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

Three-dimensional molecular dynamics simulations of void coalescence during dynamic fracture of ductile metals

Void coalescence and interaction in dynamic fracture of ductile metals have been investigated using three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. The interaction of the voids is not reflected in the volumetric asymptotic growth rate of the voids, as demonstrated here. Finally, the practice of using a single void and periodic boundary conditions to study coalescence is examined critically and shown to produce results markedly different than the coalescence of a pair of isolated voids.Comment: Accepted for publication in Physical Review

3D FEA modelling of laminated composites in bending and their failure mechanisms

keywords: 3D keywords: 3D keywords: 3D keywords: 3D keywords: 3DAbstract This paper developed three-dimensional (3D) Finite Element Analysis (FEA) to investigate the effect of fibre lay-up on the initiation of failure of laminated composites in bending. Tsai-Hill failure criterion was applied to identify the critical areas of failure in composite laminates. In accordance with the 3D FEA, unidirectional ([0]16), cross-ply ([0/90]4s) and angle-ply ([±45]4s) laminates made up of pre-preg Carbon Fibre Reinforced Plastics (CFRP) composites were manufactured and tested under three-point bending. The basic principles of Classical Laminate Theory (CLT) were extended to three-dimension, and the analytical solution was critically compared with the FEA results. The 3D FEA results revealed significant transverse normal stresses in the cross-ply laminate and in-plane shear stress in the angle-ply laminate near free edge regions which are overlooked by conventional laminate model. The microscopic images showed that these free edge effects were the main reason for stiffness reduction observed in the bending tests. The study illustrated the significant effects of fibre lay-up on the flexural failure mechanisms in composite laminates which lead to some suggestions to improve the design of composite laminates

Cellular buckling from mode interaction in I-beams under uniform bending

Beams made from thin-walled elements, whilst very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on variational principles for the ubiquitous I-beam with thin flanges under uniform bending is presented. The resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post-buckling range can be portrayed. The interaction between global lateral-torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling (snaking) being predicted theoretically for the first time. Solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling.Comment: 23 pages, 15 figures and 6 table

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

Experimental Observations of Frictional Heating in Fiber-Reinforced Ceramics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65540/1/j.1151-2916.1992.tb04162.x.pd

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

Legitimizing leisure experiences as emotional work: A post-humanist approach to gendered equine encounters

** From Crossref via Jisc Publications Router. ** Licence for VoR version of this article starting on 08-06-2018: http://onlinelibrary.wiley.com/termsAndConditions#vorThis is the peer reviewed version of the following article: Finkel, R. & Danby, P. (2018) Legitimizing leisure experiences as emotional work: A post-humanist approach to gendered equine encounters. Gender, Work & Organization, 26(3), pp. 377-391, which has been published in final form at https://doi.org/10.1111/gwao.12268. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.Due to changes in lifestyle and work patterns, education and values associated with wellbeing, non‐human animals are now incorporated into a range of human experiences and environments. This research specifically focuses on human–equine relations, examining blurred boundaries between therapeutic and recreational interspecies encounters. It is acknowledged that human–equine relations are often gendered and this research focuses mainly on women's narratives. Viewed through the post‐humanist lens, horses now form kinship and companionship roles, particularly for women, where relations have become mutually emotionally dependent as a result of interspecies communication and embodied encounters. Research utilizes feminist post‐humanist and cultural politics of emotion frameworks associate with the co‐agency on the co‐agency of animals. Embedded in the concept of equiscapes, or post‐humanist leisure spaces, research methods employ qualitative approaches, including in‐depth interviews, participant diaries and multispecies ethnography. Findings reveal how women make considerable investments in equine activities, which develops mutual welfare and wellbeing. Yet, despite these benefits, emotional and other expenditures are justified in work discourses to legitimize them as valuable to themselves, their families and their communities.div_BaM26pub5397pub

Enhancement of wave damping within metamaterials having embedded negative stiffness inclusions

The wave dissipation properties of layered periodic structures are modelled by FE as well as analytical approaches. A linear oscillator incorporating a negative stiffness element and having exceptional energy dissipation properties is exhibited and incorporated within the modelled structures. The structural dynamic stability of both the oscillator and the modelled waveguides is discussed and ensured. The numerical results provide evidence of a drastic increase of several orders of magnitude for the damping ratio of the flexural waves propagating within the structures