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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Finite-size effects on long-range correlations: implications for analyzing DNA sequences

We analyze the fluctuations in the correlation exponents obtained for noncoding DNA sequences. We find prominent sample-to-sample variations as well as variations within a single sample in the scaling exponent. To determine if these fluctuations may result from finite system size, we generate correlated random sequences of comparable length and study the fluctuations in this control system. We find that the DNA exponent fluctuations are consistent with those obtained from the control sequences having long-range power-law correlations. Finally, we compare our exponents for the DNA sequences with the exponents obtained from power-spectrum analysis and correlation-function techniques, and demonstrate that the original "DNA-walk" method is intrinsically more accurate due to reduced noise.

NASA Discipline Cardiopulmonary↗
NASA NTRS2012

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. The standard technique for forced response analysis to assess structural integrity is to decompose a CFD generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non-harmonic excitation sources that become present in complex flows. These complications suggest the question of whether frequency domain analysis is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, have been performed. The first is of a bladed disk with each blade modeled by simple beam elements. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. The results showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists.

Brown, Andrew M.↗
NASA NTRS2003

Use of an Ultrasonic/Sonic Driller/Corer to Obtain Sample Powder for CHEMIN, a Combined XRD/XRF Instrument

A miniature CHEMIN XRD/XRF (X-Ray Diffraction/X-Ray Fluourescence) instrument is currently being developed for definitive mineralogic analysis of soils and rocks on Mars. One of the technical issues that must be addressed in order to enable XRD analysis on an extraterrestrial body is how best to obtain a representative sample powder for analysis. For XRD powder diffraction analyses, it is beneficial to have a fine-grained sample to reduce preferred orientation effects and to provide a statistically significant number of crystallites to the X-ray beam. Although a 2-dimensional detector as used in the CHEMIN instrument will produce good results with poorly prepared powders, the quality of the data will improve if the sample is fine-grained and randomly oriented. An Ultrasonic/Sonic Driller/Corer (USDC) currently being developed at JPL is an effective mechanism of sampling rock to produce cores and powdered cuttings. It requires low axial load (< 5N) and thus offers significant advantages for operation from lightweight platforms and in low gravity environments. The USDC is lightweight (<0.5kg), and can be driven at low power (<5W) using duty cycling. It consists of an actuator with a piezoelectric stack, ultrasonic horn, free-mass, and drill bit. The stack is driven with a 20 kHz AC voltage at resonance. The strain generated by the piezoelectric is amplified by the horn by a factor of up to 10 times the displacement amplitude. The tip impacts the free-mass and drives it into the drill bit in a hammering action. The free-mass rebounds to interact with the horn tip leading to a cyclic rebound at frequencies in the range of 60-1000 Hz. It does not require lubricants, drilling fluid or bit sharpening and it has the potential to operate at high and low temperatures using a suitable choice of piezoelectric material. To assess whether the powder from an ultrasonic drill would be adequate for analyses by an XRD/XRF spectrometer such as CHEMIN, powders obtained from the JPL ultrasonic drill were analyzed and the results were compared to carefully prepared powders obtained using a laboratory bench scale Retsch mill.

Chipera, S. J.↗
NASA NTRS1980

Lear jet boundary layer/shear layer laser propagation experiments

Optical degradations of aircraft turbulent boundary layers with shear layers generated by aerodynamic fences are analyzed. A collimated 2.5 cm diameter helium-neon laser (0.63 microns) traversed the approximate 5 cm thick natural aircraft boundary layer in double pass via a reflective airfoil. In addition, several flights examined shear layer-induced optical degradation. Flight altitudes ranged from 1.5 to 12 km, while Mach numbers were varied from 0.3 to 0.8. Average line spread function (LSF) and Modulation Transfer Function (MTF) data were obtained by averaging a large number of tilt-removed curves. Fourier transforming the resulting average MTF yields an LSF, thus affording a direct comparison of the two optical measurements. Agreement was good for the aerodynamic fence arrangement, but only fair in the case of a turbulent boundary layer. Values of phase variance inferred from the LSF instrument for a single pass through the random flow and corrected for a large aperture ranged from 0.08 to 0.11 waves (lambda = .63 microns) for the boundary layer. Corresponding values for the fence vary from 0.08 to 0.16 waves. Extrapolation of these values to 10.6 microns suggests negligible degradation for a CO2 laser transmitted through a 5 cm thick, subsonic turbulent boundary layer.

Gilbert, K.↗
NASA NTRS2013

Probabilistic Modeling of the Renal Stone Formation Module

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

kidney stones↗
NASA NTRS2019

Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors

Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

Bayesian statistics↗
NASA NTRS1995

A FFT Method for the Quasiclassical Selection of Initial Ro-Vibrational States of Triatomic Molecules

This paper describes the use of an exact fast Fourier transform (FFT) method to prepare specified vibrational-rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating-rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state selected. For example, in the case of the ground vibrational state of a non-rotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001 h(bar) of the specified quantization values and energies within 5 cm(sup -1) of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of "fundamental" frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labelling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the ro-vibrational states of H2O.

Eaker, Charles W.↗
NASA NTRS2021

Scheduling the NASA Deep Space Network with Deep Reinforcement Learning

With three complexes spread evenly across the Earth, NASA’s Deep Space Network (DSN) is the primary means of communications as well as a significant scientific instrument for dozens of active missions around the world. A rapidly rising number of spacecraft and increasingly complex scientific instruments with higher bandwidth requirements have resulted in demand that exceeds the network’s capacity across its 12 antennae. The existing DSN scheduling process operates on a rolling weekly basis and is time-consuming; for a given week, generation of the final baseline schedule of spacecraft tracking passes takes roughly 5 months from the initial requirements submission deadline, with several weeks of peer-to-peer negotiations in between. This paper proposes a deep reinforcement learning (RL) approach to generate candidate DSN schedules from mission requests and spacecraft ephemeris data with demonstrated capability to address real-world operational constraints. A deep RL agent is developed that takes mission requests for a given week as input, and interacts with a DSN scheduling environment to allocate tracks such that its reward signal is maximized. A comparison is made between an agent trained using Proximal Policy Optimization and its random, untrained counterpart. The results represent a proof-of-concept that, given a well-shaped reward signal, a deep RL agent can learn the complex heuristics used by experts to schedule the DSN. A trained agent can potentially be used to generate candidate schedules to bootstrap the scheduling process and thus reduce the turnaround cycle for DSN scheduling.

Wilson, Brian↗
NASA NTRS2011

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Lei, Ning↗
NASA NTRS2010

NASA-DoD Lead-Free Electronics Project: Vibration Test

Vibration testing was conducted by Boeing Research and Technology (Seattle) for the NASA-DoD Lead-Free Electronics Solder Project. This project is a follow-on to the Joint Council on Aging Aircraft/Joint Group on Pollution Prevention (JCAA/JG-PP) Lead-Free Solder Project which was the first group to test the reliability of lead-free solder joints against the requirements of the aerospace/miLItary community. Twenty seven test vehicles were subjected to the vibration test conditions (in two batches). The random vibration Power Spectral Density (PSD) input was increased during the test every 60 minutes in an effort to fail as many components as possible within the time allotted for the test. The solder joints on the components were electrically monitored using event detectors and any solder joint failures were recorded on a Labview-based data collection system. The number of test minutes required to fail a given component attached with SnPb solder was then compared to the number of test minutes required to fail the same component attached with lead-free solder. A complete modal analysis was conducted on one test vehicle using a laser vibrometer system which measured velocities, accelerations, and displacements at one . hundred points. The laser vibrometer data was used to determine the frequencies of the major modes of the test vehicle and the shapes of the modes. In addition, laser vibrometer data collected during the vibration test was used to calculate the strains generated by the first mode (using custom software). After completion of the testing, all of the test vehicles were visually inspected and cross sections were made. Broken component leads and other unwanted failure modes were documented.

Woodrow, Thomas A.↗
NASA NTRS2010

Statistical and Probabilistic Extensions to Ground Operations' Discrete Event Simulation Modeling

NASA's human exploration initiatives will invest in technologies, public/private partnerships, and infrastructure, paving the way for the expansion of human civilization into the solar system and beyond. As it is has been for the past half century, the Kennedy Space Center will be the embarkation point for humankind's journey into the cosmos. Functioning as a next generation space launch complex, Kennedy's launch pads, integration facilities, processing areas, launch and recovery ranges will bustle with the activities of the world's space transportation providers. In developing this complex, KSC teams work through the potential operational scenarios: conducting trade studies, planning and budgeting for expensive and limited resources, and simulating alternative operational schemes. Numerous tools, among them discrete event simulation (DES), were matured during the Constellation Program to conduct such analyses with the purpose of optimizing the launch complex for maximum efficiency, safety, and flexibility while minimizing life cycle costs. Discrete event simulation is a computer-based modeling technique for complex and dynamic systems where the state of the system changes at discrete points in time and whose inputs may include random variables. DES is used to assess timelines and throughput, and to support operability studies and contingency analyses. It is applicable to any space launch campaign and informs decision-makers of the effects of varying numbers of expensive resources and the impact of off nominal scenarios on measures of performance. In order to develop representative DES models, methods were adopted, exploited, or created to extend traditional uses of DES. The Delphi method was adopted and utilized for task duration estimation. DES software was exploited for probabilistic event variation. A roll-up process was used, which was developed to reuse models and model elements in other less - detailed models. The DES team continues to innovate and expand DES capabilities to address KSC's planning needs.

Trocine, Linda↗
NASA NTRS1993

Strategies and methodologies to develop techniques for computer-assisted analysis of gas phase formation during altitude decompression

It would be of operational significance if one possessed a device that would indicate the presence of gas phase formation in the body during hypobaric decompression. Automated analysis of Doppler gas bubble signals has been attempted for 2 decades but with generally unfavorable results, except with surgically implanted transducers. Recently, efforts have intensified with the introduction of low-cost computer programs. Current NASA work is directed towards the development of a computer-assisted method specifically targeted to EVA, and we are most interested in Spencer Grade 4. We note that Spencer Doppler Grades 1 to 3 have increased in the FFT sonogram and spectrogram in the amplitude domain, and the frequency domain is sometimes increased over that created by the normal blood flow envelope. The amplitude perturbations are of very short duration, in both systole and diastole and at random temporal positions. Grade 4 is characteristic in the amplitude domain but with modest increases in the FFT sonogram and spectral frequency power from 2K to 4K over all of the cardiac cycle. Heart valve motion appears to characteristic display signals: (1) the demodulated Doppler signal amplitude is considerably above the Doppler-shifted blow flow signal (even Grade 4); and (2) demodulated Doppler frequency shifts are considerably greater (often several kHz) than the upper edge of the blood flow envelope. Knowledge of these facts will aid in the construction of a real-time, computer-assisted discriminator to eliminate cardiac motion artifacts. There could also exist perturbations in the following: (1) modifications of the pattern of blood flow in accordance with Poiseuille's Law, (2) flow changes with a change in the Reynolds number, (3) an increase in the pulsatility index, and/or (4) diminished diastolic flow or 'runoff.' Doppler ultrasound devices have been constructed with a three-transducer array and a pulsed frequency generator.

Powell, Michael R.↗
NASA NTRS1993

A tectonic resurfacing model for Venus

Two remarkable aspects of the population of impact craters on Venus are as follows: that craters at all sizes are indistinguishable from a random population; and that the vast majority of craters have not been significantly modified by tectonic strain or by volcanic flows external to the crater rim, despite evidence from Magellan images that volcanic and tectonic features are widespread on Venus. One interpretation of these observations is that most of the surface dates from the end of a catastrophic global resurfacing event that ceased about 500 My ago, and that the small fraction of craters volcanically embayed or modified by deformation indicates that volcanic and tectonic activity subsequent to that time has been at much lower levels. An alternative model, in which resurfacing occurs episodically in patches a few hundred kilometers in extent and there is a wider spectrum of surface ages, also appears to be consistent with the characteristics of impact craters on Venus. A number of potential mechanisms for catastrophic resurfacing of Venus have been proposed ranging from geologically sudden convective destabilization of the global lithosphere to strongly time-dependent heat flux and melt generation in the underlying mantle. In most of these geophysical models, resurfacing occurs implicitly or explicitly by volcanism. We explore here the hypothesis that, at least in the geologically recent history of Venus, the primary resurfacing mechanism has been tectonic deformation rather than volcanism. We show how such a hypothesis provides at least as good an explanation of a wide range of observations as do volcanic resurfacing models. Finally, we explore the implications of the tectonic resurfacing hypothesis for the controversy over the recent resurfacing history of the planet.

Solomon, Sean C.↗
NASA NTRS1993

A tectonic resurfacing model for Venus

Two remarkable aspects of the population of impact craters on Venus are that craters at all sizes are indistinguishable from a random population and that the vast majority of craters have not been significantly modified by tectonic strain or by volcanic flows external to the crater rim, despite evidence from Magellan images that volcanic and tectonic features are widespread on Venus. One interpretation of these observations is that most of the surface dates from the end of a catastrophic global resurfacing event that ceased about 500 My ago, and that the small fraction of craters volcanically embayed or modified by deformation indicates that volcanic and tectonic activity subsequent to that time has been at much lower levels. An alternative model, in which resurfacing occurs episodically in patches a few hundred kilometers in extent and there is a wider spectrum of surface ages, also appears to be consistent with the characteristics of impact craters on Venus. A number of potential mechanisms for catastrophic resurfacing of Venus have been proposed, ranging from geologically sudden convective destabilization of the global lithosphere to strongly time-dependent heat flux and melt generation in the underlying mantle. In most of these geophysical models, resurfacing occurs implicitly or explicitly by volcanism. We explore the hypothesis that, at least in the geologically recent history of Venus, the primary resurfacing mechanism has been tectonic deformation rather than volcanism. We show how such a hypothesis provides at least as good an explanation of a wide range of observations as do volcanic resurfacing models. Finally, we explore the implications of tectonic resurfacing hypothesis for the controversy over the recent resurfacing history of the planet.

Solomon, Sean C.↗
NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗
NASA NTRS1993

Investigation of spectral analysis techniques for randomly sampled velocimetry data

It is well known that velocimetry (LV) generates individual realization velocity data that are randomly or unevenly sampled in time. Spectral analysis of such data to obtain the turbulence spectra, and hence turbulence scales information, requires special techniques. The 'slotting' technique of Mayo et al, also described by Roberts and Ajmani, and the 'Direct Transform' method of Gaster and Roberts are well known in the LV community. The slotting technique is faster than the direct transform method in computation. There are practical limitations, however, as to how a high frequency and accurate estimate can be made for a given mean sampling rate. These high frequency estimates are important in obtaining the microscale information of turbulence structure. It was found from previous studies that reliable spectral estimates can be made up to about the mean sampling frequency (mean data rate) or less. If the data were evenly samples, the frequency range would be half the sampling frequency (i.e. up to Nyquist frequency); otherwise, aliasing problem would occur. The mean data rate and the sample size (total number of points) basically limit the frequency range. Also, there are large variabilities or errors associated with the high frequency estimates from randomly sampled signals. Roberts and Ajmani proposed certain pre-filtering techniques to reduce these variabilities, but at the cost of low frequency estimates. The prefiltering acts as a high-pass filter. Further, Shapiro and Silverman showed theoretically that, for Poisson sampled signals, it is possible to obtain alias-free spectral estimates far beyond the mean sampling frequency. But the question is, how far? During his tenure under 1993 NASA-ASEE Summer Faculty Fellowship Program, the author investigated from his studies on the spectral analysis techniques for randomly sampled signals that the spectral estimates can be enhanced or improved up to about 4-5 times the mean sampling frequency by using a suitable prefiltering technique. But, this increased bandwidth comes at the cost of the lower frequency estimates. The studies further showed that large data sets of the order of 100,000 points, or more, high data rates, and Poisson sampling are very crucial for obtaining reliable spectral estimates from randomly sampled data, such as LV data. Some of the results of the current study are presented.

Sree, Dave↗
NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗
NASA NTRS1994

HRMA calibration handbook: EKC gravity compensated XRCF models

This document, consisting of hardcopy printout of explanatory text, figures, and tables, represents one incarnation of the AXAF high resolution mirror assembly (HRMA) Calibration Handbook. However, as we have envisioned it, the handbook also consists of electronic versions of this hardcopy printout (in the form of postscript files), the individual scripts which produced the various figures and the associated input data, the model raytrace files, and all scripts, parameter files, and input data necessary to generate the raytraces. These data are all available electronically as either ASCII or FITS files. The handbook is intended to be a living document and will be updated as new information and/or fabrication data on the HRMA are obtained, or when the need for additional results are indicated. The SAO Mission Support Team (MST) is developing a high fidelity HRMA model, consisting of analytical and numerical calculations, computer software, and databases of fundamental physical constants, laboratory measurements, configuration data, finite element models, AXAF assembly data, and so on. This model serves as the basis for the simulations presented in the handbook. The 'core' of the model is the raytrace package OSAC, which we have substantially modified and now refer to as SAOsac. One major structural modification to the software has been to utilize the UNIX binary pipe data transport mechanism for passing rays between program modules. This change has made it possible to simulate rays which are distributed randomly over the entrance aperture of the telescope. It has also resulted in a highly efficient system for tracing large numbers of rays. In one application to date (the analysis of VETA-I ring focus data) we have employed 2 x 10(exp 7) rays, a substantial improvement over the limit of 1 x 10(exp 4) rays in the original OSAC module. A second major modification is the manner in which SAOsac incorporates low spatial frequency surface errors into the geometric raytrace. The original OSAC included the ability to use Legendre-Fourier polynomials to describe deviations from the basic optical prescription. To this we have added bicubic splines to address a deficiency in the handling of the sharper deformations in the areas of mirror support pads. SAO has developed software (TRANS-FIT) to translate the most common finite element analysis models into these forms for incorporation into the raytrace program.

Tananbaum, H. D.↗