Solid-solid phase transition in hard ellipsoids

We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [Phys. Rev. E, \textbf{75}, 020402 (2007)] showed that for aspect ratios $a/b\ge 3$ the previously suggested stretched-fcc phase [Mol. Phys., \textbf{55}, 1171 (1985)] is unstable with respect to a simple monoclinic phase with two ellipsoids of different orientations per unit cell (SM2). In order to study the stability of these crystalline phases at different aspect ratios and as a function of density we have calculated their free energies by thermodynamic integration. The integration path was sampled by an expanded ensemble method in which the weights were adjusted by the Wang-Landau algorithm. We show that for aspect ratios $a/b\ge 2.0$ the SM2 structure is more stable than the stretched-fcc structure for all densities above solid-nematic coexistence. Between $a/b=1.55$ and $a/b=2.0$ our calculations reveal a solid-solid phase transition

The statistics of the trajectory in a certain billiard in a flat two-torus

We consider a billiard in the punctured torus obtained by removing a small disk from the two-dimensional flat torus, with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. We prove that the probability measures on $[0,\infty)$ associated with the first exit time are weakly convergent when the size of the puncture tends to zero and explicitly compute the density of the limit.Comment: 21 pages, 6 figure

Assessing the material loss of the modular taper interface in retrieved metal on metal hip replacements

Measuring the amount of material loss in the case of revised hip replacements is considered to be a prerequisite of understanding and assessing the true in vivo performance of the implant. This paper outlines a method developed by the authors for quantifying taper material loss as well as more general taper interface parameters. Previous studies have mostly relied on visual inspection to assess the material loss at the taper interface, whereas this method aims to characterize any surface and form changes through the use of an out-of-roundness measurement machine. Along with assessing the volumetric wear, maximum linear penetration and taper contact length can also be determined. The method was applied to retrieved large head metal-on-metal femoral heads in order to quantify the material loss at this junction. Material loss from the female femoral head taper can be characterized as a localized area that is in contact with the stem taper surface. The study showed that this method has good repeatability and a low level of interoperability variation between operators

Features of gravity-Yang-Mills hierarchies in d-dimensions

Higher dimensional, direct analogues of the usual d=4 Einstein--Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d=4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in $2p+2\le d \le 4p$, in which dimensions the total mass-energy is finite, generalising the familiar Bartnik-McKinnon solutions in EYM theory for p=1. In d=4p, this similarity is complete. In the special case of d=2p+1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d=2p+1 purely gravitational systems, whose solutions generalise the static d=3 BTZ solutions, are discussed.Comment: 19 pages, 9 figure

Divergence of the Magnetic Gr\"{u}neisen Ratio at the Field-Induced Quantum Critical Point in YbRh2_2Si2_2

The heavy fermion compound YbRh$_2$Si$_2$ is studied by low-temperature magnetization $M(T)$ and specific-heat $C(T)$ measurements at magnetic fields close to the quantum critical point ($H_c=0.06$ T, $H\perp c$). Upon approaching the instability, $dM/dT$ is more singular than $C(T)$, leading to a divergence of the magnetic Gr\"uneisen ratio $\Gamma_{\rm mag}=-(dM/dT)/C$. Within the Fermi liquid regime, $\Gamma_{\rm mag}=-G_r(H-H_c^{fit})$ with $G_r=-0.30\pm 0.01$ and $H_c^{fit}=(0.065\pm 0.005)$ T which is consistent with scaling behavior of the specific-heat coefficient in YbRh$_2$(Si$_{0.95}$Ge$_{0.05}$)$_2$. The field-dependence of $dM/dT$ indicates an inflection point of the entropy as a function of magnetic field upon passing the line $T^\star(H)$ previously observed in Hall- and thermodynamic measurements.Comment: 4 pages, 3 Figure

Static BPS 'monopoles' in all even spacetime dimensions

Two families of SO(2n) Higgs models in $2n$ dimensional spacetime are presented. One family arises from the {\it dimensional reduction} of higher dimensional Yang-Mills systems while the construction of the other one is {\it ad hoc}, the $n=2$ member of each family coinciding with the usual SU(2) Yang-Mills--Higgs system without Higgs potential. All models support BPS 'monopole' solutions. The 'dyons' of the {\it dimensionally descended} models are also BPS, while the electrically charged solutions of the {\it ad hoc} models are not BPS.Comment: 15 pages, 3 figure

Visualizing and Predicting the Effects of Rheumatoid Arthritis on Hands

This dissertation was inspired by difficult decisions patients of chronic diseases have to make about about treatment options in light of uncertainty. We look at rheumatoid arthritis (RA), a chronic, autoimmune disease that primarily affects the synovial joints of the hands and causes pain and deformities. In this work, we focus on several parts of a computer-based decision tool that patients can interact with using gestures, ask questions about the disease, and visualize possible futures. We propose a hand gesture based interaction method that is easily setup in a doctor\u27s office and can be trained using a custom set of gestures that are least painful. Our system is versatile and can be used for operations like simple selections to navigating a 3D world. We propose a point distribution model (PDM) that is capable of modeling hand deformities that occur due to RA and a generalized fitting method for use on radiographs of hands. Using our shape model, we show novel visualization of disease progression. Using expertly staged radiographs, we propose a novel distance metric learning and embedding technique that can be used to automatically stage an unlabeled radiograph. Given a large set of expertly labeled radiographs, our data-driven approach can be used to extract different modes of deformation specific to a disease

Generalized parity measurements

Measurements play an important role in quantum computing (QC), by either providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with 1-qubit gates are universal for quantum computing. Here we generalize parity gates by using a higher dimensional (qudit) ancilla. This enables us to go beyond the stabilizer/graph state formalism and prepare other types of multi-particle entangled states. The generalized parity module introduced here can prepare in one-shot, heralded by the outcome of the ancilla, a large class of entangled states, including GHZ_n, W_n, Dicke states D_{n,k}, and, more generally, certain sums of Dicke states, like G_n states used in secret sharing. For W_n states it provides an exponential gain compared to linear optics based methods.Comment: 7 pages, 1 fig; updated to the published versio