and Andrew Whinston argue that corrective taxes and private bargaining are likely to achieve an optimum in the presence of mutual externalities between two firms only when externalities are separable, in the sense that marginal cost is independent of the level of externality. Further analysis of the concept of separability reveals that even this conclusion is too optimistic. I shall argue below that the assumptions needed to make taxes and negotiations work properly rule out the possibility of having externalities in any observable situation

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