Relative Geodesics in the Special Euclidean Group

We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of discrepancy is given as follows. A curve of transformations in the special Euclidean group SE(2) is said to be admissible if it maps the source curve to the target curve under the point-wise action of SE(2) on the plane. After endowing the group SE(2) with a left-invariant metric, we define a relative geodesic in SE(2) to be a critical point of the energy functional associated to the metric, over all admissible curves. The discrepancy is then defined as the value of the energy of the minimizing relative geodesic. In the first part of the paper, we derive a scalar ODE which is a necessary condition for a curve in SE(2) to be a relative geodesic, and we discuss some of the properties of the discrepancy. In the second part of the paper, we consider discrete curves, and by means of a variational principle, we derive a system of discrete equations for the relative geodesics. We finish with several examples

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

The structure of epitaxial V2O3 films and their surfaces : a medium energy ion scattering study

Medium energy ion scattering, using 100 keV H+ incident ions, has been used to investigate the growth of epitaxial films, up to thicknesses of ~200 Å, of V2O3 on both Pd(111) and Au(111). Scattered-ion energy spectra provide a measure of the average film thickness and the variations in this thickness, and show that, with suitable annealing, the crystalline quality is good. Plots of the scattering yield as a function of scattering angle, so-called blocking curves, have been measured for two different incidence directions and have been used to determine the surface structure. Specifically, scattering simulations for a range of different model structures show poor agreement with experiment for half-metal (….V’O3V) and vanadyl (….V’O3V=O) terminations, with and without surface interlayer relaxations. However, good agreement with experiment is found for the modified oxygen-termination structure, first proposed by Kresse et al., in which a subsurface V half-metal layer is moved up into the outermost V buckled metal layer to produce a VO2 overlayer on the underlying V2O3, with an associated layer structure of ….O3VV’’V’O3

Long-term weight maintenance and cardiovascular risk factors are not different following weight loss on carbohydrate-restricted diets high in either monounsaturated fat or protein in obese hyperinsulinaemic men and women

The aim of this study was to determine after 52 weeks whether advice to follow a lower carbohydrate diet, either high in monounsaturated fat or low fat, high in protein had differential effects in a free-living community setting. Following weight loss on either a high monounsaturated fat, standard protein (HMF; 50 % fat, 20 % protein (67 g/d), 30 % carbohydrate) or a high protein, moderate fat (HP) (40 % protein (136 g/d), 30 % fat, 30 % carbohydrate) energy-restricted diet (6000 kJ/d) subjects were asked to maintain the same dietary pattern without intensive dietary counselling for the following 36 weeks. Overall weight loss was 6·2 (sd 7·3) kg (P < 0·01 for time with no diet effect, 7·6 (sd 8·1) kg, HMF v. 4·8 (sd 6·6) kg, HP). In a multivariate regression model predictors of weight loss at the end of the study were sex, age and reported percentage energy from protein (R2 0·22, P < 0·05 for the whole model). Fasting plasma insulin decreased (P < 0·01, with no difference between diets), 13·9 (sd 4·6) to 10·2 (sd 5·2) mIU/l, but fasting plasma glucose was not reduced. Neither total cholesterol nor LDL-cholesterol were different but HDL was higher, 1·19 (sd 0·26) v. 1·04 (sd 0·29) (P < 0·001 for time, no diet effect), while TAG was lower, 1·87 (sd 1·23) v. 2·22 (sd 1·15) mmol/l (P < 0·05 for time, no diet effect). C-reactive protein decreased (3·97 (sd 2·84) to 2·43 (sd 2·29) mg/l, P < 0·01). Food records showed that compliance to the prescribed dietary patterns was poor. After 1 year there remained a clinically significant weight loss and improvement in cardiovascular risk factors with no adverse effects of a high monounsaturated fat diet.Jennifer B. Keogh, Natalie D. Luscombe-Marsh, Manny Noakes, Gary A. Wittert and Peter M. Clifto

Noble gas films on a decagonal AlNiCo quasicrystal

Thermodynamic properties of Ne, Ar, Kr, and Xe adsorbed on an Al-Ni-Co quasicrystalline surface (QC) are studied with Grand Canonical Monte Carlo by employing Lennard-Jones interactions with parameter values derived from experiments and traditional combining rules. In all the gas/QC systems, a layer-by-layer film growth is observed at low temperature. The monolayers have regular epitaxial fivefold arrangements which evolve toward sixfold close-packed structures as the pressure is increased. The final states can contain either considerable or negligible amounts of defects. In the latter case, there occurs a structural transition from five to sixfold symmetry which can be described by introducing an order parameter, whose evolution characterizes the transition to be continuous or discontinuous as in the case of Xe/QC (first-order transition with associated latent heat). By simulating fictitious noble gases, we find that the existence of the transition is correlated with the size mismatch between adsorbate and substrate's characteristic lengths. A simple rule is proposed to predict the phenomenon.Comment: 19 pages. 8 figures. (color figures can be seen at http://alpha.mems.duke.edu/wahyu/ or http://www.iop.org/EJ/abstract/0953-8984/19/1/016007/

Composition profiles of InAs–GaAs quantum dots determined by medium-energy ion scattering

The composition profile along the [001] growth direction of low-growth-rate InAs–GaAs quantum dots (QDs) has been determined using medium-energy ion scattering (MEIS). A linear profile of In concentration from 100% In at the top of the QDs to 20% at their base provides the best fit to MEIS energy spectra

Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr_2GdCu_2O_8 studied by muon spin rotation (\mu SR) and DC-magnetization

We have investigated the magnetic and the superconducting properties of the hybrid ruthenate-cuprate compound RuSr_{2}GdCu_{2}O_{8} by means of zero-field muon spin rotation- (ZF-$\mu$SR) and DC magnetization measurements. The DC-magnetisation data establish that this material exhibits ferromagnetic order of the Ru-moments ($\mu (Ru) \approx 1 \mu_{B}$) below T_{Curie} = 133 K and becomes superconducting at a much lower temperature T_c = 16 K. The ZF-$\mu$SR experiments indicate that the ferromagnetic phase is homogeneous on a microscopic scale and accounts for most of the sample volume. They also suggest that the magnetic order is not significantly modified at the onset of superconductivity.Comment: improved version submitted to Phys. Rev.

Haemoglobin mass and running time trial performance after recombinant human erythropoietin administration in trained men

&lt;p&gt;Recombinant human erythropoietin (rHuEpo) increases haemoglobin mass (Hbmass) and maximal oxygen uptake (v˙ O2 max).&lt;/p&gt; &lt;p&gt;Purpose: This study defined the time course of changes in Hbmass, v˙ O2 max as well as running time trial performance following 4 weeks of rHuEpo administration to determine whether the laboratory observations would translate into actual improvements in running performance in the field.&lt;/p&gt; &lt;p&gt;Methods: 19 trained men received rHuEpo injections of 50 IUNkg21 body mass every two days for 4 weeks. Hbmass was determined weekly using the optimized carbon monoxide rebreathing method until 4 weeks after administration. v˙ O2 max and 3,000 m time trial performance were measured pre, post administration and at the end of the study.&lt;/p&gt; &lt;p&gt;Results: Relative to baseline, running performance significantly improved by ,6% after administration (10:3061:07 min:sec vs. 11:0861:15 min:sec, p,0.001) and remained significantly enhanced by ,3% 4 weeks after administration (10:4661:13 min:sec, p,0.001), while v˙ O2 max was also significantly increased post administration (60.765.8 mLNmin21Nkg21 vs. 56.066.2 mLNmin21Nkg21, p,0.001) and remained significantly increased 4 weeks after rHuEpo (58.065.6 mLNmin21Nkg21, p = 0.021). Hbmass was significantly increased at the end of administration compared to baseline (15.261.5 gNkg21 vs. 12.761.2 gNkg21, p,0.001). The rate of decrease in Hbmass toward baseline values post rHuEpo was similar to that of the increase during administration (20.53 gNkg21Nwk21, 95% confidence interval (CI) (20.68, 20.38) vs. 0.54 gNkg21Nwk21, CI (0.46, 0.63)) but Hbmass was still significantly elevated 4 weeks after administration compared to baseline (13.761.1 gNkg21, p&#60;0.001).&lt;/p&gt; &lt;p&gt;Conclusion: Running performance was improved following 4 weeks of rHuEpo and remained elevated 4 weeks after administration compared to baseline. These field performance effects coincided with rHuEpo-induced elevated v˙ O2 max and Hbmass.&lt;/p&gt