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

Competing Quantum Orderings in Cuprate Superconductors: A Minimal Model

We present a minimal model for cuprate superconductors. At the unrestricted mean-field level, the model produces homogeneous superconductivity at large doping, striped superconductivity in the underdoped regime and various antiferromagnetic phases at low doping and for high temperatures. On the underdoped side, the superconductor is intrinsically inhomogeneous and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. The model is applied to calculate experimentally measurable ARPES spectra.Comment: 5 pages, 4 eps included figure

Models of granular ratchets

We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement is observed.Comment: 15 pages, 4 figures, to be published on Journal of Statistical Mechanics: Theory and Experiment

Direct simulation for a homogenous gas

A probabilistic analysis of the direct simulation of a homogeneous gas is given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced probability densities is derived. By invoking the molecular chaos assumption, an equation similar to the Boltzmann equation for the single particle probability density and the corresponding H-theorem is derived

Mechanism of margination in confined flows of blood and other multicomponent suspensions

Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions -- wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated and thereby indicates that margination, at least in the dilute case, is largely due to the differential dynamics of homogeneous (e.g. s-s) and heterogeneous (s-f) collisionsComment: 5 Pages, 4 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

Association of drusen deposition with choroidal intercapillary pillars in the aging human eye

PURPOSE. To determine the pattern of drusen accumulation with age and to investigate the initial sites of deposition and their relationship to choroidal capillaries in human donor eyes from the eye bank of Moorfields Eye Hospital.METHODS. Wholemounted, hydrated preparations of the choriocapillaris and Bruch's membrane from donor eyes ranging from 42 to 95 years, with or without retinal pigment epithelium (RPE), were examined by conventional and confocal microscopy. Drusen were visualized by their autofluorescence.RESULTS. In all age groups studied autofluorescent drusen were present at the equator but were not found centrally where the vascular architecture is different, being tubular rather than a honeycomb pattern. Autofluorescing drusen were strongly associated with the lateral walls of the choriocapillaris (an area commonly known as the intercapillary pillars of the choriocapillaris (P = 0.028; Wilcoxon signed ranks test). Nonfluorescing drusen were occasionally seen centrally, but were not easily identified, and because of their large size, their localization with respect to capillary walls was not possible.CONCLUSIONS. These results strongly support the notion that autofluorescent drusen are not randomly distributed and have a specific spatial relationship to choroidal vessel walls. That equatorial drusen fluoresce, whereas central drusen do not, suggests that they may have different chemical compositions at the two sites and possibly different significance in age-related macular disease

Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on unstructured mesh for multiscale simulation of continuum and rarefied flow. Inheriting from the multicale transport in the unified gas-kinetic scheme (UGKS), the integral solution of kinetic model equation is employed in the construction of UGKWP method to model the flow physics in the cell size and time step scales. A novel wave-particle adaptive formulation is introduced in the UGKWP method to describe the flow dynamics in each control volume. The local gas evolution is constructed through the dynamical interaction of the deterministic hydrodynamic wave and the stochastic kinetic particle. Within the resolution of cell size and time step, the decomposition, interaction, and evolution of the hydrodynamic wave and the kinetic particle depend on the ratio of the time step to the local particle collision time. In the rarefied flow regime, the flow physics is mainly recovered by the discrete particles and the UGKWP method performs as a stochastic particle method. In the continuum flow regime, the flow behavior is solely followed by macroscopic variable evolution and the UGKWP method becomes a gas-kinetic hydrodynamic flow solver for the viscous and heat-conducting Navier--Stokes solutions. In different flow regimes, many numerical test cases are computed to validate the UGKWP method on unstructured mesh. The UGKWP method can get the same UGKS solutions in all Knudsen regimes without the requirement of the time step and mesh size being less than than the particle collision time and mean free path. With an automatic wave-particle decomposition, the UGKWP method becomes very efficient. For example, at Mach number 30 and Knudsen number 0.1, in comparison with UGKS several-order-of-magnitude reductions in computational cost and memory requirement have been achieved by UGKWP

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.

Partitioning of energy in highly polydisperse granular gases

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.Comment: 10 pages; 5 figure