Icosahedral multi-component model sets

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Gentle Perturbations of the Free Bose Gas I

It is demonstrated that the thermal structure of the noncritical free Bose Gas is completely described by certain periodic generalized Gaussian stochastic process or equivalently by certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure have been established. Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular new models of non-Gaussian thermal structures have been constructed and a new functional integral representation of the corresponding euclidean-time Green functions have been obtained rigorously.Comment: 51 pages, LaTeX fil

Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS

Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a Non-Gibbsian Steady-State of a Drift-Diffusion System

Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these phenomena cannot be explained by a hypothesis of ``criticality''. Instead, they require the effective Hamiltonian of the system to contain very long-range potentials, making the invariant probability measures formally ``non-Gibbsian''.Comment: 4 pages, Latex Version 2.09, 1 Postscript figur

Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.Comment: 14 pages, 8 figure

Structure of the icosahedral Ti-Zr-Ni quasicrystal

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of the canonical cell tiling geometry. The initial decoration model is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1 approximant structure of the quasicrystal. The decoration model is optimized using a new method of structural analysis combining a least-squares refinement of diffraction data with results from ab initio calculations. The resulting structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration rule and structural details are discussed.Comment: 12 pages, 8 figure

The evolution of sex-specific virulence in infectious diseases

Fatality rates of infectious diseases are often higher in men than women. Although this difference is often attributed to a stronger immune response in women, we show that differences in the transmission routes that the sexes provide can result in evolution favouring pathogens with sex-specific virulence. Because women can transmit pathogens during pregnancy, birth or breast-feeding, pathogens adapt, evolving lower virulence in women. This can resolve the long-standing puzzle on progression from Human T-cell Lymphotropic Virus Type 1 (HTLV-1) infection to lethal Adult T-cell Leukaemia (ATL); a progression that is more likely in Japanese men than women, while it is equally likely in Caribbean women and men. We argue that breastfeeding, being more prolonged in Japan than in the Caribbean, may have driven the difference in virulence between the two populations. Our finding signifies the importance of investigating the differences in genetic expression profile of pathogens in males and females

Debye screening

The existence and exponential clustering of correlation functions for a classical coulomb system at low density or high temperature are proven using methods from constructive quantum field theory, the sine gordon transformation and the Glimm, Jaffe, Spencer expansion about mean field theory. This is a vindication of a belief of long standing among physicists, known as Debye screening. That is, because of special properties of the coulomb potential, the configurations of significant probability are those in which the long range parts of r −1 are mostly cancelled, leaving an effective exponentially decaying potential acting between charge clouds. This paper generalizes a previous paper of one of the authors in which these results were obtained for a special lattice system. The present treatment covers the continuous mechanics situation, with essentially arbitrary short range forces and charge species. Charge symmetry is not assumed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46519/1/220_2005_Article_BF01197700.pd

Epidemiology of a Daphnia-Multiparasite System and Its Implications for the Red Queen

The Red Queen hypothesis can explain the maintenance of host and parasite diversity. However, the Red Queen requires genetic specificity for infection risk (i.e., that infection depends on the exact combination of host and parasite genotypes) and strongly virulent effects of infection on host fitness. A European crustacean (Daphnia magna) - bacterium (Pasteuria ramosa) system typifies such specificity and high virulence. We studied the North American host Daphnia dentifera and its natural parasite Pasteuria ramosa, and also found strong genetic specificity for infection success and high virulence. These results suggest that Pasteuria could promote Red Queen dynamics with D. dentifera populations as well. However, the Red Queen might be undermined in this system by selection from a more common yeast parasite (Metschnikowia bicuspidata). Resistance to the yeast did not correlate with resistance to Pasteuria among host genotypes, suggesting that selection by Metschnikowia should proceed relatively independently of selection by Pasteuria