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

Velocity Slip and Temperature Jump in Hypersonic Aerothermodynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76543/1/AIAA-2007-208-226.pd

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

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

Multiscale modeling and simulation for polymer melt flows between parallel plates

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, visco-elastic liquid, and visco-elastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for $\omega\tau^R\lesssim 1$, and the crossover between the liquid-like and solid-like regime takes place around $\omega\tau^\alpha\simeq 1$ (where $\omega$ is the angular frequency of the plate and $\tau^R$ and $\tau^\alpha$ are Rouse and $\alpha$ relaxation time, respectively).Comment: 13pages, 12figure

Hydrodynamics of confined colloidal fluids in two dimensions

We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal discs in confined geometries. We calculate the velocity autocorrelation functions, and observe the predicted $t^{-1}$ long time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the $t^{-1}$ tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge, but instead depends logarithmically on the overall size of the system.Comment: RevTex 13 pages, 9 figure