Stationary motion of a self gravitating toroidal incompressible liquid layer

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stratum we show the existence of stationary motions during which the stratum is approximatly a round torus (with radii r, R and R>>r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R that connects the centers of the cross sections of the torus

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Typicality versus thermality: An analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure

Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles

The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for symmetric equilibrium configurations of magnetized plasma including flow. In particular, helical symmetry is considered and results on axial and translational symmetries are retrieved as special cases of the helical configurations. The symmetry condition, which allows the description in terms of a magnetic flux function, is exploited to deduce a symmetric form of the noncanonical Poisson bracket of MHD. Casimir invariants are then obtained directly from the Poisson bracket. Equilibria are obtained from an energy-Casimir principle and reduced forms of this variational principle are obtained by the elimination of algebraic constraints.Comment: submitted to Physics of Plasmas, 16 page

Three-Dimensional Identification and Reconstruction of Galaxy Systems within Deep Redshift Surveys

We have developed a new geometrical method for identifying and reconstructing a homogeneous and highly complete set of galaxy groups in the next generation of deep, flux-limited redshift surveys. Our method combines information from the three-dimensional Voronoi diagram and its dual, the Delaunay triangulation, to obtain group and cluster catalogs that are remarkably robust over wide ranges in redshift and degree of density enhancement. Using the mock DEEP2 catalogs, we demonstrate that the VDM algorithm can be used to identify a homogeneous set of groups in a magnitude-limited sample (I\sbr{AB}\le23.5) throughout the survey redshift window $0.7 < z < 1.2$. The actual group membership can be effectively reconstructed even in the distorted redshift space environment for systems with line of sight velocity dispersion $\sigma_{los}$ greater than $\approx 200$ \kms. By comparing the galaxy cluster catalog derived from the mock DEEP2 observations to the underlying distribution of clusters found in real space with much fainter galaxies included (which should more closely trace mass in the cluster), we can assess completeness in velocity dispersion directly. We conclude that the recovered DEEP2 group and cluster sample should be statistically complete for $\sigma_{los} \gtrsim 400$ \kms. Finally, we argue that the reconstructed bivariate distribution of systems as a function of redshift and velocity dispersion reproduces with high fidelity the underlying real space distribution and can thus be used robustly to constrain cosmological parametersComment: Latex, 21 pages, ApJ submitte

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Fibre Distribution and the Process-Property Dilemma

The options for the fibre reinforcement of polymer matrix composites cover a range from short-fibre chopped strand mat, through woven fabric to unidirectional pre-impregnated (prepreg) reinforcements. The modelling of such materials may be simplified by assumptions such as perfect regular packing of fibres and the total absence of fibre waviness. However, these and other features such as the crimp or waviness in woven fabrics make real materials more complex than the simplified models. Clustering of fibres creates fibre-rich and resin-rich volumes (FRV and RRV respectively) in the composites. Prior to impregnation, large RRV will be pore-space that can expedite the flow of resin in liquid composite moulding processes (especially resin transfer moulding (RTM) and resin infusion under flexible tooling (RIFT). In the composite, the clustering of fibres tends to reduce the mechanical properties. The use of image processing and analysis can permit micro-/meso-structural characterisation which may correlate to the respective properties. This chapter considers the quantification of microstructure images in the context of the process-property dilemma for woven carbon-fibre reinforced composites with the aim of increasing understanding of the balance between processability and mechanical performance

Towards Jetography

As the LHC prepares to start taking data, this review is intended to provide a QCD theorist's understanding and views on jet finding at hadron colliders, including recent developments. My hope is that it will serve both as a primer for the newcomer to jets and as a quick reference for those with some experience of the subject. It is devoted to the questions of how one defines jets, how jets relate to partons, and to the emerging subject of how best to use jets at the LHC.Comment: 95 pages, 28 figures, an extended version of lectures given at the CTEQ/MCNET school, Debrecen, Hungary, August 2008; v2 includes additional discussion in several places, as well as other clarifications and additional references