A Relation Between the Kauffman and the HOMFLY Polynomials for Torus Knots

Polynomial invariants corresponding to the fundamental representation of the gauge group $SO(N)$ are computed for arbitrary torus knots in the framework of Chern-Simons gauge theory making use of knot operators. As a result, a formula which relates the Kauffman and the HOMFLY polynomials for torus knots is presented.Comment: 47 pages, macropackage phyzzx.tex, minor corrections made, version to appear in Journal of Mathematical Physic

The Role of Non-Parity Fundamentals in Exchange Rate Determination: Australia and the Asia Pacific Region

This paper extends the literature by looking at the contribution of non-parity variables after extracting the impact of parity variables on exchange rates of Australia and the Asia Pacific countries. Exchange rates are examined using high- and low-frequency multi-country panel time series data for a group of trade-related nations in the Asia Pacific, including Japan. Our findings suggest that exchange rate is affected by growth rate, and trade and capital flows: other less significant variables include sovereign debt; balance of payments; money supply; and trade openness. It also confirms that interest rate has significant effect on exchange rates while price effect is not significant in short run regressions. These key findings are robust across different time intervals, thus showing new findings on the exchange rate dynamics consistent with theories.

Quantum Simulation of the Hubbard Model: The Attractive Route

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.Comment: 11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added reference

Robust H∞ control with missing measurements and time delays

Copyright [2007] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the robust control problem is investigated for a class of stochastic uncertain discrete time-delay systems with missing measurements. The parameter uncertainties enter into the state matrices, and the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. The purpose of the problem is to design a full-order dynamic feedback controller such that, for all possible missing observations and admissible parameter uncertainties, the closed-loop system is asymptotically mean-square stable and satisfies the prescribed performance constraint. Delay-dependent conditions are derived under which the desired solution exists, and the controller parameters are designed by solving a linear matrix inequality (LMI). A numerical example is provided to illustrate the usefulness of the proposed design method

Evaluation of materials and design modifications for aircraft brakes

A test program is described which was carried out to evaluate several proposed design modifications and several high-temperature friction materials for use in aircraft disk brakes. The evaluation program was carried out on a specially built test apparatus utilizing a disk brake and wheel half from a small het aircraft. The apparatus enabled control of brake pressure, velocity, and braking time. Tests were run under both constant and variable velocity conditions and covered a kinetic energy range similar to that encountered in aircraft brake service. The results of the design evaluation program showed that some improvement in brake performance can be realized by making design changes in the components of the brake containing friction material. The materials evaluation showed that two friction materials show potential for use in aircraft disk brakes. One of the materials is a nickel-based sintered composite, while the other is a molybdenum-based material. Both materials show much lower wear rates than conventional copper-based materials and are better able to withstand the high temperatures encountered during braking. Additional materials improvement is necessary since both materials show a significant negative slope of the friction-velocity curve at low velocities

A micro-electro-mechanical-system-based thermal shear-stress sensor with self-frequency compensation

By applying the micro-electro-mechanical-system (MEMS) fabrication technology, we developed a micro-thermal sensor to measure surface shear stress. The heat transfer from a polysilicon heater depends on the normal velocity gradient and thus provides the surface shear stress. However, the sensitivity of the shear-stress measurements in air is less than desirable due to the low heat capacity of air. A unique feature of this micro-sensor is that the heating element, a film 1 µm thick, is separated from the substrate by a vacuum cavity 2 µm thick. The vacuum cavity prevents the conduction of heat to the substrate and therefore improves the sensitivity by an order of magnitude. Owing to the low thermal inertia of the miniature sensing element, this shear-stress micro-sensor can provide instantaneous measurements of small-scale turbulence. Furthermore, MEMS technology allows us make multiple sensors on a single chip so that we can perform distributed measurements. In this study, we use multiple polysilicon sensor elements to improve the dynamic performance of the sensor itself. It is demonstrated that the frequency-response range of a constant-current sensor can be extended from the order of 100 Hz to 100 kHz

Deconfinement and cold atoms in optical lattices

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.Comment: Proceedings of the conference on "Quantum Many Body Theories 13", to be published by World Scientifi

Semimetalic graphene in a modulated electric potential

The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a field could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. There exist infinite Fermi-momentum states in sharply contrast with two crossing points (Dirac points) for graphene without external fields. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states.Comment: 12pages, 5 figure