Direct calculation of first- and second-order density matrices - The higher RPA method
First and second order density matrices calculation of pure state N fermion systems, using higher random phase approximation
Simons, J.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The correlation function of galaxy ellipticities produced by gravitational lensing
The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.
Miralda-Escude, Jordi↗
Probabilistic nonlinear finite element analysis of composite structures
A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed, and results are presented in the form of mean and variance of the structural response. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.
Engelstad, S. P.↗
Time Course of Atrophic Remodeling: Effects of Exercise on Cardiac Morpology and Function
Early and consistent evaluation of cardiac morphology and function throughout an atrophic stimulus is critically important for the design and optimization of interventions. Exercise training is one intervention that has been shown to confer favorable improvements in LV mass and function during unloading. However, the format and intensity of exercise required to induce optimal cardiac improvements has not been investigated. PURPOSE: This randomized, controlled trial was designed to 1) comprehensively characterize the time course of unloading-induced morpho-functional remodeling, and 2) examine the effects of high intensity exercise training on cardiac structural and functional parameters during unloading. METHODS: Twenty six subjects completed 70 days of head down tilt bed rest (HDBR): 17 were randomized to exercise training (ExBR) and 9 remained sedentary. Exercise consisted of integrated high intensity, continuous, and resistance exercise. We assessed cardiac morphology (left ventricular mass; LVM) and function (speckle-tracking assessment of longitudinal, radial, and circumferential strain and twist) before (BR-2), during (BR7,21,31,70), and following (BR+0, +3) HDBR. Cardiorespiratory fitness (VO2max) was evaluated before (BR- 3), during (BR4,25,46,68) and following (BR+0) HDBR. RESULTS: Sedentary HDBR resulted in a progressive decline in LVM, longitudinal, radial, and circumferential strain, and an increase in twist. ExBR mitigated decreases in LVM and function. Change in twist was significantly related to change in VO2max (R=0.68, p<0.01). CONCLUSIONS: Alterations in cardiac morphology and function begin early during unloading. High-intensity exercise attenuates atrophic morphological and functional remodeling.
Scott, J. M.↗
Evaluation of a stochastic model of particle dispersion in a turbulent round jet
A stochastic model of particle dispersion by turbulence, proposed by Gosman and Ioannides (1981), is evaluated. The method employs a k-epsilon model to estimate turbulence properties. Dispersion is determined by computing particle motion, with random sampling to obtain instantaneous flow properties for a statistically significant number of particle trajectories. The stochastic model yields good results particularly when eddy lifetimes are evaluated. The method allows the effects of large relative velocities between the particles and the flow, drag properties at Reynolds numbers greater than the Stokes flow regime, and the variations of local turbulence properties to be readily handled, at least for boundary layer flows.
Shuen, J.-S.↗
Fabricating Radial Groove Gratings Using Projection Photolithography
Projection photolithography has been used as a fabrication method for radial grove gratings. Use of photolithographic method for diffraction grating fabrication represents the most significant breakthrough in grating technology in the last 60 years, since the introduction of holographic written gratings. Unlike traditional methods utilized for grating fabrication, this method has the advantage of producing complex diffractive groove contours that can be designed at pixel-by-pixel level, with pixel size currently at the level of 45 45 nm. Typical placement accuracy of the grating pixels is 10 nm over 30 nm. It is far superior to holographic, mechanically ruled or direct e-beam written gratings and results in high spatial coherence and low spectral cross-talk. Due to the smooth surface produced by reactive ion etch, such gratings have a low level of randomly scattered light. Also, due to high fidelity and good surface roughness, this method is ideally suited for fabrication of radial groove gratings. The projection mask is created using a laser writer. A single crystal silicon wafer is coated with photoresist, and then the projection mask, with its layer of photoresist, is exposed for patterning in a stepper or scanner. To develop the photoresist, the fabricator either removes the exposed areas (positive resist) of the unexposed areas (negative resist). Next, the patterned and developed photoresist silicon substrate is subjected to reactive ion etching. After this step, the substrate is cleaned. The projection mask is fabricated according to electronic design files that may be generated in GDS file format using any suitable CAD (computer-aided design) or other software program. Radial groove gratings in off-axis grazing angle of incidence mount are of special interest for x-ray spectroscopy, as they allow achieving higher spectral resolution for the same grating area and have lower alignment tolerances than traditional in-plane grating scheme. This is especially critical for NASA Constellation- X project that will utilize hundreds of gratings all of which need to be precisely aligned for x-ray observation of space.
Iazikov, Dmitri↗
Statistical Characterization of Environmental Error Sources Affecting Electronically Scanned Pressure Transducers
Minimization of uncertainty is essential to extend the usable range of the 15-psid Electronically Scanned Pressure (ESP) transducer measurements to the low free-stream static pressures found in hypersonic wind tunnels. Statistical characterization of environmental error sources inducing much of this uncertainty requires a well defined and controlled calibration method. Employing such a controlled calibration system, several studies were conducted that provide quantitative information detailing the required controls needed to minimize environmental and human induced error sources. Results of temperature, environmental pressure, over-pressurization, and set point randomization studies for the 15-psid transducers are presented along with a comparison of two regression methods using data acquired with both 0.36-psid and 15-psid transducers. Together these results provide insight into procedural and environmental controls required for long term high-accuracy pressure measurements near 0.01 psia in the hypersonic testing environment using 15-psid ESP transducers.
Green, Del L.↗
Statistical Characterization of Environmental Error Sources Affecting Electronically Scanned Pressure Transducers
Minimization of uncertainty is essential to extend the usable range of the 15-psid Electronically Scanned Pressure [ESP) transducer measurements to the low free-stream static pressures found in hypersonic wind tunnels. Statistical characterization of environmental error sources inducing much of this uncertainty requires a well defined and controlled calibration method. Employing such a controlled calibration system, several studies were conducted that provide quantitative information detailing the required controls needed to minimize environmental and human induced error sources. Results of temperature, environmental pressure, over-pressurization, and set point randomization studies for the 15-psid transducers are presented along with a comparison of two regression methods using data acquired with both 0.36-psid and 15-psid transducers. Together these results provide insight into procedural and environmental controls required for long term high-accuracy pressure measurements near 0.01 psia in the hypersonic testing environment using 15-psid ESP transducers.
Green, Del L.↗
Robustness-Based Design Optimization Under Data Uncertainty
This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.
Zaman, Kais↗
Statistical Analysis of Fading Power Vectors for Real-Time Atmospheric Channel Emulation
The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode- limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.
free-space optical communication↗
Statistical Analysis of Fading Power Vectors for Real-Time Atmospheric Channel Emulation
The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.
free-space optical communication↗
Optimum coherent imaging of a limited field of view in the presence of angular and aperture noise
The question of image distribution reconstruction for coherent illumination of an object located in the aperture far zone is considered from first principles without postulating any particular optical spread function. The object function is mathematically modeled as a complex random function of angular coordinates, and it is assumed that the object distribution of interest is angularly limited to a certain a priori assigned field of view (FOV). A linear reconstruction procedure that is uniformly optimal in the FOV is established by using the methods of statistical estimation. Two special cases are examined: imaging a limited sector of a wide-angle random scene and objects in the FOV immersed in a wide-angle background of angular noise. It is noted that the domain of application of the reconstruction method is restricted to microwave frequencies.
Borgiotti, G. V.↗
Probabilistic structural analysis methods for improving Space Shuttle engine reliability
Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.
Boyce, L.↗
Taguchi method of experimental design in materials education
Some of the advantages and disadvantages of the Taguchi Method of experimental design as applied to Materials Science will be discussed. This is a fractional factorial method that employs the minimum number of experimental trials for the information obtained. The analysis is also very simple to use and teach, which is quite advantageous in the classroom. In addition, the Taguchi loss function can be easily incorporated to emphasize that improvements in reproducibility are often at least as important as optimization of the response. The disadvantages of the Taguchi Method include the fact that factor interactions are normally not accounted for, there are zero degrees of freedom if all of the possible factors are used, and randomization is normally not used to prevent environmental biasing. In spite of these disadvantages it is felt that the Taguchi Method is extremely useful for both teaching experimental design and as a research tool, as will be shown with a number of brief examples.
Weiser, Martin W.↗
Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens
Modeling the effects of atmospheric turbulence on optical beam propagation is a key element in the design and analysis of free-space optical communication systems. Numerical wave optics simulations provide a particularly useful technique for understanding the degradation of the optical field in the receiver plane when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such an application, we use a split-step method modeling the turbulence along the propagation path as a series of thin random phase screens with modified von Karman refractive index statistics using the Hufnagel-Valley turbulence profile to determine the effective structure constant for each screen. In this work, we employ a space-to-ground case study to examine the irradiance and phase statistics for both uniformly and non-uniformly spaced screens along the propagation path and compare to analytical results. We find that better agreement with the analytical theory is obtained using a non-uniform spacing with the effective structure constant for each screen chosen to minimize its contribution to the scintillation in the receiver plane. We evaluate this method as a flexible alternative to other standard layered models used in astronomical imaging applications.
Chahine, Yousef K.↗
Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted
Pohorille, Andrew↗
Random motion analysis of flexible satellite structures
A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.
Huang, T. C.↗
Autonomous Information Unit for Fine-Grain Data Access Control and Information Protection in a Net-Centric System
As communication and networking technologies advance, networks will become highly complex and heterogeneous, interconnecting different network domains. There is a need to provide user authentication and data protection in order to further facilitate critical mission operations, especially in the tactical and mission-critical net-centric networking environment. The Autonomous Information Unit (AIU) technology was designed to provide the fine-grain data access and user control in a net-centric system-testing environment to meet these objectives. The AIU is a fundamental capability designed to enable fine-grain data access and user control in the cross-domain networking environments, where an AIU is composed of the mission data, metadata, and policy. An AIU provides a mechanism to establish trust among deployed AIUs based on recombining shared secrets, authentication and verify users with a username, X.509 certificate, enclave information, and classification level. AIU achieves data protection through (1) splitting data into multiple information pieces using the Shamir's secret sharing algorithm, (2) encrypting each individual information piece using military-grade AES-256 encryption, and (3) randomizing the position of the encrypted data based on the unbiased and memory efficient in-place Fisher-Yates shuffle method. Therefore, it becomes virtually impossible for attackers to compromise data since attackers need to obtain all distributed information as well as the encryption key and the random seeds to properly arrange the data. In addition, since policy can be associated with data in the AIU, different user access and data control strategies can be included. The AIU technology can greatly enhance information assurance and security management in the bandwidth-limited and ad hoc net-centric environments. In addition, AIU technology can be applicable to general complex network domains and applications where distributed user authentication and data protection are necessary. AIU achieves fine-grain data access and user control, reducing the security risk significantly, simplifying the complexity of various security operations, and providing the high information assurance across different network domains.
Chow, Edward T.↗