Uniform existence of the integrated density of states for random Schr\"odinger operators on metric graphs over Zd\mathbb{Z}^d

We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss percolation models.Comment: 17 pages; typos removed, references updated, definition of subgraph densities explaine

Pure Point spectrum for measure dynamical systems on locally compact Abelian groups

We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our approach is based on a study of almost periodicity in a Hilbert space. It allows us to set up a perturbation theory for arbitrary equivariant measurable perturbations.Comment: 22 page

A generic model for lipid monolayers, bilayers, and membranes

We describe a simple coarse-grained model which is suited to study lipid layers and their phase transitions. Lipids are modeled by short semiflexible chains of beads with a solvophilic head and a solvophobic tail component. They are forced to self-assemble into bilayers by a computationally cheap `phantom solvent' environment. The model reproduces the most important phases and phase transitions of monolayers and bilayers. Technical issues such as Monte Carlo parallelization schemes are briefly discussed.Comment: 4 pages, 4 figures conference paper for the CCP 2006 (Gyeongju, Korea

Center Vortices, Instantons, and Confinement

We study the relation between center vortices and instantons in lattice QCD.Comment: 3 pages, 1 color figure, LaTeX209 using BoxedEPS and esprc2.sty (provided); talk presented by J.W. Negele to be published in Lattice99 (Topology); email to [email protected]

Confining Effective Theories Based on Instantons and Merons

An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.Comment: 53 pages, 41 figure

Trapping of Projectiles in Fixed Scatterer Calculations

We study multiple scattering off nuclei in the closure approximation. Instead of reducing the dynamics to one particle potential scattering, the scattering amplitude for fixed target configurations is averaged over the target groundstate density via stochastic integration. At low energies a strong coupling limit is found which can not be obtained in a first order optical potential approximation. As its physical explanation, we propose it to be caused by trapping of the projectile. We analyse this phenomenon in mean field and random potential approximations. (PACS: 24.10.-i)Comment: 15 page

Seeking systematicity in variation : theoretical and methodological considerations on the “variety” concept

One centennial discussion in linguistics concerns whether languages, or linguistic systems, are, essentially, homogeneous or rather show “structured heterogeneity.” In this contribution, the question is addressed whether and how sociolinguistically defined systems (or ‘varieties’) are to be distinguished in a heterogeneous linguistic landscape: to what extent can structure be found in the myriads of language variants heard in everyday language use? We first elaborate on the theoretical importance of this ‘variety question’ by relating it to current approaches from, among others, generative linguistics (competing grammars), sociolinguistics (style-shifting, polylanguaging), and cognitive linguistics (prototype theory). Possible criteria for defining and detecting varieties are introduced, which are subsequently tested empirically, using a self-compiled corpus of spoken Dutch in West Flanders (Belgium). This empirical study demonstrates that the speech repertoire of the studied West Flemish speakers consists of four varieties, viz. a fairly stable dialect variety, a more or less virtual standard Dutch variety, and two intermediate varieties, which we will label ‘cleaned-up dialect’ and ‘substandard.’ On the methodological level, this case-study underscores the importance of speech corpora comprising both inter- and intra-speaker variation on the one hand, and the merits of triangulating qualitative and quantitative approaches on the other

A Simple Computer Model for Liquid Lipid Bilayers

We present a simple coarse-grained bead-and-spring model for lipid bilayers. The system has been developed to reproduce the main (gel-liquid) transition of biological membranes on intermediate length scales of a couple of nanometres and is very efficient from a computational point of view. For the solvent environment, two different models are proposed. The first model forces the lipids to form bilayers by confining their heads in two parallel planes. In the second model, the bilayer is stabilised by a surrounding gas of "phantom" solvent beads, which do not interact with each other. This model takes only slightly more computing time than the first one, while retaining the full membrane flexibility. We calculate the liquid-gel phase boundaries for both models and find that they are very similar.Comment: 11 pages, 6 figure