Solution of systems of nonlinear equations Final report

Algorithm and computer program of diagonal discrimination method for computing nonlinear and transcendental function

Affirmative Action and Diversity in Public Education — Legal Developments

The first part of this report briefly reviews the judicial evolution of race-based affirmative action, particularly in relation to public education. Recent rulings challenging the use of racial admissions and hiring practices by public educational institutions are then considered for their implications on the future development of affirmative action law

Production of photons by the parametric resonance in the dynamical Casimir effect

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of other works considering only $2 \omega_1$, where $\omega_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time-evolution of quantum fields, we introduce a new method which is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.Comment: 15 pages, RevTeX, no figure

Quantum lattice solitons in ultracold bosons near Feshbach resonance

Quantum lattice solitons in a system of two ultracold bosons near Feshbach resonance are investigated. It is shown that their binding energy, effective mass, and spatial width, can be manipulated varying the detuning from the Feshbach resonance. In the case of attractive atomic interactions, the molecule creation stabilizes the solitons. In the case of repulsive interactions, the molecule creation leads to the possibility of existence of bright solitons in some interval of detunings. Due to quantum fluctuations the soliton width is a random quantity. Its standard deviation is larger than the mean value for such a small number of particles

The Schrodinger particle in an oscillating spherical cavity

We study a Schrodinger particle in an infinite spherical well with an oscillating wall. Parametric resonances emerge when the oscillation frequency is equal to the energy difference between two eigenstates of the static cavity. Whereas an analytic calculation based on a two-level system approximation reproduces the numerical results at low driving amplitudes, epsilon, we observe a drastic change of behaviour when epsilon > 0.1, when new resonance states appear bearing no apparent relation to the eigenstates of the static system.Comment: 9 pages, 6 figures, corrected typo

Numerical approach to the dynamical Casimir effect

The dynamical Casimir effect for a massless scalar field in 1+1-dimensions is studied numerically by solving a system of coupled first-order differential equations. The number of scalar particles created from vacuum is given by the solutions to this system which can be found by means of standard numerics. The formalism already used in a former work is derived in detail and is applied to resonant as well as off-resonant cavity oscillations.Comment: 15 pages, 4 figures, accepted for publication in J. Phys. A (special issue: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005

Dark Matter Constraints from the Sagittarius Dwarf and Tail System

2MASS has provided a three-dimensional map of the >360 degree, wrapped tidal tails of the Sagittarius (Sgr) dwarf spheroidal galaxy, as traced by M giant stars. With the inclusion of radial velocity data for stars along these tails, strong constraints exist for dynamical models of the Milky Way-Sgr interaction. N-body simulations of Sgr disruption with model parameters spanning a range of initial conditions (e.g., Sgr mass and orbit, Galactic rotation curve, halo flattening) are used to find parameterizations that match almost every extant observational constraint of the Sgr system. We discuss the implications of the Sgr data and models for the orbit, mass and M/L of the Sgr bound core as well as the strength, flattening, and lumpiness of the Milky Way potential.Comment: 6 pages, 0 figures. Contribution to proceedings of ``IAU Symposium 220: Dark Matter in Galaxies'', eds. S. Ryder, D.J. Pisano, M. Walker, and K. Freema