A study of the application of singular perturbation theory

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions

Electron focusing, mode spectroscopy and mass enhancement in small GaAs/AlGaAs rings

A new electron focusing effect has been discovered in small single and coupled GaAs/AlGaAs rings. The focusing in the single ring is attributed solely to internal orbits. The focusing effect allows the ring to be used as a small mass spectrometer. The focusing causes peaks in the magnetoresistance at low fields, and the peak positions were used to study the dispersion relation of the one-dimensional magnetoelectric subbands. The electron effective mass increases with the applied magnetic field by a factor of $50$, at a magnetic field of $0.5T$. This is the first time this increase has been measured directly. General agreement obtains between the experiment and the subband calculations for straight channels.Comment: 13 pages figures are available by reques

Phase coherent transport in (Ga,Mn)As

Quantum interference effects and resulting quantum corrections of the conductivity have been intensively studied in disordered conductors over the last decades. The knowledge of phase coherence lengths and underlying dephasing mechanisms are crucial to understand quantum corrections to the resistivity in the different material systems. Due to the internal magnetic field and the associated breaking of time-reversal symmetry quantum interference effects in ferromagnetic materials have been scarcely explored. Below we describe the investigation of phase coherent transport phenomena in the newly discovered ferromagnetic semiconductor (Ga,Mn)As. We explore universal conductance fluctuations in mesoscopic (Ga,Mn)As wires and rings, the Aharonov-Bohm effect in nanoscale rings and weak localization in arrays of wires, made of the ferromagnetic semiconductor material. The experiments allow to probe the phase coherence length L_phi and the spin flip length L_SO as well as the temperature dependence of dephasing.Comment: 22 pages, 10 figure

Photoconductive and polarization properties of individual CdTe nanowires

Metal-Cd0.42Te0.58-metal nanowires were electrodeposited into the pores of anodized aluminum oxide (AAO) membranes, and the polarization sensitive photoconductance was analyzed for individual nanostructures. Non-linear I–V curves were observed, and the short-circuit current density, open-circuit voltage, and fill factor were determined. These nanowires exhibited a power conversion efficiency of 0.56%, which is higher than some comparable nanomaterials of greater complexity

Theory of superconductor-insulator transition in single Josephson junctions

A non-band theory is developed to describe the superconductor-insulator (SI) transtition in resistively shunted, single Josephson junctions. The $I-V$ characteristic is formulated by a Landauer-like formula and evaluated by the path-integral transfer-matrix method. The result is consistent with the recent experiments at around 80 $mK$. However, the insulator phase shrinks with decreasing temperature indicating that the single Josephson junction becomes all superconducting at absolute zero temperature, as long as dissipation is present.Comment: 4 pages, 3 figure

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

A Randomized, Controlled, Supervised, Excerise Trial in Young Overweight Men and Women: The Midwest Exercise Trial II (MET2)

We evaluated weight loss response to 16 months of supervised exercise (45 minutes/d, 5 d/wk, 75% heart-rate-reserve) in sedentary, overweight/obese participants without energy restriction in the Midwest Exercise Trial (MET1). Results indicated men lost weight, women did not. The gender differences were associated with differences in the energy expenditure of exercise (EEEx) (men = 667 ± 116; women = 439 ± 88 kcal/session) when exercise was prescribed by frequency, intensity and duration. MET2 is a randomized control trial designed and powered to examine differences in weight loss and gender in response to EEEx for men and women of 400 or 600 kcal/session, 5d/wk, for 10 months without energy restriction. One hundred forty one participants will be randomized to 1 of 2 exercise groups or a non-exercise control. EEEx will be verified by indirect calorimetry monthly during the intervention. This study will evaluate: (1) the weight change response to two levels of EEEx versus non-exercise control; (2) gender differences in weight response to two levels of EEEx; (3) potential compensatory changes in energy intake and/or daily physical activity that may explain the observed weight changes. Results from this study may impact how exercise is prescribed for weight loss and prevention of weight regain and may clarify if men and women differ in response to exercise

Mesoscopic Behavior Near a Two-Dimensional Metal-Insulator Transition

We study conductance fluctuations in a two-dimensional electron gas as a function of chemical potential (or gate voltage) from the strongly insulating to the metallic regime. Power spectra of the fluctuations decay with two distinct exponents (1/v_l and 1/v_h). For conductivity $\sigma\sim 0.1 e^{2}/h$, we find a third exponent (1/v_i) in the shortest samples, and non-monotonic dependence of v_i and v_l on \sigma. We study the dependence of v_i, v_l, v_h, and the variances of corresponding fluctuations on \sigma, sample size, and temperature. The anomalies near $\sigma\simeq 0.1 e^{2}/h$ indicate that the dielectric response and screening length are critically behaved, i.e. that Coulomb correlations dominate the physics.Comment: Revised according to referee remark

Phonon Universal Transmission Fluctuations and Localization in Semiconductor Superlattices with a Controlled Degree of Order

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks- Teller superlattice exhibits a transition from periodic ordering, with alterna- ting layers, to the phase separated opposite limit; including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any $N$ conse- cutive layers) and long range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a {\it universal\/} curve irrespective of the specific type of disorder of the SL. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal transmission fluctuations.Comment: 16-pages, Revte