Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index $n$, on the leading order gravitational waveforms is studied.Comment: 31 pages, 7 figures, typos correcte

Multivariate Fitting and the Error Matrix in Global Analysis of Data

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative method that significantly improves the reliability of the error matrix calculation. To obtain even better estimates of the uncertainties on predictions of physical observables, we also present a Lagrange multiplier method that explores the entire parameter space and avoids the linear approximations assumed in conventional error propagation calculations. These methods are illustrated by an example from the global analysis of parton distribution functions.Comment: 13 pages, 5 figures, Latex; minor clarifications, fortran program made available; Normalization of Hessian matrix changed to HEP standar

Chemical equilibrium and stable stratification of a multi-component fluid: thermodynamics and application to neutron stars

A general thermodynamic argument shows that multi-component matter in full chemical equilibrium, with uniform entropy per baryon, is generally stably stratified. This is particularly relevant for neutron stars, in which the effects of entropy are negligible compared to those of the equilibrium composition gradient established by weak interactions. It can therefore be asserted that, regardless of the uncertainties in the equation of state of dense matter, neutron stars are stably stratified. This has important, previously discussed consequences for their oscillation modes, magnetic field evolution, and internal angular momentum transport.Comment: AASTeX, 8 pages, including 1 PS figure. Accepted for publication in The Astrophysical Journa

Innermost Stable Circular Orbit of a Spinning Particle in Kerr Spacetime

We study stability of a circular orbit of a spinning test particle in a Kerr spacetime. We find that some of the circular orbits become unstable in the direction perpendicular to the equatorial plane, although the orbits are still stable in the radial direction. Then for the large spin case ($S < \sim O(1)), the innermost stable circular orbit (ISCO) appears before the minimum of the effective potential in the equatorial plane disappears. This changes the radius of ISCO and then the frequency of the last circular orbit.Comment: 25 pages including 8 figure

General-relativistic coupling between orbital motion and internal degrees of freedom for inspiraling binary neutron stars

We analyze the coupling between the internal degrees of freedom of neutron stars in a close binary, and the stars' orbital motion. Our analysis is based on the method of matched asymptotic expansions and is valid to all orders in the strength of internal gravity in each star, but is perturbative in the ``tidal expansion parameter'' (stellar radius)/(orbital separation). At first order in the tidal expansion parameter, we show that the internal structure of each star is unaffected by its companion, in agreement with post-1-Newtonian results of Wiseman (gr-qc/9704018). We also show that relativistic interactions that scale as higher powers of the tidal expansion parameter produce qualitatively similar effects to their Newtonian counterparts: there are corrections to the Newtonian tidal distortion of each star, both of which occur at third order in the tidal expansion parameter, and there are corrections to the Newtonian decrease in central density of each star (Newtonian ``tidal stabilization''), both of which are sixth order in the tidal expansion parameter. There are additional interactions with no Newtonian analogs, but these do not change the central density of each star up to sixth order in the tidal expansion parameter. These results, in combination with previous analyses of Newtonian tidal interactions, indicate that (i) there are no large general-relativistic crushing forces that could cause the stars to collapse to black holes prior to the dynamical orbital instability, and (ii) the conventional wisdom with respect to coalescing binary neutron stars as sources of gravitational-wave bursts is correct: namely, the finite-stellar-size corrections to the gravitational waveform will be unimportant for the purpose of detecting the coalescences.Comment: 22 pages, 2 figures. Replaced 13 July: proof corrected, result unchange

Modulation of the high mobility two-dimensional electrons in Si/SiGe using atomic-layer-deposited gate dielectric

Metal-oxide-semiconductor field-effect transistors (MOSFET's) using atomic-layer-deposited (ALD) Al$_2$O$_3$ as the gate dielectric are fabricated on the Si/Si$_{1-x}$Ge$_x$ heterostructures. The low-temperature carrier density of a two-dimensional electron system (2DES) in the strained Si quantum well can be controllably tuned from 2.5$\times10^{11}$cm$^{-2}$ to 4.5$\times10^{11}$cm$^{-2}$, virtually without any gate leakage current. Magnetotransport data show the homogeneous depletion of 2DES under gate biases. The characteristic of vertical modulation using ALD dielectric is shown to be better than that using Schottky barrier or the SiO$_2$ dielectric formed by plasma-enhanced chemical-vapor-deposition(PECVD).Comment: 3 pages Revtex4, 4 figure