Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included

Motion software for a synergistic six-degree-of-freedom motion base

Computer software for the conversion of fixed-base simulations into moving-base simulations utilizing a synergistic six-degree-of-freedom motion simulator has been developed. This software includes an actuator extension transformation, inverse actuator extension transformation, a centroid transformation, and a washout circuit. Particular emphasis is placed upon the washout circuitry as adapted to fit the synergistic motion simulator. The description of the washout circuitry and illustration by means of a sample flight emphasize that translational cue representation may be of good fidelity, but care in the selection of parameters is very necessary, particularly in regard to anomalous rotational cues

Fundamental length in quantum theories with PT-symmetric Hamiltonians

The direct observability of coordinates x is often lost in PT-symmetric quantum theories. A manifestly non-local Hilbert-space metric $\Theta$ enters the double-integral normalization of wave functions $\psi(x)$ there. In the context of scattering, the (necessary) return to the asymptotically fully local metric has been shown feasible, for certain family of PT-symmetric toy Hamiltonians H at least, in paper I (M. Znojil, Phys. Rev. D 78 (2008) 025026). Now we show that in a confined-motion dynamical regime the same toy model proves also suitable for an explicit control of the measure or width $\theta$ of its non-locality. For this purpose each H is assigned here, constructively, the complete menu of its hermitizing metrics $\Theta=\Theta_\theta$ distinguished by their optional "fundamental lengths" $\theta\in (0,\infty)$. The local metric of paper I recurs at $\theta=0$ while the most popular CPT-symmetric hermitization proves long-ranged, with $\theta=\infty$.Comment: 31 pp, 3 figure

Maximal rank for ΩPn

International Mathematical Forum, Vol. 6, 2011, no. 8, 389 - 398Full Tex

A simulation study of curved, descending, decelerating, landing approaches for transport aircraft

A system which is capable of controlling an aircraft automatically along a curved, descending, decelerating approach was described. A simulation study was conducted to determine the necessary modifications to the basic flight-proven control system. This basic system is presently being used to accomplish straight-in automatic landing approaches on a short-haul transport aircraft (B-737 terminal configured vehicle). This study shows that both 3 deg (normal) and 5 deg (steep) approaches could be accomplished with only minor modifications to the basic control system

Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs are considered here in detail, with non-Hermiticities introduced by interactions attached to the vertices. The facilitated feasibility of the analysis of their spectra is achieved via their systematic approximative Runge-Kutta-inspired reduction to star-shaped discrete lattices. The resulting bound-state spectra are found real in a discretization-independent interval of couplings. This conclusion is reinterpreted as the existence of a hidden Hermiticity of our models, i.e., as the standard and manifest Hermiticity of the underlying Hamiltonian in one of less usual, {\em ad hoc} representations ${\cal H}_j$ of the Hilbert space of states in which the inner product is local (at $j=0$) or increasingly nonlocal (at $j=1,2, ...$). Explicit examples of these (of course, Hamiltonian-dependent) hermitizing inner products are offered in closed form. In this way each initial quantum graph is assigned a menu of optional, non-equivalent standard probabilistic interpretations exhibiting a controlled, tunable nonlocality.Comment: 33 pp., 6 figure

Compensation based on linearized analysis for a six degree of freedom motion simulator

The inertial response characteristics of a synergistic, six-degree-of-freedom motion base are presented in terms of amplitude ratio and phase lag as functions of frequency data for the frequency range of interest (0 to 2 Hz) in real time, digital, flight simulators. The notch filters which smooth the digital-drive signals to continuous drive signals are presented, and appropriate compensation, based on the inertial response data, is suggested. The existence of an inverse transformation that converts actuator extensions into inertial positions makes it possible to gather the response data in the inertial axis system

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi-Pasta-Ulam (FPU) paradox. We study $q$-breathers in one- two- and three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices -- theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of $q$-breathers is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter $q$-breathers delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into strong mode-mode interaction regime. In particular this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of $q$-breathers supplements these findings. For three-dimensional lattices, we find $q$-breather vortices, which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.Comment: 19 pages, 9 figure

PT-symmetric deformations of Calogero models

We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems

High prevalence of secondary resistance mutations in Venezuelan HIV-1 isolates.

The genetic variability was studied in HIV-1 from Venezuelan patients with and without treatment, in order to evaluate the presence of polymorphisms and drug resistance mutations. Proviral DNA from peripheral blood mononuclear cells or viral RNA from plasma was extracted from the blood of 30 patients. Two regions from the polymerase gene, protease (Pr) and reverse transcriptase (RT) and one genomic fragment from the envelope (Env) gene were amplified and sequenced. All HIV-1 samples analyzed were classified as subtype B, without evidence of recombination. Although no primary protease mutations were detected, a high frequency of secondary mutations (86%, 19/22), associated to restoration of viral replicative fitness, was observed in strains circulating both in treated and non-treated patients. Resistance mutations to nucleoside RT inhibitors (NRTI) and non-nucleoside RT inhibitors (NNRTI) were detected in 35% (6/17) and 12% (2/17) of the viruses circulating in treated patients, respectively. Resistance mutations were also present in the virus infecting one antiretroviral naive individual (7.7%), suggesting that local screening for resistant mutation in naive patient might be important to minimize therapy failure. Future studies are warranted to assess the role of secondary mutation in the success of viral infection