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

Preliminary design characteristics of a subsonic business jet concept employing laminar flow control

Aircraft configurations were developed with laminar flow control (LFC) and without LFC. The LFC configuration had approximately eleven percent less parasite drag and a seven percent increase in the maximum lift-to drag ratio. Although these aerodynamic advantages were partially offset by the additional weight of the LFC system, the LFC aircraft burned from six to eight percent less fuel for comparable missions. For the trans-atlantic design mission with the gross weight fixed, the LFC configuration would carry a greater payload for ten percent fuel per passenger mile

Design of a large span-distributed load flying-wing cargo airplane with laminar flow control

A design study was conducted to add laminar flow control to a previously design span-distributed load airplane while maintaining constant range and payload. With laminar flow control applied to 100 percent of the wing and vertical tail chords, the empty weight increased by 4.2 percent, the drag decreased by 27.4 percent, the required engine thrust decreased by 14.8 percent, and the fuel consumption decreased by 21.8 percent. When laminar flow control was applied to a lesser extent of the chord (approximately 80 percent), the empty weight increased by 3.4 percent, the drag decreased by 20.0 percent, the required engine thrust decreased by 13.0 percent, and the fuel consumption decreased by 16.2 percent. In both cases the required take-off gross weight of the aircraft was less than the original turbulent aircraft

Preliminary design characteristics of a subsonic business jet concept employing an aspect ratio 25 strut braced wing

The advantages of replacing the conventional wing on a transatlantic business jet with a larger, strut braced wing of aspect ratio 25 were evaluated. The lifting struts reduce both the induced drag and structural weight of the heavier, high aspect ratio wing. Compared to the conventional airplane, the strut braced wing design offers significantly higher lift to drag ratios achieved at higher lift coefficients and, consequently, a combination of lower speeds and higher altitudes. The strut braced wing airplane provides fuel savings with an attendant increase in construction costs

A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation

We present a new approach to the design of optical microstructured fibers that have group velocity dispersion (GVD) and effective nonlinear coefficient (gamma ) tailored for supercontinuum (SC) generation. This hybrid approach combines a genetic algorithm (GA) with pulse propagation modeling, but without include it into the GA loop, to allow the efficient design of fibers that are capable of generating highly coherent and large bandwidth SC in the mid-infrared (Mid-IR) spectrum. To the best of our knowledge, this is the first use of a GA to design fiber for SC generation. We investigate the robustness of these fiber designs to variation in the fiber's structural parameters. The optimized fiber structure based on a type of tellurite glass (70TeO(2) - 10 Na(2)O - 20 ZnF(2)) is predicted to have near-zero group velocity dispersion (< +/-2 ps/nm/km) from 2 to 3 microm, and a effective nonlinear coefficient of gamma approximately 174 W(-1)km(-1) at 2 microm. The SC output of this fiber shows a significant bandwidth and coherence increase compare to a fiber with a single zero group velocity dispersion wavelength at 2 microm.Wen Qi Zhang, Shahraam Afshar V. and Tanya M. Monr

Theory of radiation trapping by the accelerating solitons in optical fibers

We present a theory describing trapping of the normally dispersive radiation by the Raman solitons in optical fibers. Frequency of the radiation component is continuously blue shifting, while the soliton is red shifting. Underlying physics of the trapping effect is in the existence of the inertial gravity-like force acting on light in the accelerating frame of reference. We present analytical calculations of the rate of the opposing frequency shifts of the soliton and trapped radiation and find it to be greater than the rate of the red shift of the bare Raman soliton. Our findings are essential for understanding of the continuous shift of the high frequency edge of the supercontinuum spectra generated in photonic crystal fibers towards higher frequencies.Comment: Several misprints in text and formulas corrected. 10 pages, 9 figures, submitted to Phys. Rev.

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

Flux Periodicities in Loops of Nodal Superconductors

Supercurrents in superconducting flux threaded loops are expected to oscillate with the magnetic flux with a period of hc/2e. This is indeed true for s-wave superconductors larger than the coherence length xi_0. Here we show that for superconductors with gap nodes, there is no such strict condition for the supercurrent to be hc/2e rather than hc/e periodic. For nodal superconductors, the flux induced Doppler shift of the near nodal states leads to a flux dependent occupation probability of quasi-particles circulating clockwise and counter clockwise around the loop, which leads to an hc/e periodic component of the supercurrent, even at zero temperature. We analyze this phenomenon on a cylinder in an approximative analytic approach and also numerically within the framework of the BCS theory. Specifically for d-wave pairing, we show that the hc/e periodic current component decreases with the inverse radius of the loop and investigate its temperature dependence

Kolmogorov Similarity Hypotheses for Scalar Fields: Sampling Intermittent Turbulent Mixing in the Ocean and Galaxy

Kolmogorov's three universal similarity hypotheses are extrapolated to describe scalar fields like temperature mixed by turbulence. By the analogous Kolmogorov third hypothesis for scalars, temperature dissipation rates chi averaged over lengths r > L_K should be lognormally distributed with intermittency factors I that increase with increasing turbulence energy length scales L_O as I_chi-r = m_T ln(L_O/r). Tests of Kolmogorovian velocity and scalar universal similarity hypotheses for very large ranges of turbulence length and time scales are provided by data from the ocean and the Galactic interstellar medium. The universal constant for turbulent mixing intermittency m_T is estimated from oceanic data to be 0.44+-0.01, which is remarkably close to estimates for Kolmogorov's turbulence intermittency constant m_u of 0.45+-0.05 from Galactic as well as atmospheric data. Extreme intermittency complicates the oceanic sampling problem, and may lead to quantitative and qualitative undersampling errors in estimates of mean oceanic dissipation rates and fluxes. Intermittency of turbulence and mixing in the interstellar medium may be a factor in the formation of stars.Comment: 23 pages original of Proc. Roy. Soc. article, 8 figures; in "Turbulence and Stochastic Processes: Kolmogorov's ideas 50 years on", London The Royal Society, 1991, J.C.R. Hunt, O.M. Phillips, D. Williams Eds., pages 1-240, vol. 434 (no. 1890) Proc. Roy. Soc. Lond. A, PDF fil

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