Principles of Discrete Time Mechanics: IV. The Dirac Equation, Particles and Oscillons

We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.Comment: 27 pages LateX; published versio

Latino Destinations and Environmental Inequality: Estimated Cancer Risk from Air Toxics in Latino Traditional and New Destinations

Since the 1990s, Latino migration patterns have shifted from traditional destinations to new destinations away from the Mexico border. Scholars note disparities between destinations in housing, crime, and health care, yet no study has examined environmental inequalities. In this article we employ theories of spatial assimilation and environmental inequality to evaluate health risks across Latino destinations by asking the question, is there a difference in estimated cancer risk from air toxics among established, new, and nondestination locations? Using county-level data with spatial lag regression analyses, we find that early new destinations (i.e., counties with significant Latino growth from 1990 to 2000) and recent new destinations (i.e., counties with significant Latino growth from 1990 to 2010) have higher estimated cancer risk from air toxics than established destinations (i.e., counties at or greater than the national average of Latinos in 1990) and nondestinations. The effect remains significant when controlling for various economic indicators

Intensity measurements on RHEED patterns from the silicon (001) surface

Imperial Users onl

A Preliminary Study of Airplane Performance

Flight tests were carried out at the Langley Field laboratory of the NACA, on several airplanes for the purpose of determining their relative performance with the same engine and the same propeller. The method used consisted in flying each airplane on a level course and measuring the airspeed for the whole range of engine revolutions. In general the results show that a small change in the wing section or the wing area has but a slight effect upon the performance, but changes in those parts which cause the structural resistance have a very important effect

An Internet-Based Tool for Weather Risk Management

This paper introduces a web-based computer program designed to evaluate weather risk man-agement and weather insurance in the United States. The paper outlines the economics of weather risk in terms of agricultural production and household well-being; defines weather risk in terms of intensity, duration, and frequency; and illustrates the computer program use by comparing heat and precipitation risks at Ardmore, Oklahoma, and Ithaca, New York.weather insurance, heat insurance, precipitation insurance, crop insurance, weather derivatives, Risk and Uncertainty,

Self-recording portable soil penetrometer

A lightweight portable penetrometer for testing soil characteristics is described. The penetrometer is composed of a handle, data recording, and probe components detachably joined together. The data recording component has an easily removed recording drum which rotates according to the downward force applied on the handle, and a stylus means for marking the drum along its height according to the penetration depth of probe into the soil

ESTIMATING THE EFFECTS OF PESTICIDE USE ON BURLEY AND FLUE-CURED TOBACCO

Crop Production/Industries,