98,906 research outputs found
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
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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
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