A study of electric motors for use in liquid and gaseous helium Engineering report no. 3530

Electric motor design and operation in liquid and gaseous helium environment

The effect of varying strain-ratio on the hydraulic bulging behaviour of aluminium sheet

Annealed commercial-purity aluminium sheet was cold-rolled up to 32%, and the effect of this treatment on the strain-ratio (r) in various directions in the sheet plane was evaluated. Up to approximately 16% cold reduction ro, r454 and r901 remained approximately constant, while the average strain-ratio, r, showed no change. At cold reductions in excess of 16% ro, and rgo, fall steadily, while the fall in r4s, is less pronounced. Specimens were then 'electromarked' with an array of 0.1 in. dia. circles and bulged, using a pvc 'punch' technique. Plots of natural thickness strain (e) vs. bulge height (h max) show that, for a given height, the strain distribution is more even for an annealed material than for a cold-worked one, due to the effect of work-hardening. The relationship between polar thickness strain and uniaxial uniform elongation (eu) shows a discontinuity at about 10% eu and a further plot of h and r against eu suggests that this is associated with the change in strain-ratio. Thus, bulge height increases linearly with increasing uniform elongation at a constant strain-ratio, but in a more complex fashion with varying strain-ratio. Increased r gives decreased € at the pole, producing a more even strain distribution over the bulge

Three-manifold invariant from functional integration

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant

Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook

A crucial task in the analysis of on-line social-networking systems is to identify important people --- those linked by strong social ties --- within an individual's network neighborhood. Here we investigate this question for a particular category of strong ties, those involving spouses or romantic partners. We organize our analysis around a basic question: given all the connections among a person's friends, can you recognize his or her romantic partner from the network structure alone? Using data from a large sample of Facebook users, we find that this task can be accomplished with high accuracy, but doing so requires the development of a new measure of tie strength that we term `dispersion' --- the extent to which two people's mutual friends are not themselves well-connected. The results offer methods for identifying types of structurally significant people in on-line applications, and suggest a potential expansion of existing theories of tie strength.Comment: Proc. 17th ACM Conference on Computer Supported Cooperative Work and Social Computing (CSCW), 201

A Theorem on the origin of Phase Transitions

For physical systems described by smooth, finite-range and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that unless the equipotential hypersurfaces of configuration space \Sigma_v ={(q_1,...,q_N)\in R^N | V(q_1,...,q_N) = v}, v \in R, change topology at some v_c in a given interval [v_0, v_1] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (\beta(v_0), \beta(v_1)) also in the N -> \infty$limit. Thus the occurrence of a phase transition at some \beta_c =\beta(v_c) is necessarily the consequence of the loss of diffeomorphicity among the {\Sigma_v}_{v < v_c}$ and the {\Sigma_v}_{v > v_c}, which is the consequence of the existence of critical points of V on \Sigma_{v=v_c}, that is points where \nabla V=0.Comment: 10 pages, Statistical Mechanics, Phase Transitions, General Theory. Phys. Rev. Lett., in pres

Subcutaneous Leiomyosarcoma of the Frenulum

Leiomyosarcomas of the penis are rare, with only 29 reported cases to date. We record the case of a patient who presented with a 2-year history of a seemingly indolent penile skin lesion. On histopathology of the local resection, a diagnosis of subcutaneous leiomyosarcoma was made. Specifically, leiomyosarcoma of the penile frenulum has not been clearly reported previously. The patient underwent a further excision to ensure an adequate resection margin and has had no disease recurrence at subsequent follow-up. Our case was of a lesion that, although clinically benign, was malignant and this possibility should be borne in mind when assessing patients

Remarks on Legendrian Self-Linking

The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our definition is based upon a reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.Comment: 42 pages, many figures; v2: minor revisions, published versio