Velocity field distributions due to ideal line vortices

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on ``nearest neighbor'' contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity ``tail'' on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the circle, but instead correspond to both higher and lower mean-field energies than those associated with the uniform vorticity distribution. We find substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E (http://pre.aps.org/) in May 200

A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow

A Bayesian approach to the estimation of maps between riemannian manifolds

Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s 31, 41, 4

C4-free subgraphs with large average degree

Motivated by a longstanding conjecture of Thomassen, we study how large the average degree of a graph needs to be to imply that it contains a C4-free subgraph with average degree at least t. Kühn and Osthus showed that an average degree bound which is double exponential in t is sufficient. We give a short proof of this bound, before reducing it to a single exponential. That is, we show that any graph G with average degree at least 2ct2log t (for some constant c > 0) contains a C4-free subgraph with average degree at least t. Finally, we give a construction which improves the lower bound for this problem, showing that this initial average degree must be at least t3−o(1)

Haplotype analysis of the PPARgamma Pro12Ala and C1431T variants reveals opposing associations with body weight.

BACKGROUND: Variation at the PPARG locus may influence susceptibility to type 2 diabetes and related traits. The Pro12Ala polymorphism may modulate receptor activity and is associated with protection from type 2 diabetes. However, there have been inconsistent reports of its association with obesity. The silent C1431T polymorphism has not been as extensively studied, but the rare T allele has also been inconsistently linked to increases in weight. Both rare alleles are in linkage disequilibrium and the independent associations of these two polymorphisms have not been addressed. RESULTS: We have genotyped a large population with type 2 diabetes (n = 1107), two populations of non-diabetics from Glasgow (n = 186) and Dundee (n = 254) and also a healthy group undergoing physical training (n = 148) and investigated the association of genotype with body mass index. This analysis has demonstrated that the Ala12 and T1431 alleles are present together in approximately 70% of the carriers. By considering the other 30% of individuals with haplotypes that only carry one of these polymorphisms, we have demonstrated that the Ala12 allele is consistently associated with a lower BMI, whilst the T1431 allele is consistently associated with higher BMI. CONCLUSION: This study has therefore revealed an opposing interaction of these polymorphisms, which may help to explain previous inconsistencies in the association of PPARG polymorphisms and body weight

Bearing tester data compilation, analysis and reporting and bearing math modeling, volume 1

Thermal and mechanical models of high speed angular contact ball bearings operating in LOX and LN2 were developed and verified with limited test data in an effort to further understand the parameters that determine or effect the SSME turbopump bearing operational characteristics and service life. The SHABERTH bearing analysis program which was adapted to evaluate shaft bearing systems in cryogenics is not capable of accommodating varying thermal properties and two phase flow. A bearing model with this capability was developed using the SINDA thermal analyzer. Iteration between the SHABERTH and the SINDA models enable the establishment of preliminary bounds for stable operation in LN2. These limits were established in terms of fluid flow, fluid inlet temperature, and axial load for a shaft speed of 30,000 RPM

On the Alexandrov Topology of sub-Lorentzian Manifolds

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.Comment: 20 page