Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure

Preheating after multifield inflation with nonminimal couplings, II: Resonance Structure

This is the second in a series of papers on preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. In this paper, we work in the rigid-spacetime approximation and consider field trajectories within the single-field attractor, which is a generic feature of these models. We construct the Floquet charts to find regions of parameter space in which particle production is efficient for both the adiabatic and isocurvature modes, and analyze the resonance structure using analytic and semi-analytic techniques. Particle production in the adiabatic direction is characterized by the existence of an asymptotic scaling solution at large values of the nonminimal couplings, $\xi_I \gg 1$, in which the dominant instability band arises in the long-wavelength limit, for comoving wavenumbers $k \rightarrow 0$. However, the large-$\xi_I$ regime is not reached until $\xi_I \geq {\cal O} (100)$. In the intermediate regime, with $\xi_I \sim {\cal O}(1 - 10)$, the resonance structure depends strongly on wavenumber and couplings. The resonance structure for isocurvature perturbations is distinct and more complicated than its adiabatic counterpart. An intermediate regime, for $\xi_I \sim {\cal O} (1 - 10)$, is again evident. For large values of $\xi_I$, the Floquet chart consists of densely spaced, nearly parallel instability bands, suggesting a very efficient preheating behavior. The increased efficiency arises from features of the nontrivial field-space manifold in the Einstein frame, which itself arises from the fields' nonminimal couplings in the Jordan frame, and has no analogue in models with minimal couplings. Quantitatively, the approach to the large-$\xi_I$ asymptotic solution for isocurvature modes is slower than in the case of the adiabatic modes.Comment: 46 pages, 23 figures. References added and minor edits made to match published versio

On Heatshield Shapes for Mars Entry Capsules

The 70deg sphere-cone - the standard geometry for all US Mars entry missions - is thoroughly examined via flow field simulations at a select few peak heating points along candidate flight trajectories. Emphasis is placed on turbulent heating based on the Baldwin- Lomax turbulence model. It is shown that increased leeward turbulent heating for a 70 sphere-cone flying at angle of attack is primarily due to the discontinuity in curvature between the spherical nose cap and the conical frustum - the attachment of the sonic line at this sphere-cone junction leads to a supersonic edge Mach number over the leeward acreage. In an attempt to mitigate this problem of elevated turbulent heating, alternate geometries, without any curvature discontinuities in the acreage, are developed. Two approaches, one based on nonlinear optimization with constraints, and one based on the use of non-uniform rational B-splines, are considered. All configurations examined remain axisymmetric. The aerothermal performance of alternate geometries is shown to be superior to that of the 70 sphere-cone

Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime results

This paper concludes our semi-analytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of paper I in this series, we extend the rigid-spacetime results of paper II by considering both the expansion of the universe during preheating, as well as the effect of the coupled metric perturbations on particle production. The adiabatic and isocurvature perturbations are governed by different effective masses that scale differently with the nonminimal couplings and evolve differently in time. The effective mass for the adiabatic modes is dominated by contributions from the coupled metric perturbations immediately after inflation. The metric perturbations contribute an oscillating tachyonic term that enhances an early period of significant particle production for the adiabatic modes, which ceases on a time-scale governed by the nonminimal couplings $\xi_I$. The effective mass of the isocurvature perturbations, on the other hand, is dominated by contributions from the fields' potential and from the curvature of the field-space manifold (in the Einstein frame), the balance between which shifts on a time-scale governed by $\xi_I$. As in papers I and II, we identify distinct behavior depending on whether the nonminimal couplings are small ($\xi_I \lesssim {\cal O} (1)$), intermediate ($\xi_I \sim {\cal O} (1 - 10)$), or large ($\xi_I \geq 100$).Comment: 34 pages, 11 figures. References added and minor edits made to match published versio

Comparison of Two Types of Mouse Running Wheels.

Voluntary wheel running of mice has been used as a measure of physical activity in a multitude of studies. The aim of this study was to validate low profile wireless running wheels (Med Associates Inc.) against solid-surface, traditionally-mounted vertical running wheels. All animal procedures were approved by the Texas A &M IACUC. Eleven week old female C57BL/6J mice (Jackson Labs, Bar Harbor, ME) were randomly assigned to either vertical running wheels (n=5) or low profile running wheels (n=5). Daily distance run was monitored for 12 days following initial wheel orientation exposure. Average daily distance run by the mice was not different (p=0.37) between the two types of wheels, with the mice on vertical wheels averaging 6.74(±1.74 km/day; average ±SD) versus 8.58(±1.87km/day) on the low profile wheels. The distance run by the mice on the low profile wheels was also compared to the distance the same mice ran on the vertical wheels (8.6±1.04 km/day; p=0.96). Thus data collected on the low-profile wheels was similar to the vertical running wheels not only among two age and sex-matched groups of mice, but also when the same group of mice ran on the two wheel types. However, on the low-profile wheels, the inability to measure duration of wheel running due to software limitations of the data-collection bin size eliminates the calculation of running speed, both of which are important phenotypes of physical activity. Additionally, there were also numerous observations of the mice coasting on the low-profile wheels, an issue not present on the traditional, solid-surface wheels. The presence of coasting would inflate distance measures over true measures of activity and may have been responsible for the non-significant elevation of distance on the low-profile wheels. Thus, if accurate measures of distance or measurement of duration and speed are not required, the low-profile wheel is a valid methodology

Chemical Compositions of Four Metal-poor Giants

We present the chemical compositions of four K giants CS 22877-1, CS 22166-16, CS22169-35 and BS 16085 - 0050 that have [Fe/H] in the range -2.4 to -3.1. Metal-poor stars with [Fe/H] < -2.5 are known to exhibit considerable star - to - star variations of many elements. This quartet confirms this conclusion. CS 22877-1 and CS 22166-16 are carbon-rich. There is significant spread for [$\alpha$/Fe] within our sample where [$\alpha$/Fe] is computed from the mean of the [Mg/Fe], and [Ca/Fe] ratios. BS 16085 - 0050 is remarkably $\alpha$ enriched with a mean [$\alpha$/Fe] of $+$0.7 but CS 22169-35 is $\alpha$-poor. The aluminium abundance also shows a significant variation over the sample. A parallel and unsuccessful search among high-velocity late-type stars for metal-poor stars is described.Comment: 14 pages (text), 4 tables, 3 figures, Accepted for publication in PAS

OCT-BASED THREE DIMENSIONAL MODELING OF STENT DEPLOYMENT

Stent deployment has been widely used to treat narrowed coronary artery. Its acute outcome in terms of stent under expansion and malapposition depends on the extent and shape of calcifications. However, no clear understanding as to how to quantify or categorize the impact of calcification. We have conducted ex vivo stenting characterized by the optical coherence tomography (OCT). The goal of this work is to capture the ex vivo stent deployment and quantify the effect of calcium morphology on the stenting. A three dimensional model of calcified plaque was reconstructed from ex vivo OCT images. The crimping, balloon expansion and recoil process of the Express stent were characterized. Three cross-sections with different calcium percentages were chosen to evaluated the effect of the calcium in terms of stress/strain, lumen gains and malapposition. Results will be used to the pre-surgical planning

Trajectory Simulation of Meteors Assuming Mass Loss and Fragmentation

Program used to simulate atmospheric flight trajectories of entry capsules [1] Includes models of atmospheres of different planetary destinations - Earth, Mars, Venus, Jupiter, Saturn, Uranus, Titan, ... Solves 3-degrees of freedom (3DoF) equations for a single body treated as a point mass. Also supports 6-DoF trajectory simula4on and Monte Carlo analyses. Uses Fehlberg-Runge-Kuna (4th-5th order) time integraion with automaic step size control. Includes rotating spheroidal planet with gravitational field having a J2 harmonic. Includes a variety of engineering aerodynamic and heat flux models. Capable of specifying events - heatshield jettison, parachute deployment, etc. - at predefined altitudes or Mach number. Has material thermal response models of typical aerospace materials integrated