Fluctuating Interfaces in Liquid Crystals

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations

Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem

Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or otherwise restricting the local motion of the elements of the system. The onset of collectivity occurs because, when one particle is blocked, it may lead to the blocking of a neighbor. That particle may then block one of its neighbors, these effects propagating across some typical domain of size named the dynamical correlation length. When this length diverges, the system becomes immobile. Even where it is finite but large the dynamics is dramatically slowed. Such phenomena lead to glasses, gels, and other very long-lived nonequilibrium solids. The bootstrap percolation models are the simplest examples describing these spatio-temporal correlations. We have been able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest. We believe that the nature of these correlations and the method we devise to solve the problem are quite general. Both should be of considerable help in further developing this field.Comment: 17 pages, 4 figure

The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance

The raise and peel model describes the stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes, and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects (D). The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster changing its shape. If a tile hits two adjacent defects, the defect annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction D + D -->0, in which the particles (defects) D hop at long distances changing the medium and annihilate. Between the hops the medium also changes (tiles hit clusters changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformal invariant quantum chain.Comment: 8 pages, 12figure

Interpretation of genetic association studies: Markers with replicated highly significant odds ratios may be poor classifiers

Recent successful discoveries of potentially causal single nucleotide polymorphisms (SNPs) for complex diseases hold great promise, and commercialization of genomics in personalized medicine has already begun. The hope is that genetic testing will benefit patients and their families, and encourage positive lifestyle changes and guide clinical decisions. However, for many complex diseases, it is arguable whether the era of genomics in personalized medicine is here yet. We focus on the clinical validity of genetic testing with an emphasis on two popular statistical methods for evaluating markers. The two methods, logistic regression and receiver operating characteristic (ROC) curve analysis, are applied to our age-related macular degeneration dataset. By using an additive model of the CFH, LOC387715, and C2 variants, the odds ratios are 2.9, 3.4, and 0.4, with p-values of 10 -13, 10-13, and 10-3, respectively. The area under the ROC curve (AUC) is 0.79, but assuming prevalences of 15%, 5.5%, and 1.5% (which are realistic for age groups 80 y, 65 y, and 40 y and older, respectively), only 30%, 12%, and 3% of the group classified as high risk are cases. Additionally, we present examples for four other diseases for which strongly associated variants have been discovered. In type 2 diabetes, our classification model of 12 SNPs has an AUC of only 0.64, and two SNPs achieve an AUC of only 0.56 for prostate cancer. Nine SNPs were not sufficient to improve the discrimination power over that of nongenetic predictors for risk of cardiovascular events. Finally, in Crohn's disease, a model of five SNPs, one with a quite low odds ratio of 0.26, has an AUC of only 0.66. Our analyses and examples show that strong association, although very valuable for establishing etiological hypotheses, does not guarantee effective discrimination between cases and controls. The scientific community should be cautious to avoid overstating the value of association findings in terms of personalized medicine before their time. © 2009 Jakobsdottir et al

On Closed Einstein-de Sitter Universes

We briefly summarize the idea of cosmological models with compact, flat spatial sections. It has been suggested that, because of the COBE satellite's maps of the microwave background, such models cannot be small in the sense of Ellis, and hence are no longer interesting. Here we use Lehoucq et al.'s method of cosmic crystallography to show that these models are physically meaningful even if the size of the spatial sections is of the same order of magnitude as the radius of the observational horizon.Comment: 8 pages, 1 figure. Revision includes comment on "top-down" and "bottom-up" pictures of structure formation. Figure is unmodifie

Some spaces are more equal than others

It has generally been thought that in perturbed Friedmann-Lemaitre-Robertson-Walker models of the Universe, global topology should not have any feedback effects on dynamics. However, a weak-field limit heuristical argument, assuming a finite particle horizon for the transmission of gravitational signals, shows that a residual acceleration effect can occur. The nature of this effect differs algebraically between different constant curvature 3-manifolds. This potentially provides a selection mechanism for the 3-manifold of comoving space.Comment: 4 pages, proceedings of the Grassmannian Conference in Fundamental Cosmology, Szczecin, 14-19 Sep 2009, to be refereed by Annalen der Physi

Low-Temperature Series for Ising Model by Finite-Lattice Method

We have calculated the low-temperature series for the second moment of the correlation function in $d=3$ Ising model to order $u^{26}$ and for the free energy of Absolute Value Solid-on-Solid (ASOS) model to order $u^{23}$, using the finite-lattice method.Comment: 3pages, latex, no figures, talk given at LATTICE'94, to appear in the proceeding

A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data

It has been suggested by Roukema and coworkers (hereafter R04) that the topology of the Universe as probed by the ``matched circles'' method using the first year release of the WMAP CMB data, might be that of the Poincar\'e dodecahedral space (PDS) model. An excess in the correlation of the ``identified circles'' was reported by R04, for circles of angular radius of ~11 deg for a relative phase twist -36deg, hinting that this could be due to a Clifford translation, if the hypothesized model were true. R04 did not however specify the statistical significance of the correlation signal. We investigate the statistical significance of the signal using Monte Carlo CMB simulations in a simply connected Universe, and present an updated analysis using the three-year WMAP data. We find that our analyses of the first and three year WMAP data provide results that are consistent with the simply connected space at a confidence level as low as 68%.Comment: 8 pages, 6 figures, typo corrected/replaced to match version published in A&

Detectability of Cosmic Topology in Flat Universes

Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We first give a complete description of the diffeomorphic classification of compact flat 3-manifolds, and derive the expressions for the injectivity radii, and for the volume of each class of Euclidean 3-manifolds. There emerges from our calculations the undetectability conditions for each (topological) class of flat universes. To illustrate the detectability of flat topologies we construct toy models by using an assumption by Bernshtein and Shvartsman which permits to establish a relation between topological typical lengths to the dynamics of flat models.Comment: 17 pages, 1 figure, latex2e. New references added. Inserted clarifying points. To appear in Phys. Lett. A (2003) in the present for