A trace method for directly synthesizing Liapunov functions of aperiodic systems
Liapunov functions synthesis for aperiodic linear systems by inspecting traces of state matrix and products
Chen, C. F.↗
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Optimal control of aperiodic discrete-time systems.
Optimal control and trajectory optimization in aperiodic discrete time functional systems
APERIODIC FUNCTION↗
Construction of complementary code sequence sets, part 7.1D
A set of code sequences is a complementary code sequence set if the sum of the aperiodic autocorrelation functions for the sequences is zero everywhere except at the origin. A simple construction for sets of complementary code sequences is discussed.
Sarwate, D. V.↗
The X-ray halo of Cygnus X-1
Four Einstein HRI images of Cygnus X-1 were examined for the presence of a halo due to scattering of X-rays by interstellar grains. The analysis technique exploits the intrinsic aperiodic variability of the source to map the point response function of the optics. A residual, nonvariable component to the surface brightness distribution (comprising approximately more than 12 percent of the source flux) is interpreted as a scattered halo. The halo flux does not reflect the short term time variability of the central source as it is smoothed by differential time delays of order days. The Cygnus X-1 halo is consistent with those of other sources derived in previous studies using different techniques. Comparison is made with a scattering model, and the sensitivity of the halo flux to maximal grain size is demonstrated.
Bode, M. F.↗
Search for scattered X-ray halos around variable sources - The X-ray halo of Cygnus X-1
The results of a program to search for the presence of halos due to X-ray scattering by interstellar grains in the line-of-sight to variable X-ray sources are reported. As part of this program, four Einstein HRI images of Cyg X-1 were examined. The analysis technique exploits the intrinsic aperiodic variability of this source to map the point response function of the optics. Any scattered halo present will not reflect short-term central source time variability, since such variability is smoothed by differential time delays of order days. Thus, a residual, nonvariable component to the surface brightness distribution (comprising about 12 percent or more of the source flux) is interpreted as a scattered halo. The Cyg X-1 halo is consistent with those of other sources found in previous studies using different techniques. Comparison is also made with a scattering model and, despite uncertainties in source spectrum and distance, reasonable agreement with the observatons is found using a standard interstellar grain model. The potential of X-ray scattering as a probe of the properties of interstellar grains is demonstrated.
Bode, M. F.↗
Steady, periodic, and aperiodic atmospheric flows
Atmospheric weather patterns usually occur on scales of a 1000 km or 5000 km and greater, and quasisteady situations can be caused by the appearance of high pressure, blocking zones. Attention is given to the wave-wave interactions and their effects on atmospheric flows on the large scale. The discussion is performed with the beta-plane model for a spherical geometry and a large number of degrees of freedom. The barotropic potential vorticity equation is defined, and discretization of the topography of the sphere results in a spectral truncation with 25 components. The solutions are generated as a function of a forcing and a dissipative parameter. The model yields steady, periodic, and aperiodic solutions, which are shown to be analogous to zonal and blocked atmospheric flows.
Legras, B.↗
Static aeroelasticity and the flying wing, revisited
The roll dynamic behavior of some wing configurations is examined. Analysis shows that the static divergence instability which occurs for symmetrical or clamped sweptforward wings is modified by roll freedom. The instability found in the present highly idealized analysis is still of an aperiodic nature, but at a speed above the conventional divergence speed. The magnitude of this difference is seen to be a function of the ratio of the wing roll mass moment of inertia to the mass moment of inertia of the wing about the roll axis, and this difference may be quite significant.
Weisshaar, T. A.↗
Chaos in a spatially-developing plane mixing layer
A spatially-developing plane mixing layer was analyzed for chaotic behavior. A direct numerical simulation of the Navier-Stokes equations in a 2-D domain infinite in y and having inflow-outflow boundary conditions in x was used for data. Spectra, correlation dimension and the largest Lyapunov exponent were computed as functions of downstream distance x. When forced at a single (fundamental) frequency with maximum amplitude, the flow is periodic at the inflow but becomes aperiodic with increasing x. The aperiodic behavior is caused by the presence of a noisy subharmonic caused by the feedback between the necessarily nonphysical inflow and outflow boundary conditions. In order to overshadow this noise the flow was also studied with the same fundamental forcing and added random forcing of amplitude upsilon prime sub R/delta U = 0.01 at the inlet. Results were qualitatively the same in both cases: for small x, spectral peaks were sharp and dimension was nearly 1, but as x increased a narrowband spectral peak grew, spectra decayed exponentially at high frequencies and dimension increased to greater than 3. Based on these results, the flow appears to exhibit deterministic chaos. However, at no location was the largest Lyapunov exponent found to be significantly greater than zero.
Broze, J. G.↗
Alpha: A real-time decentralized operating system for mission-oriented system integration and operation
Alpha is a new kind of operating system that is unique in two highly significant ways. First, it is decentralized transparently providing reliable resource management across physically dispersed nodes, so that distributed applications programming can be done largely as though it were centralized. And second, it provides comprehensive, high technology support for real-time system integration and operation, an application area which consists predominately of aperiodic activities having critical time constraints such as deadlines. Alpha is extremely adaptable so that it can be easily optimized for a wide range of problem-specific functionality, performance, and cost. Alpha is the first systems effort of the Archons Project, and the prototype was created at Carnegie-Mellon University directly on modified Sun multiprocessor workstation hardware. It has been demonstrated with a real-time C(sup 2) application. Continuing research is leading to a series of enhanced follow-ons to Alpha; these are portable but initially hosted on Concurrent's MASSCOMP line of multiprocessor products.
Jensen, E. Douglas↗
Ultra Low Power, Radiation Tolerant UHF Radio Technologies for In Situ Communication Applications
For future deep space missions, significant reductions in the mass and power requirements for short-range telecommunication systems will be critical in enabling a wide variety of new mission concepts. These possibilities include penetrators, gliders, miniature rovers, and sensor networks. Under joint funding from NASA's Cross Enterprise and JPL's Telecommunications and Mission technology programs, recent development activity has focused on the design of ultralow mass and power transceiver systems and subsystems suitable for operation in a flight environment. For these efforts, the functionality of the transceiver has been targeted towards a specific Mars communications scenario. However, the overall architecture is well suited to any short or medium range application where a remote probe will aperiodically communicate with a base station, possibly an orbiter, for the eventual purpose of relaying science information back to Earth. In 2001, these sponsors have been augmented with collaborative expertise and funding from JPL's Center for Integrated Space Microsystems in order to migrate existing concepts and designs to a System on a Chip (SOAC) solution. Additional information is contained in the original extended abstract.
Lay, N. E.↗
Investigation of Aperiodic Time Processes with Autocorrelation and Fourier Analysis
Autocorrelation and frequency analyses of a series of aperiodic time events, in particular, filtered noises and sibilant sounds, were made. The position and band width of the frequency ranges are best obtained from the frequency analysis, but the energies contained in the several bands are most easily obtained from the autocorrelation function. The mean number of zero crossings of the time function was determined from the curvature of the latter function in the vicinity of the zero crossing, and also with the aid of a decimal counter. The second method was found to be more exact.
Exner, Marie Luise↗
Fuzzy operators and cyclic behavior in formal neuronal networks
Formal neuronal networks (FNN), which are comprised of threshold gates, make use of the unit step function. It is regarded as a degenerated distribution function (DDF) and will be referred to here as a non-fuzzy threshold operator (nFTO). Special networks of this kind generating long cycles of states are modified by introduction of fuzzy threshold operators (FTO), i.e., non-degenerated distribution functions (nDDF). The cyclic behavior of the new nets is compared with the original ones. The interconnection matrix and threshold values are not modified. It is concluded that the original long cycles change the fixed points and short cycles, and as the computer simulations demonstrate, the aperiodic motion that is associated with chaotic behavior appears. The emergence of the above changes depend on the steepness of the threshold operators.
Labos, E.↗
2023 Astrophotonics Roadmap: Pathways to Realizing Multi-Functional Integrated Astrophotonic Instruments
Photonic technologies offer numerous functionalities that can be used to realize astrophotonic instruments. The most spectacular example to date is the ESO Gravity instrument at the Very Large Telescope in Chile that combines the light-gathering power of four 8 m telescopes through a complex photonic interferometer. Fully integrated astrophotonic devices stand to offer critical advantages for instrument development, including extreme miniaturization when operating at the diffraction-limit, as well as integration, superior thermal and mechanical stabilization owing to the small footprint, and high replicability offering significant cost savings. Numerous astrophotonic technologies have been developed to address shortcomings of conventional instruments to date, including for example the development of photonic lanterns to convert from multimode inputs to single mode outputs, complex aperiodic fiber Bragg gratings to filter OH emission from the atmosphere, complex beam combiners to enable long baseline interferometry with for example, ESO Gravity, and laser frequency combs for high precision spectral calibration of spectrometers. Despite these successes, the facility implementation of photonic solutions in astronomical instrumentation is currently limited because of (1) low throughputs from coupling to fibers, coupling fibers to chips, propagation and bend losses, device losses, etc, (2) difficulties with scaling to large channel count devices needed for large bandwidths and high resolutions, and (3) efficient integration of photonics with detectors, to name a few. In this roadmap, we identify 24 key areas that need further development. We outline the challenges and advances needed across those areas covering design tools, simulation capabilities, fabrication processes, the need for entirely new components, integration and hybridization and the characterization of devices. To realize these advances the astrophotonics community will have to work cooperatively with industrial partners who have more advanced manufacturing capabilities. With the advances described herein, multi-functional integrated instruments will be realized leading to novel observing capabilities for both ground and space based platforms, enabling new scientific studies and discoveries.
astrophotonics↗
The Chaotic Light Curves of Accreting Black Holes
We present model light curves for accreting Black Hole Candidates (BHC) based on a recently developed model of these sources. According to this model, the observed light curves and aperiodic variability of BHC are due to a series of soft photon injections at random (Poisson) intervals and the stochastic nature of the Comptonization process in converting these soft photons to the observed high energy radiation. The additional assumption of our model is that the Comptonization process takes place in an extended but non-uniform hot plasma corona surrounding the compact object. We compute the corresponding Power Spectral Densities (PSD), autocorrelation functions, time skewness of the light curves and time lags between the light curves of the sources at different photon energies and compare our results to observation. Our model reproduces the observed light curves well, in that it provides good fits to their overall morphology (as manifest by the autocorrelation and time skewness) and also to their PSDs and time lags, by producing most of the variability power at time scales 2 a few seconds, while at the same time allowing for shots of a few msec in duration, in accordance with observation. We suggest that refinement of this type of model along with spectral and phase lag information can be used to probe the structure of this class of high energy sources.
Kazanas, Demosthenes↗
The search for, and study of black holes in the galaxy
The study of the short-term (less than 10 s) time variability of Cygnus X-1 is reviewed, with attention given to measurements of the autocorrelation function and of the cross-correlation between different energy bandwidths, as well as to a simple shot noise model for describing all such short-term variations. Observational questions with regard to Cygnus X-1 are discussed, relating to the average shape of the randomly occurring flares, energy dependence in the cross-correlation and the dependence on energy of the X-ray polarization. Concerning the study of the Cyg X-1-like aperiodic X-ray sources, an estimate is made of what can be accomplished at the limits of sensitivity where Poisson fluctuations are at least as important as the intrinsic variability of the source, considering the third moment due to the source fluctuations.
Weisskopf, M. C.↗
Chirped-Superlattice, Blocked-Intersubband QWIP
An Al(x)Ga(1-x)As/GaAs quantum-well infrared photodetector (QWIP) of the blocked-intersubband-detector (BID) type, now undergoing development, features a chirped (that is, aperiodic) superlattice. The purpose of the chirped superlattice is to increase the quantum efficiency of the device. A somewhat lengthy background discussion is necessary to give meaning to a brief description of the present developmental QWIP. A BID QWIP was described in "MQW Based Block Intersubband Detector for Low-Background Operation" (NPO-21073), NASA Tech Briefs Vol. 25, No. 7 (July 2001), page 46. To recapitulate: The BID design was conceived in response to the deleterious effects of operation of a QWIP at low temperature under low background radiation. These effects can be summarized as a buildup of space charge and an associated high impedance and diminution of responsivity with increasing modulation frequency. The BID design, which reduces these deleterious effects, calls for a heavily doped multiple-quantum-well (MQW) emitter section with barriers that are thinner than in prior MQW devices. The thinning of the barriers results in a large overlap of sublevel wave functions, thereby creating a miniband. Because of sequential resonant quantum-mechanical tunneling of electrons from the negative ohmic contact to and between wells, any space charge is quickly neutralized. At the same time, what would otherwise be a large component of dark current attributable to tunneling current through the whole device is suppressed by placing a relatively thick, undoped, impurity-free AlxGa1 x As blocking barrier layer between the MQW emitter section and the positive ohmic contact. [This layer is similar to the thick, undoped Al(x)Ga(1-x)As layers used in photodetectors of the blocked-impurity-band (BIB) type.] Notwithstanding the aforementioned advantage afforded by the BID design, the responsivity of a BID QWIP is very low because of low collection efficiency, which, in turn, is a result of low electrostatic- potential drop across the superlattice emitter. Because the emitter must be electrically conductive to prevent the buildup of space charge in depleted quantum wells, most of the externally applied bias voltage drop occurs across the blocking-barrier layer. This completes the background discussion. In the developmental QWIP, the periodic superlattice of the prior BID design is to be replaced with the chirped superlattice, which is expected to provide a built-in electric field. As a result, the efficiency of collection of photoexcited charge carriers (and, hence, the net quantum efficiency and thus responsivity) should increase significantly.
Gunapala, Sarath↗