Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

Superconductivity in the Two-Dimensional tt-JJ Model at Low Hole Doping

By combining a generalized Lanczos scheme with the variational Monte Carlo method we can optimize the short- and long-range properties of the groundstate separately. This allows us to measure the long-range order of the groundstate of the $t$-$J$ model as a function of the coupling constant $J/t$, and identify a region of finite d-wave superconducting long-range order. With a lattice size of 50 sites we can reliably examine hole densities down to 0.16.Comment: 12 pages and 4 PostScript figures, ReVTeX 3.0, ETH-TH/94-1

Hybrid fuzzy and sliding-mode control for motorised tether spin-up when coupled with axial vibration

A hybrid fuzzy sliding mode controller is applied to the control of motorised tether spin-up coupled with an axial oscillation phenomenon. A six degree of freedom dynamic model of a motorised momentum exchange tether is used as a basis for interplanetary payload exchange. The tether comprises a symmetrical double payload configuration, with an outrigger counter inertia and massive central facility. It is shown that including axial elasticity permits an enhanced level of performance prediction accuracy and a useful departure from the usual rigid body representations, particularly for accurate payload positioning at strategic points. A special simulation program has been devised in MATLAB and MATHEMATICA for a given initial condition data case

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part III: Twist Number Method

We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--D\'emoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.Comment: To be published in Ap

Non-Universality in Random Matrix Ensembles with Soft Level Confinement

Two families of strongly non-Gaussian random matrix ensembles (RME) are considered. They are statistically equivalent to a one-dimensional plasma of particles interacting logarithmically and confined by the potential that has the long-range behavior $V(\epsilon)\sim |\epsilon|^{\alpha}$ ($0<\alpha<1$), or $V(\epsilon)\sim \ln^{2}|\epsilon|$. The direct Monte Carlo simulations on the effective plasma model shows that the spacing distribution function (SDF) in such RME can deviate from that of the classical Gaussian ensembles. For power-law potentials, this deviation is seen only near the origin $\epsilon\sim 0$, while for the double-logarithmic potential the SDF shows the cross-over from the Wigner-Dyson to Poisson behavior in the bulk of the spectrum.Comment: 4 pages, REVTEX, 3 postscript figures appended, ICTP/9/94/ckw.

Molecular beam epitaxial growth of high-quality InSb on InP and GaAs substrates

Epitaxial layers of InSb were grown on InP and GaAs substrates by molecular beam epitaxy. The dependence of the epilayer quality on flux ratio, J sub Sb4/J sub In, was studied. Deviation from an optimum value of J sub Sb4/J sub In (approx. 2) during growth led to deterioration in the surface morphology and the electrical and crystalline qualities of the films. Room temperature electron mobilities as high as 70,000 and 53,000 sq cm /V-s were measured in InSb layers grown on InP and GaAs substrates, respectively. Unlike the previous results, the conductivity in these films is n-type even at T = 13 K, and no degradation of the electron mobility due to the high density of dislocations was observed. The measured electron mobilities (and carrier concentrations) at 77 K in InSb layers grown on InP and GaAs substrates are 110,000 sq cm/V-s (3 x 10(15) cm(-3)) and 55,000 sq cm/V-s (4.95 x 10(15) cm(-3)), respectively, suggesting their application to electronic devices at cryogenic temperatures

Utility investigation of artificial time delay in displacement-noise-free interferometers

Laser interferometer gravitational wave detectors are usually limited by displacement noise in their lower frequency band. Recently, theoretical proposals have been put forward to construct schemes of interferometry that are insusceptible to displacement noise as well as classical laser noise. These so-called displacement-noise-free interferometry (DFI) schemes take advantage of the difference between gravitational waves and displacement noise in their effects on light propagation. However, since this difference diminishes in lower frequencies (i.e., Omega>[script L]D/c) into the interferometry scheme, with the hope of improving low-frequency sensitivity. We found that sensitivity can only be improved by schemes in which fluctuations in the artificial time delays are not canceled

A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds. In this note we proved that there exists no proper doubly warped product contact CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page