Random waves on T3\mathbb{T}^3: nodal area variance and lattice point correlations

We consider the ensemble of random Gaussian Laplace eigenfunctions on $\mathbb{T}^3=\mathbb{R}^3/\mathbb{Z}^3$ (`$3d$ arithmetic random waves'), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or `energy', of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.Comment: To appear in IMR

Physical insight into the simultaneous optimization of structure and control

Recent trends in spacecraft design which yield larger structures with more stringent performance requirements place many flexible modes of the structure within the bandwidth of active controllers. The resulting complications to the spacecraft design make it highly desirable to understand the impact of structural changes on an optimally controlled structure. This work uses low structural models with optimal H(sub 2) and H(sub infinity) controllers to develop some basic insight into this problem. This insight concentrates on several basic approaches to improving controlled performance and how these approaches interact in determining the optimal designs. A numerical example is presented to demonstrate how this insight can be generalized to more complex problems

The correlation between water production rates and visual magnitudes in comets

From the visual magnitudes of the International Comet Quarterly data base and the OH radio lines measured at the Nancay radio telescope, the law log Q(H2O) = 30.74 (+/-0.02) - 0.240 (+/-.003) m(sub h) is derived from a sample of 13 comets

Singe ferroelectric and chiral magnetic domain of single-crystalline BiFeO3_3 in an electric field

We report polarized neutron scattering and piezoresponse force microscopy studies of millimeter-sized single crystals of multiferroic BiFeO$_3$. The crystals, grown below the Curie temperature, consist of a single ferroelectric domain. Two unique electric polarization directions, as well as the populations of equivalent spiral magnetic domains, can be switched reversibly by an electric field. A ferroelectric monodomain with a single-$q$ single-helicity spin spiral can be obtained. This level of control, so far unachievable in thin films, makes single-crystal BiFeO$_3$ a promising object for multiferroics research.Comment: 4 figures in separate jpg file

Amy and Vicky\u27s Cause: Perils of the Federal Restitution Framework for Child Pornography Victims

Child pornography is unique among violent crimes in atleast one aspect: victims are harmed not only from their initial abuse but also from knowing that people on theInternet continue to view the images. In recent years, asplit has arisen among federal courts on whether victimsof child pornography are entitled to restitution from non-production offenders, i.e., offenders that were not involvedin the initial abuse of victims. The controversy hassurrounded 18 U.S.C. § 2259-the mandatory restitutionstatute for sex offenses. While some courts find victimharm not sufficiently traceable to the crimes at issue togrant restitution, other courts emphasize Congress\u27s intentto compensate victims in ordering restitution. Theproblem with restitution in the child pornography context,however, is deeper than just interpreting § 2259 for non-production offenses. This Note suggests that a mandatoryfine for non-production offenders would alleviate not onlythe causality problem but also other issues plaguing therestitution framework

Sustainable product development strategies: Business planning and performance implications

Copyright © 2012 by Institution of Mechanical Engineers. This is the author's accepted manuscript. The final published article is available from the link below.Manufacturing firms are under many financial and competitive pressures which focus attention on the performance of their manufacturing processes. In this paper the opportunities for improving the environmental impact of products within the constraints of existing manufacturing infrastructure are examined. Approaches which support sustainability in two aspects are proposed, firstly, the provision of products to the users in ways which extend the product life and secondly, manufacturing approaches which reduce resource usage. This paper outlines three different sustainable development strategies for different product types and describes the cost implications for manufacturers across the life-cycle. The performance measures affected by these strategies are examined drawing on product development case studies from a number of high technology sectors to highlight the different approaches taken. The results are intended to aid manufacturers during the earliest stages of business planning to consider alternative product development approaches which are more sustainable