Numerical solutions of a boundary value problem on the sphere using radial basis functions

Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article, we construct numerical solutions to a boundary value problem defined on a spherical sub-domain (with a sufficiently smooth boundary) using radial basis functions (RBF). The error analysis between the exact solution and the approximation is provided. Numerical experiments are presented to confirm theoretical estimates

Computer code for the prediction of nozzle admittance

A procedure which can accurately characterize injector designs for large thrust (0.5 to 1.5 million pounds), high pressure (500 to 3000 psia) LOX/hydrocarbon engines is currently under development. In this procedure, a rectangular cross-sectional combustion chamber is to be used to simulate the lower traverse frequency modes of the large scale chamber. The chamber will be sized so that the first width mode of the rectangular chamber corresponds to the first tangential mode of the full-scale chamber. Test data to be obtained from the rectangular chamber will be used to assess the full scale engine stability. This requires the development of combustion stability models for rectangular chambers. As part of the combustion stability model development, a computer code, NOAD based on existing theory was developed to calculate the nozzle admittances for both rectangular and axisymmetric nozzles. This code is detailed

A Traditional and Textualist Analysis of the Goals of Antitrust: Efficiency, Preventing Theft from Consumers, and Consumer Choice

This Article ascertains the overall purpose of the antitrust statutes in two very different ways. First, it performs a traditional analysis of the legislative history of the antitrust laws by analyzing relevant legislative debates and committee reports. Second, it undertakes a textualist or “plain meaning” analysis of the purpose of the antitrust statutes, using Justice Scalia’s methodology. It does this by analyzing the meaning of key terms as they were used in contemporary dictionaries, legal treatises, common law cases, and the earliest U.S. antitrust cases, and it does this in light of the history of the relevant times. Both approaches demonstrate that the overriding purpose of the antitrust statutes is to prevent firms from stealing from consumers by charging them supracompetitive prices. When firms use their market power to raise prices to supracompetitive levels, purchasers pay more for their goods and services, and these overcharges constitute a taking of purchasers’ property. Economic efficiency was only a secondary concern. In addition, the textualist approach leads to the surprising conclusion that neither the Sherman Act nor the Clayton Act contain an exception for monopolies attained by efficient business conduct. A “plain meaning” analysis of the antitrust statutes reveals that they are supposed to prevent and condemn all privately created monopolies

A practical degradation based method to predict long-term moisture incursion and colour change in high power LEDs

The effect of relative humidity on LEDs and how the moisture incursion is associated to the color shift is studied. This paper proposes a different approach to describe the lumen degradation of LEDs due to the long-term effects of humidity. Using the lumen degradation data of different types of LEDs under varying conditions of relative humidity, a humidity based degradation model (HBDM) is developed. A practical estimation method from the degradation behaviour is proposed to quantitatively gauge the effect of moisture incursion by means of a humidity index. This index demonstrates a high correlation with the color shift indicated by the LED's yellow to blue output intensity ratio. Physical analyses of the LEDs provide a qualitative validation of the model, which provides good accuracy with longer periods of moisture exposure. The results demonstrate that the HBDM is an effective indicator to predict the extent of the long-term impact of humidity and associated relative color shift