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

Low Frequency Scattering by a Planar Crack

The detection of cracks with the aid of ultrasonics is an important nondestructive evaluation technique. The corresponding theoretical problem of the scattering of elastic waves by cracks has attracted considerable attention. Scattering of time harmonic plane wave by an isolated two dimensional Griffith, or an penny-shaped crack in an unbounded elastic medium has been studied extensively. However, studies of the scattering problem by a three dimensional crack other than circular shape have been rather limited. Few studies of scattering from an elliptical crack in an elastic body of infinite extent can be found in the literature. Datta[1] studied the problem using the method of matched asymptotic expansion. Gubernatis et al. [2] and Budiansky and O’Connell [3] have used the elastostatic approximation to determine the scattered field. The backscattered field from an elliptical crack has been obtained by Kino [4] in the low frequency limit by a formula derived from elastodynamic reciprocity theorem. An integro-differential equation technique was employed by Roy [5]–[6] to study the same problem.</p

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

The Interaction of Failure Modes in the Compression Response and Failure of Laminated Composites

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97075/1/AIAA2012-1895.pd

Modeling the large inelastic deformation response of non-filled and silica filled SL5170 cured resin

In recent years, important efforts have been focused on rapid production of tools using Rapid Prototyping and Manufacturing (RP&M) technologies such as the Stereo-Lithography Apparatus (SLA). One of the applications is the development of rapid polymer tooling such as dies for injection molding. For these applications, optimal thermal as well as mechanical properties of final tools are of significance. In order to characterize the mechanical response of materials made by SLA, a standard set of material tests, including uniaxial tension and compression tests under different strain rates and different temperatures, was conducted for both silica filled and non-filled resin. In this paper, the mechanical response of the non-filled SL5170 cured resin is discussed in terms of an elastic-viscoplastic material model. Further, a new model for silica filled SL5170 cured resin was developed to estimate the stress-strain relationship of the composite. This composite model is an extension of the elastic-viscoplastic model for non-filled resin to include the elastic deformation of the silica particles. The stress-strain curves predicted by the models under homogeneous deformation show good agreement with the experimental results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44781/1/10853_2005_Article_903.pd