A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.co

Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder, A. Deza, and A. Ivic Weiss (eds), Springe

Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space

Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions

We present a systematic approach to studying the geometric aspects of Vinberg theta-representations. The main idea is to use the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles. Our main technical tool is to use free resolutions as an "enhanced" version of degeneracy loci formulas. We illustrate our approach on several examples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.Comment: 41 pages, uses tabmac.sty, Dedicated to David Eisenbud on the occasion of his 65th birthday; v2: fixed some typos and added reference

Calabi-Yau Duals of Torus Orientifolds

We study a duality that relates the T^6/Z_2 orientifold with N=2 flux to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T^4) fibrations over P^1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H_1(X,Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description. The analysis is facilitated by the existence of an explicit Calabi-Yau metric on an open subset of the geometry that becomes an arbitrarily good approximation to the actual metric (at most points) in the limit that the fiber is much smaller than the base.Comment: 39 pages; uses harvmac.tex, amssym.tex; v4: minor correction

Tackling bovine TB

On 18 December Defra revealed that during 2018, 32,601 badgers were killed, bringing the total number slaughtered under licence since 2013 to almost 67,000.1 ‘Effectiveness’ claims relate not to the impact on cattle TB, but rather to the ability of the contracted shooters to kill sufficient badgers to satisfy their licence requirements, which they can hardly fail to reach given that target numbers are ‘adjusted’ by Natural England part-way through the culls according to the contractors’ progress. Sixty per cent of the badgers have been killed by ‘controlled shooting’, a method rejected by both the government’s Independent Expert Panel2 and the BVA3 because of animal welfare concerns. During 2018 Natural England directly monitored just 89 (0.43 per cent) of controlled shooting events. It is deplorable that the chief veterinary officer (CVO) continues to support the roll-out of a policy that permits controlled shooting, when veterinary organisations have condemned the method on animal welfare grounds. It is particularly concerning that the CVO appears to have deflected responsibility for humaneness to Natural England’s chief scientist who, as far as we are aware, has no background in animal welfare science. It is also unacceptable for government to attribute reductions in herd bovine TB (bTB) incidents over the first four years of culling in the original ‘pilot’ cull zones to its badger culling policy.4 Independent analysis of this and more recent data from the Gloucestershire pilot cull zone5 indicate that new herd incidence is rising sharply, with 22 herd breakdowns in the 12 months to September 2017 (an increase of 29.4 per cent when compared to the 17 breakdowns reported by APHA for the previous 12 months). Analysis of the 2018 figures indicates that both incidence and prevalence are now rising even faster, with a further 24 herd breakdowns occurring between 1 January and 5 December 2018. To date, the government and its officials cite data that are two years out of date, but have declined to comment on this emerging evidence that, far from resulting in a substantial disease control benefit, badger culls may be leading to a sharp increase in bTB in cattle. Natural England’s chief scientist and the UK’s CVO continue to endorse a failing and inhumane policy, bringing their offices into serious disrepute. We urge them, and the BVA, to reconsider their support for further badger culling, and instead focus on the actual cause of bTB’s epidemic spread – a cattle skin test with a sensitivity of only 50 per cent,6,7 and the ongoing problems associated with cattle movements and on-farm biosecurity

A multicentre, randomised, double-blind, single-dose study assessing the efficacy of AMC/DCBA Warm lozenge or AMC/DCBA Cool lozenge in the relief of acute sore throat

<p>Abstract</p> <p>Background</p> <p>Clinically proven over-the-counter (OTC) treatment options are becoming increasingly important in the self-management of acute sore throat. The aim of this study was to determine the analgesic and sensorial benefits of two different amylmetacresol/2,4-dichlorobenzyl alcohol (AMC/DCBA) throat lozenge formulation variants, AMC/DCBA Warm lozenge and AMC/DCBA Cool lozenge, compared with an unflavoured, non-medicated placebo lozenge in the relief of acute sore throat due to upper respiratory tract infections.</p> <p>Methods</p> <p>In this multicentre, randomised, double-blind, single-dose study, 225 adult patients with acute sore throat were randomly assigned to receive either one AMC/DCBA Warm lozenge (n = 77), one AMC/DCBA Cool lozenge (n = 74) or one unflavoured, non-medicated lozenge (matched for size, shape and demulcency; n = 74). After baseline assessments, patients received their assigned lozenge and completed four rating assessments at 11 timepoints from 1 to 120 minutes post dose. Analgesic properties were assessed by comparing severity of throat soreness and sore throat relief ratings. Difficulty in swallowing, throat numbness, functional, sensorial and emotional benefits were also assessed.</p> <p>Results</p> <p>Both the AMC/DCBA Warm and AMC/DCBA Cool lozenge induced significant analgesic, functional, sensorial and emotional effects compared with the unflavoured, non-medicated lozenge. Sore throat relief, improvements in throat soreness and difficulty in swallowing, and throat numbness were observed as early as 1-5 minutes, and lasted up to 2 hours post dose. Sensorial benefits of warming and cooling associated with the AMC/DCBA Warm and AMC/DCBA Cool lozenge, respectively, were experienced soon after first dose, and in the case of the latter, it lasted long after the lozenge had dissolved. Emotional benefits of feeling better, happier, less distracted and less frustrated were reported in those taking either of the AMC/DCBA throat lozenge variants, with no differences in adverse events compared with the unflavoured, non-medicated lozenge.</p> <p>Conclusions</p> <p>AMC/DCBA Warm and AMC/DCBA Cool lozenges are well-tolerated and effective OTC treatment options, offering functional, sensorial and emotional benefits to patients with acute sore throat, over and above that of the rapid efficacy effects provided.</p> <p>Trial registration</p> <p>ISRCTN: <a href="http://www.controlled-trials.com/ISRCTN00003567">ISRCTN00003567</a></p