A Generalization of the Gram determinant of type A

The Gram determinant of type $A$ was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type $A$ by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determinant. We conclude the paper by discussing Chen's conjecture about the Gram determinant of type $Mb$ evaluated in the Klein bottle.Comment: 17 pages, 19 figure

Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model

A numerical analysis of surface plasmon dispersion, propagation, and localization on smooth lossy films is presented. Particular attention is given to determining wavelength-dependent behavior of thin Ag slab waveguides embedded in a symmetric SiO2 environment. Rather than considering Ag as a damped free electron gas, the metal is defined by the experimentally determined optical constants of Johnson and Christy and Palik. As in free electron gas models, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric field distributions—as film thickness is decreased below 50 nm. However, unlike free electron gas models, the surface plasmon wave vector remains finite at resonance with the antisymmetric-field plasmon converging to a pure photon mode for very thin films. In addition, allowed excitation modes are found to exist between the bound and radiative branches of the dispersion curve. The propagation characteristics of all modes are determined, and for thin films (depending upon electric field symmetry), propagation distances range from microns to centimeters in the near infrared. Propagation distances are correlated with both the field decay (skin depth) and energy density distribution in the metal and surrounding dielectric. While the energy density of most long-range surface plasmons exhibits a broad spatial extent with limited confinement in the waveguide, it is found that high-field confinement does not necessarily limit propagation. In fact, enhanced propagation is observed for silver films at ultraviolet wavelengths despite strong field localization in the metal. The surface plasmon characteristics described in this paper provide a numerical springboard for engineering nanoscale metal plasmon waveguides, and the results may provide a new avenue for integrated optoelectronic applications

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Critical Casimir force in 4^4He films: confirmation of finite-size scaling

We present new capacitance measurements of critical Casimir force-induced thinning of $^4$He films near the superfluid/normal transition, focused on the region below $T_{\lambda}$ where the effect is the greatest. $^4$He films of 238, 285, and 340 \AA thickness are adsorbed on N-doped silicon substrates with roughness $\approx 8 {\AA}$. The Casimir force scaling function $\vartheta$, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum $\vartheta = -1.30 \pm 0.03$ at $x=td^{1/\nu}=-9.7\pm 0.8 {\AA}^{1/\nu}$. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to $2.13 K$ of the Goldstone/surface fluctuation force, which makes the superfluid film $\sim 2 {\AA}$ thinner than the normal film.Comment: 4 pages, 3 figures, submitted to PR

Heterodyne detection of the 752.033-GHz H2O rotational absorption line

A tunable high resolution two stage heterodyne radiometer was developed for the purpose of investigating the intensity and lineshape of the 752.033 GHz rotational transition of water vapor. Single-sideband system noise temperatures of approximately 45,000 K were obtained using a sensitive GaAs Schottky diode as the first stage mixer. First local oscillator power was supplied by a CO2 laser pumped formic acid laser (761.61 GHz), generating an X-band IF signal with theoretical line center at 9.5744 GHz. Second local oscillator power was provided by means of a 3 GHz waveguide cavity filter with only 9 dB insertion loss. In absorption measurements of the H2O taken from a laboratory simulation of a high altitude rocket plume, the center frequency of the 752 GHz line was determined to within 1 MHz of the reported value. A rotational temperature 75 K, a linewidth 5 MHz and a Doppler shift 3 MHz were measured with the line-of-sight intersecting the simulated-plume axis at a distance downstream of 30 nozzle diameters. These absorption data were obtained against continuum background radiation sources at temperatures of 1175 and 300 K

The Four Stages of Youth Sports TBI Policymaking: Engagement, Enactment, Research, and Reform

This article advances, for the first time, a framework for situating public health law interventions as occurring in a predictable four-stage process. In this article, written in connection with our panel at the Public Health Law Research Conference (2014), we briefly apply this four-stage framework to youth sports TBI laws, and conclude that public health lawmaking in this area is consistent with prior high-visibility public health law interventions

Polymer lattices as mechanically tunable 3-dimensional photonic crystals operating in the infrared

Broadly tunable photonic crystals in the near- to mid-infrared region could find use in spectroscopy, non-invasive medical diagnosis, chemical and biological sensing, and military applications, but so far have not been widely realized. We report the fabrication and characterization of three-dimensional tunable photonic crystals composed of polymer nanolattices with an octahedron unit-cell geometry. These photonic crystals exhibit a strong peak in reflection in the mid-infrared that shifts substantially and reversibly with application of compressive uniaxial strain. A strain of ∼40% results in a 2.2 μm wavelength shift in the pseudo-stop band, from 7.3 μm for the as-fabricated nanolattice to 5.1 μm when strained. We found a linear relationship between the overall compressive strain in the photonic crystal and the resulting stopband shift, with a ∼50 nm blueshift in the reflection peak position per percent increase in strain. These results suggest that architected nanolattices can serve as efficient three-dimensional mechanically tunable photonic crystals, providing a foundation for new opto-mechanical components and devices across infrared and possibly visible frequencies

Maleimide scavenging enhances determination of protein S-palmitoylation state in acyl-exchange methods.

S-palmitoylation (S-acylation) is an emerging dynamic post-translational modification of cysteine residues within proteins.Current assays for protein S-palmitoylation involve either in vivo labelling or chemical cleavage of S-palmitoyl groupsto reveal a free cysteine sulfhydryl that can be subsequently labelled with an affinity handle (acyl-exchange). Assays for protein S-palmitoylation using acylexchange chemistry therefore require blocking of non-S-palmitoylated cysteines, typically using Nethylmaleimide, to prevent non-specific detection. This in turn necessitates multiple precipitation based clean-up steps to remove reagents between stages, often leading to variable sample loss, reduced signal or protein aggregation. These combine to reduce the sensitivity, reliability and accuracy of these assays and also requires a substantial amount of time to perform. By substituting these precipitation steps with chemical scavenging of N-ethylmaleimide by 2,3-dimethyl-1,3-butadiene in an aqueous Diels-Alder 4+2 cyclo-addition reaction it is possible to greatly improve sensitivity and accuracy while reducing hands-on and overall time required for assays

On framings of knots in 3-manifolds

We show that the only way of changing the framing of a knot or a link by ambient isotopy in an oriented $3$-manifold is when the manifold has a properly embedded non-separating $S^2$. This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough's work on the mapping class groups of $3$-manifolds. We also relate our results to the theory of skein modules.Comment: 12 pages, 9 figure