Routh reduction and the class of magnetic Lagrangian systems

In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after Routh reduction of Lagrangian systems with symmetry, so-called magnetic Lagrangian systems. We use these transformations in order to show that, under suitable conditions, the reduction with respect to a (full) semi-direct product group is equivalent to the reduction with respect to an Abelian normal subgroup. The results in this paper are closely related to the more general theory of Routh reduction by stages.Comment: 23 page

Routhian reduction for quasi-invariant Lagrangians

In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction of a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasi-cyclic coordinates. As an application we consider the dynamics of a charged particle in a magnetic field.Comment: 24 pages, 3 figure

A millimeter-wave antireflection coating for cryogenic silicon lenses

We have developed and tested an antireflection (AR) coating method for silicon lenses at cryogenic temperatures and millimeter wavelengths. Our particular application is a measurement of the cosmic microwave background. The coating consists of machined pieces of Cirlex glued to the silicon. The measured reflection from an AR coated flat piece is less than 1.5% at the design wavelength. The coating has been applied to flats and lenses and has survived multiple thermal cycles from 300 to 4 K. We present the manufacturing method, the material properties, the tests performed, and estimates of the loss that can be achieved in practical lenses

Point vortices on the sphere: a case with opposite vorticities

We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.Comment: 35 pages, 9 figure

Hamiltonian approach to hybrid plasma models

The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.Comment: 27 pages, no figures. To appear in J. Phys.

Changing stroke mortality trends in middle-aged people: an age-period-cohort analysis of routine mortality data in persons aged 40 to 69 in England

Background: In the UK, overall stroke mortality has declined. A similar trend has been seen in coronary heart disease, although recent reports suggest this decline might be levelling off in middle-aged adults. Aim: To investigate recent trends in stroke mortality among those aged 40–69 years in England. Methods: The authors used routine annual aggregated stroke death and population data for England for the years 1979–2005 to investigate time trends in gender-specific mortalities for adults aged 40 to 69 years. The authors applied log-linear modelling to isolate effects attributable to age, linear ‘drift’ over time, time period and birth cohort. Results; Between 1979 and 2005, age-standardised stroke mortality aged 40 to 69 years dropped from 93 to 30 per 100 000 in men and from 62 to 18 per 100 000 in women. Mortality was higher in older age groups, but the difference between the older and younger age groups appears to have decreased over time for both sexes. Modelling of the data suggests an average annual reduction in stroke deaths of 4.0% in men and 4.3% in women, although this decrease has been particularly marked in the last few years. However, we also observed a relative rate increase in mortality among those born since the mid-1940s compared with earlier cohorts; this appears to have been sustained in men, which explains the levelling off in the rate of mortality decline observed in recent years in the younger middle-aged. Conclusions: If observed trends in middle-aged adults continue, overall stroke mortalities may start to increase again

INTRA-RATER RELIABILITY OF THE MULTIPLE SINGLE-LEG HOP-STABILIZATION TEST AND RELATIONSHIPS WITH AGE, LEG DOMINANCE AND TRAINING.

BACKGROUND: Balance is a complex construct, affected by multiple components such as strength and co-ordination. However, whilst assessing an athlete's dynamic balance is an important part of clinical examination, there is no gold standard measure. The multiple single-leg hop-stabilization test is a functional test which may offer a method of evaluating the dynamic attributes of balance, but it needs to show adequate intra-tester reliability. PURPOSE: The purpose of this study was to assess the intra-rater reliability of a dynamic balance test, the multiple single-leg hop-stabilization test on the dominant and non-dominant legs. DESIGN: Intra-rater reliability study. METHODS: Fifteen active participants were tested twice with a 10-minute break between tests. The outcome measure was the multiple single-leg hop-stabilization test score, based on a clinically assessed numerical scoring system. Results were analysed using an Intraclass Correlations Coefficient (ICC2,1) and Bland-Altman plots. Regression analyses explored relationships between test scores, leg dominance, age and training (an alpha level of p = 0.05 was selected). RESULTS: ICCs for intra-rater reliability were 0.85 for the dominant and non-dominant legs (confidence intervals = 0.62-0.95 and 0.61-0.95 respectively). Bland-Altman plots showed scores within two standard deviations. A significant correlation was observed between the dominant and non-dominant leg on balance scores (R(2)=0.49, p<0.05), and better balance was associated with younger participants in their non-dominant leg (R(2)=0.28, p<0.05) and their dominant leg (R(2)=0.39, p<0.05), and a higher number of hours spent training for the non-dominant leg R(2)=0.37, p<0.05). CONCLUSIONS: The multiple single-leg hop-stabilisation test demonstrated strong intra-tester reliability with active participants. Younger participants who trained more, have better balance scores. This test may be a useful measure for evaluating the dynamic attributes of balance. LEVEL OF EVIDENCE: 3

Identification of Hemodynamically Optimal Coronary Stent Designs Based on Vessel Caliber

Coronary stent design influences local patterns of wall shear stress (WSS) that are associated with neointimal growth, restenosis, and the endothelialization of stent struts. The number of circumferentially repeating crowns NC for a given stent de- sign is often modified depending on the target vessel caliber, but the hemodynamic implications of altering NC have not previously been studied. In this investigation, we analyzed the relationship between vessel diameter and the hemodynamically optimal NC using a derivative-free optimization algorithm coupled with computational fluid dynamics. The algorithm computed the optimal vessel diameter, defined as minimizing the area of stent-induced low WSS, for various configurations (i.e., NC) of a generic slotted-tube design and designs that resemble commercially available stents. Stents were modeled in idealized coronary arteries with a vessel diameter that was allowed to vary between 2 and 5 mm. The results indicate that the optimal vessel diameter increases for stent configurations with greater NC, and the designs of current commercial stents incorporate a greater NC than hemodynamically optimal stent designs. This finding suggests that reducing the NC of current stents may improve the hemodynamic environment within stented arteries and reduce the likelihood of excessive neointimal growth and thrombus formation

Spacelike surfaces with free boundary in the Lorentz-Minkowski space

We investigate a variational problem in the Lorentz-Minkowski space \l^3 whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of spacelike hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit

Geometric, Variational Integrators for Computer Animation

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details