Spherical Orbifolds for Cosmic Topology

Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1011.427

Theoretical Framework for Microscopic Osmotic Phenomena

The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van't Hoff Law may no longer hold. In this paper we develop a general theoretical framework which captures corrections to the classical theory for the osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of N monomers confined in a spherical chamber as the bond strength is varied

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let

Bias in judgement: Comparing individuals and groups

The relative susceptibility of individuals and groups to systematic judgmental biases is considered. An overview of the relevant empirical literature reveals no clear or general pattern. However, a theoretical analysis employing J. H. Davis's (1973) social decision scheme (SDS) model reveals that the relative magnitude of individual and group bias depends upon several factors, including group size, initial individual judgment, the magnitude of bias among individuals, the type of bias, and most of all, the group-judgment process. It is concluded that there can be no simple answer to the question, "Which are more biased, individuals or groups?," but the SDS model offers a framework for specifying some of the conditions under which individuals are both more and less biased than groups

Quasicrystals: Atomic coverings and windows are dual projects

In the window approach to quasicrystals, the atomic position space E_parallel is embedded into a space E^n = E_parallel + E_perp. Windows are attached to points of a lattice Lambda \in E^n. For standard 5fold and icosahedral tiling models, the windows are perpendicular projections of dual Voronoi and Delone cells from Lambda. Their cuts by the position space E_parallel mark tiles and atomic positions. In the alternative covering approach, the position space is covered by overlapping copies of a quasi-unit cell which carries a fixed atomic configuration. The covering and window approach to quasicrystals are shown to be dual projects: D- and V- clusters are defined as projections to position space E_parallel of Delone or Voronoi cells. Decagonal V-clusters in the Penrose tiling, related to the decagon covering, and two types of pentagonal D-clusters in the triangle tiling of 5fold point symmetry with their windows are analyzed. They are linked, cover position space and have definite windows. For functions compatible with the tilings they form domains of definition. For icosahedral tilings the V-clusters are Kepler triacontahedra, the D-clusters are two icosahedra and one dodecahedron.Comment: 15 pages, 7 figures, see also http://homepages.uni-tuebingen.de/peter.kramer/ corrections, appendix A,B ne

Long term monitoring of mode switching for PSR B0329+54

The mode switching phenomenon of PSR B0329+54 is investigated based on the long-term monitoring from September 2003 to April 2009 made with the Urumqi 25m radio telescope at 1540 MHz. At that frequency, the change of relative intensity between the leading and trailing components is the predominant feature of mode switching. The intensity ratios between the leading and trailing components are measured for the individual profiles averaged over a few minutes. It is found that the ratios follow normal distributions, where the abnormal mode has a wider typical width than the normal mode, indicating that the abnormal mode is less stable than the normal mode. Our data show that 84.9% of the time for PSR B0329+54 was in the normal mode and 15.1% was in the abnormal mode. From the two passages of eight-day quasi-continuous observations in 2004, and supplemented by the daily data observed with 15 m telescope at 610 MHz at Jodrell Bank Observatory, the intrinsic distributions of mode timescales are constrained with the Bayesian inference method. It is found that the gamma distribution with the shape parameter slightly smaller than 1 is favored over the normal, lognormal and Pareto distributions. The optimal scale parameters of the gamma distribution is 31.5 minutes for the abnormal mode and 154 minutes for the normal mode. The shape parameters have very similar values, i.e. 0.75^{+0.22}_{-0.17} for the normal mode and 0.84^{+0.28}_{-0.22} for the abnormal mode, indicating the physical mechanisms in both modes may be the same. No long-term modulation of the relative intensity ratios was found for both the modes, suggesting that the mode switching was stable. The intrinsic timescale distributions, for the first time constrained for this pulsar, provide valuable information to understand the physics of mode switching.Comment: 31 pages,12 figures, Accepted by the Ap

Antechamber facilitates loading and unloading of vacuum furnace

Antechamber facilitates the use of a furnace in which materials are heat treated in a high vacuum or a gas atmosphere. It has a high vacuum pumping system, a means for backfilling with a selected gas, an access door, glove ports, and a motor driven platform

Axial symmetry and conformal Killing vectors

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content.Comment: 15 pages, Latex, no figure