The Bar Pattern Speed of NGC 1433 Estimated Via Sticky-Particle Simulations

We present detailed numerical simulations of NGC 1433, an intermediate-type barred spiral showing strong morphological features including a secondary bar, nuclear ring, inner ring, outer pseudoring, and two striking, detached spiral arcs known as ``plumes.'' This galaxy is an ideal candidate for recreating the observed morphology through dynamical models and determining the pattern speed. We derived a gravitational potential from an $H$-band image of the galaxy and simulated the behavior of a two-dimensional disk of 100,000 inelastically colliding gas particles. We find that the closest matching morphology between a $B$-band image and a simulation occurs with a pattern speed of 0.89 km s$^{-1}$ arcsec$^{-1}$ $\pm$ 5-10%. We also determine that the ratio of corotation radius to the average published bar radius is 1.7 $\pm$ 0.3, with the ambiguity in the bar radius being the largest contributor to the error.Comment: Accepted for publication by The Astronomical Journal. 34 pages, 13 figures, 2 table

Dynamical Simulations of NGC 2523 and NGC 4245

We present dynamical simulations of NGC 2523 and NGC 4245, two barred galaxies (types SB(r)b and SB(r)0/a, respectively) with prominent inner rings. Our goal is to estimate the bar pattern speeds in these galaxies by matching a sticky-particle simulation to the $B$-band morphology, using near-infrared $K_s$-band images to define the gravitational potentials. We compare the pattern speeds derived by this method with those derived in our previous paper using the well-known Tremaine-Weinberg continuity equation method. The inner rings in these galaxies, which are likely to be resonance features, help to constrain the dynamical models. We find that both methods give the same pattern speeds within the errors.Comment: 29 pages, 3 tables, 13 figures. Accepted for publication in The Astronomical Journa

THE USE OF MOTION ANALYSIS AS A COACHING AID TO IMPROVE THE INDIVIDUAL TECHNIQUE IN SPRINT HURDLES

Biomechanical data are oflen presented as a group average, which may not always help individual athletes to improve their own performance. The purpose of this study was to analyse techniques in sprint hurdles within the athlete and find critical individual aspects, which influence performance. The hurdle clearance of three athletes (eight trials each) were videotaped with four video camera recorders and analysed three-dimensionally. There were several statistically significant correlations between the critical overall horizontal velocity and other variables, especially for one athlete. Such trends in individual performance presented ideas to coaches, athletes and also to researchers, regarding what happened in less successful runs and which technical points were worth individual attention in training

Invariant distributions, Beurling transforms and tensor tomography in higher dimensions

In the recent articles \cite{PSU1,PSU3}, a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the surjectivity of the adjoint of the geodesic ray transform, or equivalently the existence of certain distributions that are invariant under geodesic flow. We prove that on any Anosov manifold, one can find invariant distributions with controlled first Fourier coefficients. The proof is based on subelliptic type estimates and a Pestov identity. We present an alternative construction valid on manifolds with nonpositive curvature, based on the fact that a natural Beurling transform on such manifolds turns out to be essentially a contraction. Finally, we obtain uniqueness results in tensor tomography both on simple and Anosov manifolds that improve earlier results by assuming a condition on the terminator value for a modified Jacobi equation.This is the accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00208-015-1169-0

SPECTRAL RIGIDITY AND INVARIANT DISTRIBUTIONS ON ANOSOV SURFACES

This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ is the given function $f$