Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Dosage compensation in birds

AbstractThe Z and W sex chromosomes of birds have evolved independently from the mammalian X and Y chromosomes [1]. Unlike mammals, female birds are heterogametic (ZW), while males are homogametic (ZZ). Therefore male birds, like female mammals, carry a double dose of sex-linked genes relative to the other sex. Other animals with nonhomologous sex chromosomes possess “dosage compensation” systems to equalize the expression of sex-linked genes. Dosage compensation occurs in animals as diverse as mammals, insects, and nematodes, although the mechanisms involved differ profoundly [2]. In birds, however, it is widely accepted that dosage compensation does not occur [3–5], and the differential expression of Z-linked genes has been suggested to underlie the avian sex-determination mechanism [6]. Here we show equivalent expression of at least six of nine Z chromosome genes in male and female chick embryos by using real-time quantitative PCR [7]. Only the Z-linked ScII gene, whose ortholog in Caenorhabditis elegans plays a crucial role in dosage compensation [8], escapes compensation by this assay. Our results imply that the majority of Z-linked genes in the chicken are dosage compensated

Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial non-linearities, thanks to the feedback of elastic forces on the flow.Comment: 10 pages, 14 figure

Semiflexible polymers under external fields confined to two dimensions

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.Comment: Accepted for publication in J. Chem. Phy

Enhancing the Pierre Auger Observatory to the 10^{17} to 10^{18.5} eV Range: Capabilities of an Infill Surface Array

The Pierre Auger Observatory has been designed to study the highest-energy cosmic rays in nature (E > 10^{18.5} eV). The determination of their arrival direction, energy and composition is performed by the analysis of the atmospheric showers they produce. The Auger Surface Array will consist of 1600 water Cerenkov detectors placed in an equilateral triangular grid of 1.5 km spacing. The aim of this paper is to show that the addition of a "small" area of surface detectors at half or less the above mentioned spacing would allow a dramatic increase of the physical scope of this Observatory, reaching lower energies at which the transition from galactic to extragalactic sources is expected.Comment: 21 pages, 5 figures, accepted for publication in Nucl. Instr. & Meth. in Phys. Res.

Multi-particle-collision dynamics: Flow around a circular and a square cylinder

A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for the recirculation length, the drag coefficient, and the Strouhal number are reported and compared with previous experimental measurements and computational fluid dynamics data. The good agreement demonstrates the potential of this method for the investigation of complex flows.Comment: 6 pages, separated figures in .jpg format, to be published in Europhysics Letter

Signature of elasticity in the Faraday instability

We investigate the onset of the Faraday instability in a vertically vibrated wormlike micelle solution. In this strongly viscoelastic fluid, the critical acceleration and wavenumber are shown to present oscillations as a function of driving frequency and fluid height. This effect, unseen neither in simple fluids nor in previous experiments on polymeric fluids, is interpreted in terms of standing elastic waves between the disturbed surface and the container bottom. It is shown that the model of S. Kumar [Phys. Rev. E, {\bf 65}, 026305 (2002)] for a viscoelastic fluid accounts qualitatively for our experimental observations. Explanations for quantitative discrepancies are proposed, such as the influence of the nonlinear rheological behaviour of this complex fluid.Comment: 4 pages, 4 figure

Continuum description of finite-size particles advected by external flows. The effect of collisions

The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of the different microscopic processes implicit in the model: the driving of the external flow, the inertia of the particles, and the collisions among them. The validity of the density description is confirmed by comparisons of numerical studies of the continuum equation with Direct Simulation Monte Carlo (DSMC) simulations of hard disks advected by a chaotic flow. We show that the collisions have two competing roles: a dispersing-like effect and a clustering effect (even for elastic collisions). An unexpected feature is also observed in the system: the presence of collisions can reverse the effect of inertia, so that grains with lower inertia are more clusterized.Comment: Final (strongly modified) version accepted in PRE; 6 pages, 3 figure

Deep shower interpretation of the cosmic ray events observed in excess of the Greisen-Zatsepin-Kuzmin energy

We consider the possibility that the ultra-high-energy cosmic ray flux has a small component of exotic particles which create showers much deeper in the atmosphere than ordinary hadronic primaries. It is shown that applying the conventional AGASA/HiRes/Auger data analysis procedures to such exotic events results in large systematic biases in the energy spectrum measurement. SubGZK exotic showers may be mis-reconstructed with much higher energies and mimick superGZK events. Alternatively, superGZK exotic showers may elude detection by conventional fluorescence analysis techniques.Comment: 22 pages, 5 figure