Thermodynamics of Solitonic Matter Waves in a Toroidal Trap

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.Comment: 4 pages, 4 figures, to be published in Physical Review A as a Rapid Communication. Related papers can be found at http://www.padova.infm.it/salasnich/tdqg.htm

Remedies for Price Overcharges: The Deadweight Loss of Coupons and Discounts

This article evaluates two different remedies for consumers who have been injured by a price overcharge on the sale of a good. Under a coupon remedy, injured consumers are awarded coupons that can be used for a limited period of time to purchase the good at a price below that which prevails after the overcharge has been eliminated, that is, below the competitive price. Under a discount remedy, any consumer, without proof of injury, may purchase the good for a limited period of time at a price that is set below the competitive price. Both remedies generally cause consumers to buy an excessive amount of the good during the remedy period. Under the coupon remedy only a subset of consumers are affected in this way (those holding a relatively high number of coupons), while under the discount remedy all consumers are affected. We show nonetheless that the resulting deadweight loss could be lower under the discount remedy. We also consider how the deadweight loss changes when the length of the remedy period is increased by extending the expiration date for the use of coupons or by employing a lower discount for a longer period of time. The deadweight loss may or may not decline under the coupon remedy, though it does decline under the discount remedy. In neither case, however, does it go to zero in the limit.

The Welfare Implications of Costly Litigation in the Theory of Liability

One of the principal results in the economic theory of liability is that, assuming litigation is costless, the rule of strict liability with compensatory damages leads the injurer to choose the socially appropriate level of care. This paper reexamines this result when litigation is costly. It is shown that strict liability with compensatory damages generally leads to a socially inappropriate level of care and to excessive litigation costs. Social welfare can be increased by adjusting compensatory damages upward or downward, with the desired direction depending on the effect of changes in the level of liability on the injurer's decision to take care and on the victim's decision to bring suit.

Optimal Awards and Penalties when the Probability of Prevailing Varies Among Plaintiffs

This article derives the optimal award to a winning plaintiff and the optimal penalty on a losing plaintiff when the probability of prevailing varies among plaintiffs. Optimality is defined in terms of achieving a specified degree of deterrence of potential injurers with the lowest litigation cost. Our main result is that the optimal penalty on a losing plaintiff is positive, in contrast to common practice in the United States. By penalizing losing plaintiffs and raising the award to winning plaintiffs (relative to what it would be if losing plaintiffs were not penalized), it is possible to discourage relatively low-probability-of-prevailing plaintiffs from suing without discouraging relatively high-probability plaintiffs, and thereby to achieve the desired degee of deterrence with lower litigation costs. This result is developed first in a model in which all suits are assumed to go to trial and then in a model in which settlements are possible.

A Damage-Revelation Rationale for Coupon Remedies

This article studies optimal remedies in a setting in which damages vary among plaintiffs and are difficult to determine. We show that giving plaintiffs a choice between cash and coupons to purchase units of the defendant's product at a discount -- a "coupon-cash remedy" -- is superior to cash alone. The optimal coupon-cash remedy offers a cash amount that is less than the value of the coupons to plaintiffs who suffer relatively high harm. Such a remedy induces these plaintiffs to choose coupons, and plaintiffs who suffer relatively low harm to choose cash. Sorting plaintiffs in this way leads to better deterrence because the costs borne by defendants (the cash payments and the cost of providing coupons) more closely approximate the harms that they have caused.

Remedies for Price Overcharges: The Deadweight Loss of Coupons and Discounts

This article evaluates two different remedies for consumers who have been injured by a price overcharge on the sale of a good. Under a coupon remedy, injured consumers are awarded coupons that can be used for a limited period of time to purchase the good at a price below that which prevails after the overcharge has been eliminated, that is, below the competitive price. Under a discount remedy, any consumer, without proof of injury, may purchase the good for a limited period of time at a price that is set below the competitive price. Both remedies generally cause consumers to buy an excessive amount of the good during the remedy period. Under the coupon remedy only a subset of consumers are affected in this way (those holding a relatively high number of coupons), while under the discount remedy all consumers are affected. We show nonetheless that the resulting deadweight loss could be lower under the discount remedy. We also consider how the deadweight loss changes when the length of the remedy period is increased.

Optimization of controlled environments for hydroponic production of leaf lettuce for human life support in CELSS

A research project in the food production group of the Closed Ecological Life Support System (CELSS) program sought to define optimum conditions for photosynthetic productivity of a higher plant food crop. The effects of radiation and various atmospheric compositions were studied

Archetypal analysis of galaxy spectra

Archetypal analysis represents each individual member of a set of data vectors as a mixture (a constrained linear combination) of the pure types or archetypes of the data set. The archetypes are themselves required to be mixtures of the data vectors. Archetypal analysis may be particularly useful in analysing data sets comprising galaxy spectra, since each spectrum is, presumably, a superposition of the emission from the various stellar populations, nebular emissions and nuclear activity making up that galaxy, and each of these emission sources corresponds to a potential archetype of the entire data set. We demonstrate archetypal analysis using sets of composite synthetic galaxy spectra, showing that the method promises to be an effective and efficient way to classify spectra. We show that archetypal analysis is robust in the presence of various types of noise.Comment: 6 pages, 5 figures, 1 style-file. Accepted for publication by MNRA