Topology Change in (2+1)-Dimensional Gravity

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-9

Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of hyperbolic 3-manifolds is presented. We discuss briefly L^2 - analytical and topological torsions of a manifold with boundary.Comment: 12 pages, LaTeX fil

Retardation of Particle Evaporation from Excited Nuclear Systems Due to Thermal Expansion

Particle evaporation rates from excited nuclear systems at equilibrium matter density are studied within the Harmonic-Interaction Fermi Gas Model (HIFGM) combined with Weisskopf's detailed balance approach. It is found that thermal expansion of a hot nucleus, as described quantitatively by HIFGM, leads to a significant retardation of particle emission, greatly extending the validity of Weisskopf's approach. The decay of such highly excited nuclei is strongly influenced by surface instabilities

Confidence Level Of Primary Care Providers In Authorizing Athletic Return-To-Play

The purpose of this study was to identify the level of confidence for primary care providers in authorizing athletic retum-to-play following sports-related injury. The Centers for Disease Control and Prevention (CDC) (as cited in Patel, Yamasaki, & Brown, 2017) reported that 2.6 million children and teens ages 0-19 years are treated annually for sports-related injuries, and 7.2 million high school students participate in sports and suffer an estimated 2 million injuries that require 500,000 doctor visits and 30,000 hospitalizations annually. Although primary care providers are providing care for musculoskeletal and concussive injuries, Benham and Geier (2016) reported that they may not have the confidence, knowledge, or skill to manage common musculoskeletal conditions in their primary care practice. Excellent provisions of such care will require providers who are safe and confident in the management and treatment of sports-related injuries to ensure high-quality patient care (Benham & Geier, 2016). Researchers distributed written surveys, and links to a survey were distributed via social media postings, email, and SurveyMonkey to qualifying participants including Doctors of Medicine (MD), Doctors of Osteopathic Medicine (DO), nurse practitioners (NP), and physician assistants (PA). Data collected indicated that only 47.6% primary care providers were confident with returning youth athletes back-to-play following a sports injury, 34.7% were confident in treating sports-related concussive injuries, and 50% were confident in treating sports-related musculoskeletal injuries. Primary care providers can use this information to expose areas for confidence improvement that can be met with continued education, in-services, and workshops. Schools of medicine and nursing can use these findings to improve musculoskeletal curricula in primary care education. Determining primary care provider confidence level in authorizing athletic retum-to-play is imperative in ensuring patient safety and access to thorough and competent care from initial injury to full resolution

Glass Bubbles Insulation for Liquid Hydrogen Storage Tanks

A full-scale field application of glass bubbles insulation has been demonstrated in a 218,000 L liquid hydrogen storage tank. This work is the evolution of extensive materials testing, laboratory scale testing, and system studies leading to the use of glass bubbles insulation as a cost efficient and high performance alternative in cryogenic storage tanks of any size. The tank utilized is part of a rocket propulsion test complex at the NASA Stennis Space Center and is a 1960's vintage spherical double wall tank with an evacuated annulus. The original perlite that was removed from the annulus was in pristine condition and showed no signs of deterioration or compaction. Test results show a significant reduction in liquid hydrogen boiloff when compared to recent baseline data prior to removal of the perlite insulation. The data also validates the previous laboratory scale testing (1000 L) and full-scale numerical modeling (3,200,000 L) of boiloff in spherical cryogenic storage tanks. The performance of the tank will continue to be monitored during operation of the tank over the coming years. KEYWORDS: Glass bubble, perlite, insulation, liquid hydrogen, storage tank

Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

The Sum over Topologies in Three-Dimensional Euclidean Quantum Gravity

In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit of small cosmological constant. The sum over topologies diverges for either sign of $\Lambda$, but for dramatically different reasons: for $\Lambda>0$, the divergent behavior comes from the contributions of very low volume, topologically complex manifolds, while for $\Lambda<0$ it is a consequence of the existence of infinite sequences of relatively high volume manifolds with converging geometries. Possible implications for four-dimensional quantum gravity are discussed.Comment: 12 pages (LaTeX), UCD-92-1