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.

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.

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

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.

Total syntheses of conformationally-locked difluorinated pentopyranose analogues and a pentopyranosyl phosphate mimetic

Trifluoroethanol has been elaborated, via a telescoped sequence involving a metalated difluoroenol, a difluoroallylic alcohol, [2,3]-Wittig rearrangement, and ultimately an RCM reaction and requiring minimal intermediate purification, to a number of cyclooctenone intermediates. Epoxidation of these intermediates followed by transannular ring opening or dihydroxylation, then transannular hemiacetalization delivers novel bicyclic analogues of pentopyranoses, which were elaborated (in one case) to an analogue of a glycosyl phosphate

Recovering the stationary phase condition for accurately obtaining scattering and tunneling times

The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl

Isotropic and Anisotropic Regimes of the Field-Dependent Spin Dynamics in Sr2IrO4: Raman Scattering Studies

A major focus of experimental interest in Sr2IrO4 has been to clarify how the magnetic excitations of this strongly spin-orbit coupled system differ from the predictions of anisotropic 2D spin-1/2 Heisenberg model and to explore the extent to which strong spin-orbit coupling affects the magnetic properties of iridates. Here, we present a high-resolution inelastic light (Raman) scattering study of the low energy magnetic excitation spectrum of Sr2IrO4 and doped Eu-doped Sr2IrO4 as functions of both temperature and applied magnetic field. We show that the high-field (H>1.5 T) in-plane spin dynamics of Sr2IrO4 are isotropic and governed by the interplay between the applied field and the small in-plane ferromagnetic spin components induced by the Dzyaloshinskii-Moriya interaction. However, the spin dynamics of Sr2IrO4 at lower fields (H<1.5 T) exhibit important effects associated with interlayer coupling and in-plane anisotropy, including a spin-flop transition at Hc in Sr2IrO4 that occurs either discontinuously or via a continuous rotation of the spins, depending upon the in-plane orientation of the applied field. These results show that in-plane anisotropy and interlayer coupling effects play important roles in the low-field magnetic and dynamical properties of Sr2IrO4.Comment: 8 pages, 4 figures, submitte

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.