Propagators and WKB-exactness in the plane wave limit of AdSxS

Green functions for the scalar, spinor and vector fields in a plane wave geometry arising as a Penrose limit of $AdS\times S$ are obtained. The Schwinger-DeWitt technique directly gives the results in the plane wave background, which turns out to be WKB-exact. Therefore the structural similarity with flat space results is unveiled. In addition, based on the local character of the Penrose limit, it is claimed that for getting the correct propagators in the limit one can rely on the first terms of the direct geodesic contribution in the Schwinger-DeWitt expansion of the original propagators . This is explicitly shown for the Einstein Static Universe, which has the same Penrose limit as $AdS\times S$ with equal radii, and for a number of other illustrative cases.Comment: 18 pages, late

Self-diffusion in dense granular shear flows

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear in a 2D Couette geometry. We find that self-diffusivities are proportional to the local shear rate with diffusivities along the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D \approx \dot\gamma a^2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and drag at the moving boundary lead to particle displacements that can appear sub- or super-diffusive. In particular, diffusion appears superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems with no obvious analog in rapid flows. Specifically, the diffusivity is supressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean flow, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Levy flights are also observed. Although correlated motion creates velocity fields qualitatively different from Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.Comment: 13 pages, 20 figures (accepted to Phys. Rev. E

Probabilistic frames: An overview

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of probabilistic frames, and we characterize one of their subclasses in terms of minimizers of some appropriate potential function. In addition, we survey a range of areas where probabilistic frames, albeit, under different names, appear. These areas include directional statistics, the geometry of convex bodies, and the theory of t-designs

Logarithmic correction to BH entropy as Noether charge

We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions. Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law. The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature. Two instances are examined in detail: Schwarzschild and a four-dimensional massless topological black hole. We also find agreement with the logarithmic correction due to one-loop contribution of conformal fields in the Schwarzschild background.Comment: 14 pages, JHEP styl

On the Detection of a Scalar Stochastic Background of Gravitational Waves

In the near future we will witness the coming to a full operational regime of laser interferometers and resonant mass detectors of spherical shape. In this work we study the sensitivity of pairs of such gravitational wave detectors to a scalar stochastic background of gravitational waves. Our computations are carried out both for minimal and non minimal coupling of the scalar fields.Comment: 25 pages, 3 figure

Genetics of human neural tube defects

Neural tube defects (NTDs) are common, severe congenital malformations whose causation involves multiple genes and environmental factors. Although more than 200 genes are known to cause NTDs in mice, there has been rather limited progress in delineating the molecular basis underlying most human NTDs. Numerous genetic studies have been carried out to investigate candidate genes in cohorts of patients, with particular reference to those that participate in folate one-carbon metabolism. Although the homocysteine remethylation gene MTHFR has emerged as a risk factor in some human populations, few other consistent findings have resulted from this approach. Similarly, attention focused on the human homologues of mouse NTD genes has contributed only limited positive findings to date, although an emerging association between genes of the non-canonical Wnt (planar cell polarity) pathway and NTDs provides candidates for future studies. Priorities for the next phase of this research include: (i) larger studies that are sufficiently powered to detect significant associations with relatively minor risk factors; (ii) analysis of multiple candidate genes in groups of well-genotyped individuals to detect possible gene–gene interactions; (iii) use of high throughput genomic technology to evaluate the role of copy number variants and to detect ‘private’ and regulatory mutations, neither of which have been studied to date; (iv) detailed analysis of patient samples stratified by phenotype to enable, for example, hypothesis-driven testing of candidates genes in groups of NTDs with specific defects of folate metabolism, or in groups of fetuses with well-defined phenotypes such as craniorachischisis

Asteroseismology of Eclipsing Binary Stars in the Kepler Era

Eclipsing binary stars have long served as benchmark systems to measure fundamental stellar properties. In the past few decades, asteroseismology - the study of stellar pulsations - has emerged as a new powerful tool to study the structure and evolution of stars across the HR diagram. Pulsating stars in eclipsing binary systems are particularly valuable since fundamental properties (such as radii and masses) can determined using two independent techniques. Furthermore, independently measured properties from binary orbits can be used to improve asteroseismic modeling for pulsating stars in which mode identifications are not straightforward. This contribution provides a review of asteroseismic detections in eclipsing binary stars, with a focus on space-based missions such as CoRoT and Kepler, and empirical tests of asteroseismic scaling relations for stochastic ("solar-like") oscillations.Comment: 28 pages, 12 figures, 2 tables; Proceedings of the AAS topical conference "Giants of Eclipse" (AASTCS-3), July 28 - August 2 2013, Monterey, C