Phase Coexistence of Complex Fluids in Shear Flow

We present some results of recent calculations of rigid rod-like particles in shear flow, based on the Doi model. This is an ideal model system for exhibiting the generic behavior of shear-thinning fluids (polymer solutions, wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We present calculations of phase coexistence under shear among weakly-aligned (paranematic) and strongly-aligned phases, including alignment in the shear plane and in the vorticity direction (log-rolling). Phase coexistence is possible, in principle, under conditions of both common shear stress and common strain rate, corresponding to different orientations of the interface between phases. We discuss arguments for resolving this degeneracy. Calculation of phase coexistence relies on the presence of inhomogeneous terms in the dynamical equations of motion, which select the appropriate pair of coexisting states. We cast this condition in terms of an equivalent dynamical system, and explore some aspects of how this differs from equilibrium phase coexistence.Comment: 16 pages, 10 figures, submitted to Faraday Discussion

Convex Optimization Methods for Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression

In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et al. [22], conducts parameter estimation and factor selection simultaneously and have been shown to enjoy nice properties in both large and finite samples. To compute the estimates, however, can be very challenging in practice because of the high dimensionality and the trace norm constraint. In this paper, we explore a variant of Nesterov's smooth method [20] and interior point methods for computing the penalized least squares estimate. The performance of these methods is then compared using a set of randomly generated instances. We show that the variant of Nesterov's smooth method [20] generally outperforms the interior point method implemented in SDPT3 version 4.0 (beta) [19] substantially . Moreover, the former method is much more memory efficient.Comment: 27 page

Hypervelocity binary stars: smoking gun of massive binary black holes

The hypervelocity stars recently found in the Galactic halo are expelled from the Galactic center through interactions between binary stars and the central massive black hole or between single stars and a hypothetical massive binary black hole. In this paper, we demonstrate that binary stars can be ejected out of the Galactic center with velocities up to 10^3 km/s, while preserving their integrity, through interactions with a massive binary black hole. Binary stars are unlikely to attain such high velocities via scattering by a single massive black hole or through any other mechanisms. Based on the above theoretical prediction, we propose a search for binary systems among the hypervelocity stars. Discovery of hypervelocity binary stars, even one, is a definitive evidence of the existence of a massive binary black hole in the Galactic center.Comment: 5 pages, 3 figures, shortened version, ApJL in pres

Strangeness production in heavy ion collisions at SPS and RHIC within two-source statistical model

The experimental data on hadron yields and ratios in central Pb+Pb and Au+Au collisions at SPS and RHIC energies, respectively, are analysed within a two-source statistical model of an ideal hadron gas. These two sources represent the expanding system of colliding heavy ions, where the hot central fireball is embedded in a larger but cooler fireball. The volume of the central source increases with rising bombarding energy. Results of the two-source model fit to RHIC experimental data at midrapidity coincide with the results of the one-source thermal model fit, indicating the formation of an extended fireball, which is three times larger than the corresponding core at SPS.Comment: Talk at "Strange Quarks in Matter" Conference (Strangeness'2001), September 2001, Frankfurt a.M., German

Determination of activation volumes of reversal in perpendicular media

We discuss a method for the determination of activation volumes of reversal in perpendicular media. This method does not require correction for the self-demagnetizing field normally associated with these media. This is achieved by performing time dependence measurements at a constant level of magnetization. From the difference in time taken for the magnetization to decay to a fixed value at two fields-separated by a small increment DeltaH, the activation volume can be determined. We report data for both CoCrPt alloy films and a multilayer film, typical of those materials under consideration for use as perpendicular media. We find activation volumes that are consistent with the hysteresis curves of the materials. The activation volume scales qualitatively with the exchange coupling. The alloy films have significantly lower activation volumes, implying that they would be capable of supporting a higher data density

Electronic structure interpolation via atomic orbitals

We present an efficient scheme for accurate electronic structure interpolations based on the systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis calculations and the converged plane wave basis calculations on some coarse $k$-point grid. They are then used to calculate the band structure of the full Brillouin zone using the linear combination of atomic orbitals (LCAO) algorithms. We find that usually 16 -- 25 orbitals per atom can give an accuracy of about 10 meV compared to the full {\it ab initio} calculations. The current scheme has several advantages over the existing interpolation schemes. The scheme is easy to implement and robust which works equally well for metallic systems and systems with complex band structures. Furthermore, the atomic orbitals have much better transferability than the Shirley's basis and Wannier functions, which is very useful for the perturbation calculations