Local existence of analytical solutions to an incompressible Lagrangian stochastic model in a periodic domain

We consider an incompressible kinetic Fokker Planck equation in the flat torus, which is a simplified version of the Lagrangian stochastic models for turbulent flows introduced by S.B. Pope in the context of computational fluid dynamics. The main difficulties in its treatment arise from a pressure type force that couples the Fokker Planck equation with a Poisson equation which strongly depends on the second order moments of the fluid velocity. In this paper we prove short time existence of analytic solutions in the one-dimensional case, for which we are able to use techniques and functional norms that have been recently introduced in the study of a related singular model.Comment: 32 page

Topography, substratum and benthic macrofaunal relationships on a tropical mesophotic shelf margin, central Great Barrier Reef, Australia

Habitats and ecological communities occurring in the mesophotic region of the central Great Barrier Reef (GBR), Australia, were investigated using autonomous underwater vehicle (AUV) from 51 to 145 m. High-resolution multibeam bathymetry of the outer-shelf at Hydrographers Passage in the central GBR revealed submerged linear reefs with tops at 50, 55, 80, 90, 100 and 130 m separated by flat, sandy inter-reefal areas punctuated by limestone pinnacles. Cluster analysis of AUV images yielded five distinct site groups based on their benthic macrofauna, with rugosity and the presence of limestone reef identified as the most significant abiotic factors explaining the distribution of macrofaunal communities. Reef-associated macrofaunal communities occurred in three distinct depth zones: (1) a shallow (75 m). The effects of depth and microhabitat topography on irradiance most likely play a critical role in controlling vertical zonation on reef substrates. The lower depth limits of zooxanthellate corals are significantly shallower than that observed in many other mesophotic coral ecosystems. This may be a result of resuspension of sediments from the sand sheets by strong currents and/or a consequence of cold water upwelling

Evolving Lorentzian Wormholes

Evolving Lorentzian wormholes with the required matter satisfying the Energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza--Klein inflation.Comment: 10 pages( RevTex, Twocolumn format), Two figures available on request from the first author. transmission errors corrected

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid

Topological charged black holes coupled with a cosmological constant in $R^{2}\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}R_{AB} = k(D-3) h_{AB}$. The global structure for the four-dimensional spacetimes with $k = 0$ is investigated systematically. The most general solutions that represent a Type $II$ fluid in such a high dimensional spacetime are found, and showed that topological charged black holes can be formed from the gravitational collapse of such a fluid. When the spacetime is (asymptotically) self-similar, the collapse always forms black holes for $k = 0, -1$, in contrast to the case $k = 1$, where it can form either balck holes or naked singularities.Comment: 14 figures, to appear in Phys. Rev.

Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity

In this paper, we study topological AdS black branes of $(n+1)$-dimensional Einstein-Maxwell-dilaton theory and investigate their properties. We use the area law, surface gravity and Gauss law interpretations to find entropy, temperature and electrical charge, respectively. We also employ the modified Brown and York subtraction method to calculate the quasilocal mass of the solutions. We obtain a Smarr-type formula for the mass as a function of the entropy and the charge, compute the temperature and the electric potential through the Smarr-type formula and show that these thermodynamic quantities coincide with their values which are calculated through using the geometry. Finally, we perform a stability analysis in the canonical ensemble and investigate the effects of the dilaton field and the size of black brane on the thermal stability of the solutions. We find that large black branes are stable but for small black brane, depending on the value of dilaton field and type of horizon, we encounter with some unstable phases.Comment: 21 pages, 21 figures, references updated, minor editing, accepted in EPJC (DOI: 10.1140/epjc/s10052-010-1483-3

Vacuum Stability in Heterotic M-Theory

The problem of the stabilization of moduli is discussed within the context of compactified strongly coupled heterotic string theory. It is shown that all geometric, vector bundle and five-brane moduli are completely fixed, within a phenomenologically acceptable range, by non-perturbative physics. This result requires, in addition to the full space of moduli, non-vanishing Neveu-Schwarz flux, gaugino condensation with threshold corrections and the explicit form of the Pfaffians in string instanton superpotentials. The stable vacuum presented here has a negative cosmological constant. The possibility of ``lifting'' this to a metastable vacuum with positive cosmological constant is briefly discussed.Comment: 39 pages, minor correction

Functional and genetic analysis of regulatory regions of coliphage H-19B: location of shiga-like toxin and lysis genes suggest a role for phage functions in toxin release

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74784/1/j.1365-2958.1998.00890.x.pd

The Superspace of Geometrodynamics

Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.Comment: 29 pages, 8 figures. To appear in the Wheeler memorial volume of General Relativity and Gravitatio