A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Duality Between Spatial and Angular Shift in Optical Reflection

We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam reflection. In the Goos-Hanchen case we show theoretically and experimentally that this unification naturally arises in the context of reflection from a lossy surface (e.g., a metal).Comment: 4 pages, 3 figure

On the number of particles which a curved quantum waveguide can bind

We discuss the discrete spectrum of N particles in a curved planar waveguide. If they are neutral fermions, the maximum number of particles which the waveguide can bind is given by a one-particle Birman-Schwinger bound in combination with the Pauli principle. On the other hand, if they are charged, e.g., electrons in a bent quantum wire, the Coulomb repulsion plays a crucial role. We prove a sufficient condition under which the discrete spectrum of such a system is empty.Comment: a LateX file, 12 page

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities

Motivated by recent theoretical and experimental works, we study the statistical fluctuations of the parametric derivative of the transmission T and reflection R coefficients in ballistic chaotic cavities in the presence of absorption. Analytical results for the variance of the parametric derivative of T and R, with and without time-reversal symmetry, are obtained for both asymmetric and left-right symmetric cavities. These results are valid for arbitrary number of channels, in completely agreement with the one channel case in the absence of absorption studied in the literature.Comment: Modified version as accepted in PR

Mesh-free simulation of complex LCD geometries

We use a novel mesh-free simulation approach to study the post aligned bistable nematic (PABN) cell. By employing the Qian-Sheng formalism for liquid crystals along with a smooth representation of the surface posts, we have been able to identify two distinct stable configurations. The three-dimensional order field configurations of these states and their elastic free energies are consistent with both experimental results and previous simulation attempts. However, alternative states suggested in previous studies do not appear to remain stable when finite post curvature is considered.</p

ELBOW FLEXOR MUSCLE FUNCTION AND UPPER ARM GIRTH FOLLOWING CONCURRENT STRENGTH AND ENDURANCE TRAINING IN NON RESISTANCETRAINED FEMALES

The study investigated the effects of eight weeks of concurrent muscular strength and endurance resistance training of the non-dominant elbow flexors on muscular strength, endurance, and upper arm girths of previously non resistance-trained females. Subjects (n=12) were assigned to one of 3 training groups. These groups were Strength (S), Endurance (E), or Combined (C) with pre and post-training tests for arm girths, 1 RM preacher curl, maximal isometric torque, peak isokinetic torque at velocities of 30 and 90" s-', and total work during 25 continuous repetitions at 90"s.'. Significant increases in prepost strength and endurance occurred in both C and S groups, but not E, in the absence of any change in arm girth. Furthermore, C training produced equivalent gains in strength and endurance to the S and E groups, respectively

Levinson's Theorem for Non-local Interactions in Two Dimensions

In the light of the Sturm-Liouville theorem, the Levinson theorem for the Schr\"{o}dinger equation with both local and non-local cylindrically symmetric potentials is studied. It is proved that the two-dimensional Levinson theorem holds for the case with both local and non-local cylindrically symmetric cutoff potentials, which is not necessarily separable. In addition, the problems related to the positive-energy bound states and the physically redundant state are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email: [email protected], [email protected]

Winter Conditions Influence Biological Responses of Migrating Hummingbirds

Conserving biological diversity given ongoing environmental changes requires the knowledge of how organisms respond biologically to these changes; however, we rarely have this information. This data deficiency can be addressed with coordinated monitoring programs that provide field data across temporal and spatial scales and with process-based models, which provide a method for predicting how species, in particular migrating species that face different conditions across their range, will respond to climate change. We evaluate whether environmental conditions in the wintering grounds of broad-tailed hummingbirds influence physiological and behavioral attributes of their migration. To quantify winter ground conditions, we used operative temperature as a proxy for physiological constraint, and precipitation and the normalized difference vegetation index (NDVI) as surrogates of resource availability. We measured four biological response variables: molt stage, timing of arrival at stopover sites, body mass, and fat. Consistent with our predictions, we found that birds migrating north were in earlier stages of molt and arrived at stopover sites later when NDVI was low. These results indicate that wintering conditions impact the timing and condition of birds as they migrate north. In addition, our results suggest that biologically informed environmental surrogates provide a valuable tool for predicting how climate variability across years influences the animal populations