Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

From Earth to Orbit: An assessment of transportation options

The report assesses the requirements, benefits, technological feasibility, and roles of Earth-to-Orbit transportation systems and options that could be developed in support of future national space programs. Transportation requirements, including those for Mission-to-Planet Earth, Space Station Freedom assembly and operation, human exploration of space, space science missions, and other major civil space missions are examined. These requirements are compared with existing, planned, and potential launch capabilities, including expendable launch vehicles (ELV's), the Space Shuttle, the National Launch System (NLS), and new launch options. In addition, the report examines propulsion systems in the context of various launch vehicles. These include the Advanced Solid Rocket Motor (ASRM), the Redesigned Solid Rocket Motor (RSRM), the Solid Rocket Motor Upgrade (SRMU), the Space Shuttle Main Engine (SSME), the Space Transportation Main Engine (STME), existing expendable launch vehicle engines, and liquid-oxygen/hydrocarbon engines. Consideration is given to systems that have been proposed to accomplish the national interests in relatively cost effective ways, with the recognition that safety and reliability contribute to cost-effectiveness. Related resources, including technology, propulsion test facilities, and manufacturing capabilities are also discussed

Superconductors with Magnetic Impurities: Instantons and Sub-gap States

When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

Ultrasonic Flaw Detection in Turbine Rotor Component Web Geometries

Nondestructive detection of flaws in jet engine components is an essential part of assessing the integrity of the parts, and optimal design of experimental configurations is essential for high reliability detection. Due to the high cost of experimental evaluation, it would be highly desirable to accomplish this through the use of computer simulation of the detection/measurement process. This paper presents a first generation simulation model for the problem of ultrasonic detection of flaws in turbine rotor components. Included is the derivation of the model, the results of limited experimental validation of the software, and an example of its use to model the detection of penny shaped cracks in the plate-like geometry of a turbine rotor component web region

Human factors and missed solutions to Enigma design weaknesses

The German World War II Enigma suffered from design weaknesses that facilitated its large-scale decryption by the British throughout the war. The author shows that the main technical weaknesses (self-coding and reciprocal coding) could have been avoided using simple contemporary technology, and therefore the true cause of the weaknesses is not technological but must be sought elsewhere. Specifically, human factors issues resulted in the persistent failure to seek out more effective designs. Similar limitations seem to beset the literature on the period, which misunderstands the Enigma weaknesses and therefore inhibits broader thinking about design or realising the critical role of human factors engineering in cryptography

Ecology good, aut-ecology better; Improving the sustainability of designed plantings

© 2015 European Council of Landscape Architecture Schools (ECLAS). This paper explores how contemporary ecological science, and aut-ecology in particular, can improve the sustainability of designed vegetation. It is proposed that ecological understanding can be applied to design at three levels: 1) as representation, 2) as process, and 3) as aut-ecology, representing a gradient from the least to the most profound. Key ecological interactions that determine the success of designed plantings are explored via a review of relevant ecological research, challenging some widely held but unhelpful constructs about how both semi-natural and designed vegetation actually function. The paper concludes that there are real benefits to integrating aut-ecological understanding in the design of vegetation at all scales but that this will require ecological theory to be taught as a design toolkit rather than largely as descriptive knowledge

Care in the time of catastrophe: citizenship, community and the ecological imagination

Published without an abstract