Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion

We investigate the quantum decoherence of frequency and polarization variables of photons via polarization mode dispersion in optical fibers. By observing the analogy between the propagation equation of the field and the Schr\"odinger equation, we develop a master equation under Markovian approximation and analytically solve for the field density matrix. We identify distinct decay behaviors for the polarization and frequency variables for single-photon and two-photon states. For the single photon case, purity functions indicate that complete decoherence for each variable is possible only for infinite fiber length. For entangled two-photon states passing through separate fibers, entanglement associated with each variable can be completely destroyed after characteristic finite propagation distances. In particular, we show that frequency disentanglement is independent of the initial polarization status. For propagation of two photons in a common fiber, the evolution of a polarization singlet state is addressed. We show that while complete polarization disentanglement occurs at a finite propagation distance, frequency entanglement could survive at any finite distance for gaussian states.Comment: 2 figure

Diffusive Evolution of Stable and Metastable Phases II: Theory of Non-Equilibrium Behaviour in Colloid-Polymer Mixtures

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics therefore impinges on many areas of thermodynamics and phase-ordering. An exact solution is found for the motion of a single, planar interface separating a growing phase of uniform high density from a supersaturated low density phase, whose diffusive depletion drives the interfacial motion. In addition, an approximate solution is found for the one-dimensional evolution of two interfaces, separated by a slab of a metastable phase at intermediate density. The theory predicts a critical supersaturation of the low-density phase, above which the two interfaces become unbound and the metastable phase grows ad infinitum. The growth of the stable phase is suppressed in this regime.Comment: 27 pages, Latex, eps

Variability in surface electromyogram during gait analysis of low back pain patients

This paper describes the analysis of the variance of the amplitude of surface electromyogram (SEMG) recorded from the L4/ L5 region of the erector spinae for healthy participants and people suffering with low back pain (LBP) when they were walking and running on a treadmill. The results indicate that there was no significant difference in the variance and in the change of variance over time of the exercise between the two groups when the participants were walking. However, when the participants were running, there was a significant difference between the two cohorts. While there was an increase in the variance over the duration of the exercise for both of the groups, the increase in variance of the LBP group was much greater (order of ten times) compared with that of the healthy participants. The difference between the two groups was also very significant when observing the change of variance over time. From these results, it is suggested that variance of SEMG of the muscles of the lower back, recorded when the participants are running, can be used to identify LBP patients

Role of Multipoles in Counterion-Mediated Interactions between Charged Surfaces: Strong and Weak Coupling

We present general arguments for the importance, or lack thereof, of the structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean-field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.Comment: 12 pages, 3 figure

The Role of Solid Friction in the Sedimentation of Strongly Attractive Colloidal Gels

We study experimentally and theoretically the sedimentation of gels made of strongly aggregated colloidal particles, focussing on the long time behavior, when mechanical equilibrium is asymptotically reached. The asymptotic gel height is found to vary linearly with the initial height, a finding in stark contrast with a recent study on similar gels [Manley \textit{et al.} 2005 \textit{Phys. Rev. Lett.} \textbf{94} 218302]. We show that the asymptotic compaction results from the balance between gravity pull, network elasticity, and solid friction between the gel and the container walls. Based on these ingredients, we propose a simple model to account for the dependence of the height loss on the initial height and volume fraction. As a result of our analysis, we show that the static friction coefficient between the gel and the container walls strongly depends on volume fraction: the higher the volume fraction, the weaker the solid friction. This nonintuitive behavior is explained using simple scaling arguments.Comment: 13 pages, 5 figures. Submitted to JSTA

Low-loss broadband bi-layer edge couplers for visible light

Low-loss broadband fiber-to-chip coupling is currently challenging for visible-light photonic-integrated circuits (PICs) that need both high confinement waveguides for high-density integration and a minimum feature size above foundry lithographical limit. Here, we demonstrate bi-layer silicon nitride (SiN) edge couplers that have ≤ 4 dB/facet coupling loss with the Nufern S405-XP fiber over a broad optical wavelength range from 445 to 640 nm. The design uses a thin layer of SiN to expand the mode at the facet and adiabatically transfers the input light into a high-confinement single-mode waveguide (150-nm thick) for routing, while keeping the minimum nominal lithographic feature size at 150 nm. The achieved fiber-to-chip coupling loss is about 3 to 5 dB lower than that of single-layer designs with the same waveguide confinement and minimum feature size limitation