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

Laser-assisted photothermal imprinting of nanocomposite

We report on a laser-assisted photothermal imprinting method for directly patterning carbon nanofiber-reinforced polyethylene nanocomposite. A single laser pulse from a solid state Nd:YAG laser (10 ns pulse, 532 nm and 355 nm wavelengths) is used to melt/soften a thin skin layer of the polymer nanocomposite. Meanwhile, a fused quartz mold with micro-sized surface relief structures is pressed against the surface of the composite. Successful pattern transfer is realized upon releasing the quartz mold. Although polyethylene is transparent to the laser beam, the carbon nanofibers in the high density polyethylene (HDPE) matrix absorb the laser energy and convert it into heat. Numerical heat conduction simulation shows the HDPE matrix is partially melted or softened, allowing for easier imprinting of the relief pattern of the quartz mold.Mechanical Engineerin

The Static Dielectric Constant of a Colloidal Suspension

We derive an expression for the static dielectric constant of the colloidal susp ensions based on the electrokinetic equations. The analysis assumes that the ions have the same diffusivity, and that the double layer is much thinner than the radius of curvature of the particles. It is shown that the dielectric increment of the double layer polarization mechanism is originated from the free energy stored in the salt concentration inhomogeniety. We also show that the dominant polarization charges in the theory are at the electrodes, rather than close to the particles.Comment: 15 pages, 1 figur

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

Fault-tolerant linear optics quantum computation by error-detecting quantum state transfer

A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding error-detection capability. Photons are assumed to be subjected to both photon loss and depolarization, and the threshold region of their strengths for scalable quantum computation is obtained, together with the amount of physical resources consumed. Compared to currently known results, the present scheme reduces the resource requirement, while yielding a comparable threshold region.Comment: 9 pages, 7 figure