X,Y,Z-Waves: Extended Structures in Nonlinear Lattices

Motivated by recent experimental and theoretical results on optical X-waves, we propose a new type of waveforms in 2D and 3D discrete media -- multi-legged extended nonlinear structures (ENS), built as arrays of lattice solitons (tiles or stones, in the 2D and 3D cases, respectively). First, we study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices. The predicted patterns are relevant to a variety of physical settings, such as Bose-Einstein condensates in deep optical lattices, lattices built of microresonators, photorefractive crystals with optically induced lattices (in the 2D case) and others.Comment: 4 pages, 4 figure

Baryon Asymmetry of the Universe without Boltzmann or Kadanoff-Baym

We present a formalism that allows the computation of the baryon asymmetry of the universe from first principles of statistical physics and quantum field theory that is applicable to certain types of beyond the Standard Model physics (such as the neutrino Minimal Standard Model -- $\nu$MSM) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of Standard Model particles is very weakly coupled to a new sector (sterile neutrinos in the $\nu$MSM case) that is out-of-equilibrium. The key point that allows a computation without kinetic equations is that the number of sterile neutrinos produced during the relevant cosmological period remains small. In such a case, it is possible to expand the formal solution of the von Neumann equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose a toy model (containing only two active and two sterile neutrinos) to illustrate the use of the formalism, but it could be applied to other models.Comment: 26 pages, 10 figure

Multifractal earth topography

International audienceThis paper shows how modern ideas of scaling can be used to model topography with various morphologies and also to accurately characterize topography over wide ranges of scales. Our argument is divided in two parts. We first survey the main topographic models and show that they are based on convolutions of basic structures (singularities) with noises. Focusing on models with large numbers of degrees of freedom (fractional Brownian motion (fBm), fractional Levy motion (fLm), multifractal fractionally integrated flux (FIF) model), we show that they are distinguished by the type of underlying noise. In addition, realistic models require anisotropic singularities; we show how to generalize the basic isotropic (self-similar) models to anisotropic ones. Using numerical simulations, we display the subtle interplay between statistics, singularity structure and resulting topographic morphology. We show how the existence of anisotropic singularities with highly variable statistics can lead to unwarranted conclusions about scale breaking. We then analyze topographic transects from four Digital Elevation Models (DEMs) which collectively span scales from planetary down to 50 cm (4 orders of magnitude larger than in previous studies) and contain more than 2×108 pixels (a hundred times more data than in previous studies). We use power spectra and multiscaling analysis tools to study the global properties of topography. We show that the isotropic scaling for moments of order =2 holds to within ±45% down to scales ˜40 m. We also show that the multifractal FIF is easily compatible with the data, while the monofractal fBm and fLm are not. We estimate the universal parameters (a, C1) characterizing the underlying FIF noise to be (1.79, 0.12), where a is the degree of multifractality (0=a=2, 0 means monofractal) and C1 is the degree of sparseness of the surface (0=C1, 0 means space filling). In the same way, we investigate the variation of multifractal parameters between continents, oceans and continental margins. Our analyses show that no significant variation is found for (a, C1) and that the third parameter H, which is a degree of smoothing (higher H means smoother), is variable: our estimates are H=0.46, 0.66, 0.77 for bathymetry, continents and continental margins. An application we developped here is to use (a, C1) values to correct standard spectra of DEMs for multifractal resolution effects

Evaluating elbow osteoarthritis within the prehistoric Tiwanaku state using generalized estimating equations (GEE).

OBJECTIVES:Studies of osteoarthritis (OA) in human skeletal remains can come with scalar problems. If OA measurement is noted as present or absent in one joint, like the elbow, results may not identify specific articular pathology data and the sample size may be insufficient to address research questions. If calculated on a per data point basis (i.e., each articular surface within a joint), results may prove too data heavy to comprehensively understand arthritic changes, or one individual with multiple positive scores may skew results and violate the data independence required for statistical tests. The objective of this article is to show that the statistical methodology Generalized Estimating Equations (GEE) can solve scalar issues in bioarchaeological studies. MATERIALS AND METHODS:Using GEE, a population-averaged statistical model, 1,195 adults from the core and one colony of the prehistoric Tiwanaku state (AD 500-1,100) were evaluated bilaterally for OA on the seven articular surfaces of the elbow joint. RESULTS:GEE linked the articular surfaces within each individual specimen, permitting the largest possible unbiased dataset, and showed significant differences between core and colony Tiwanaku peoples in the overall elbow joint, while also pinpointing specific articular surfaces with OA. Data groupings by sex and age at death also demonstrated significant variation. A pattern of elbow rotation noted for core Tiwanaku people may indicate a specific pattern of movement. DISCUSSION:GEE is effective and should be encouraged in bioarchaeological studies as a way to address scalar issues and to retain all pathology information

Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev\'e transcendent. In each case the potential can be chosen to be time-independent.Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark solutio

Universal Heat Conduction in YBa_2Cu_3O_6.9

The thermal conductivity of YBa_2Cu_3O_6.9 was measured at low temperatures in untwinned single crystals with concentrations of Zn impurities from 0 to 3% of Cu. A linear term kappa_0/T = 0.19 mW/K^2.cm is clearly resolved as T -> 0, and found to be virtually independent of Zn concentration. The existence of this residual normal fluid strongly validates the basic theory of transport in unconventional superconductors. Moreover, the observed universal behavior is in quantitative agreement with calculations for a gap function of d-wave symmetry.Comment: Latex file, 4 pages, 3 EPS figures, to appear in Physical Review Letter

Limits on Lorentz Violation from the Highest Energy Cosmic Rays

We place several new limits on Lorentz violating effects, which can modify particles' dispersion relations, by considering the highest energy cosmic rays observed. Since these are hadrons, this involves considering the partonic content of such cosmic rays. We get a number of bounds on differences in maximum propagation speeds, which are typically bounded at the 10^{-21} level, and on momentum dependent dispersion corrections of the form v = 1 +- p^2/Lambda^2, which typically bound Lambda > 10^{21} GeV, well above the Planck scale. For (CPT violating) dispersion correction of the form v = 1 + p/Lambda, the bounds are up to 15 orders of magnitude beyond the Planck scale.Comment: 24 pages, no figures. Added references, very slight changes. Version published in Physical Review

Flexible macrocycles as versatile supports for catalytically active metal clusters

Here we present three structurally diverse clusters stabilised by the same macrocyclic polyphenol; t-butylcalix[8]arene. This work demonstrates the range of conformations the flexible ligand is capable of adopting, highlighting its versatility in metal coordination. In addition, a Ti complex displays activity for the ring-opening polymerisation of lactide

Angular position of nodes in the superconducting gap of YBCO

The thermal conductivity of a YBCO single crystal has been studied as a function of the relative orientation of the crystal axes and a magnetic field rotating in the Cu-O planes. Measurements were carried out at several temperatures below T_c and at a fixed field of 30 kOe. A four-fold symmetry characteristic of a superconducting gap with nodes at odd multiples of 45 degrees in k-space was resolved. Experiments were performed to exclude a possible macroscopic origin for such a four-fold symmetry such as sample shape or anisotropic pinning. Our results impose an upper limit of 10% on the weight of the s-wave component of the essentially d-wave superconducting order parameter of YBCO.Comment: 10 pages, 4 figure

Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure