Perturbation theory in terms of reduced density matrices
Perturbation theory for reduced density matrices representable as functions of independent parameters
Harriman, J. E.↗
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Methods for the direct calculation of reduced density matrices
Methods for direct calculation of reduced density matrices in formulating atomic and molecular quantum mechanics
Simons, J. P.↗
A perturbation theory in terms of reduced matrices
Perturbation theory for reduced density matrices
Harriman, J. E.↗
Estimation of proportions in mixed pixels through their region characterization
A region of mixed pixels can be characterized through the probability density function of proportions of classes in the pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability density functions of proportions. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonalizes the covariance matrices of the two classes. If the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estmates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.
Chittineni, C. B.↗
Model reductions using a projection formulation
A new methodology for model reduction of MIMO systems exploits the notion of an oblique projection. A reduced model is uniquely defined by a projector whose range space and orthogonal to the null space are chosen among the ranges of generalized controllability and observability matrices. The reduced order models match various combinations (chosen by the designer) of four types of parameters of the full order system associated with (1) low frequency response, (2) high frequency response, (3) low frequency power spectral density, and (4) high frequency power spectral density. Thus, the proposed method is a computationally simple substitute for many existing methods, has an extreme flexibility to embrace combinations of existing methods and offers some new features.
De Villemagne, Christian↗
Compliance matrices for cracked bodies
An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).
Ballarini, R.↗
New Propellants and Cryofuels
The proposed research will investigate the stability and cryogenic properties of solid propellants that are critical to NASA s goal of realizing practical propellant designs for future spacecraft. We will determine the stability and thermal properties of a solid hydrogen-liquid helium stabilizer in a laboratory environment in order to design a practical propellant. In particular, we will explore methods of embedding atomic species and metallic nano-particulates in hydrogen matrices suspended in liquid helium. We will also measure the characteristic lifetimes and diffusion of atomic species in these candidate cryofuels. The most promising large-scale advance in rocket propulsion is the use of atomic propellants; most notably atomic hydrogen stabilized in cryogenic environments, and metallized-gelled liquid hydrogen (MGH) or densified gelled hydrogen (DGH). The new propellants offer very significant improvements over classic liquid oxygen/hydrogen fuels because of two factors: (1) the high energy-release, and (ii) the density increase per unit energy release. These two changes can lead to significant reduced mission costs and increased payload to orbit weight ratios. An achievable 5 to 10 percent improvement in specific impulse for the atomic propellants or MGH fuels can result in a doubling or tripling of system payloads. The high-energy atomic propellants must be stored in a stabilizing medium such as solid hydrogen to inhibit or delay their recombination into molecules. The goal of the proposed research is to determine the stability and thermal properties of the solid hydrogen-liquid helium stabilizer. Magnetic resonance techniques will be used to measure the thermal lifetimes and the diffusive motions of atomic species stored in solid hydrogen grains. The properties of metallic nano-particulates embedded in hydrogen matrices will also be studied and analyzed. Dynamic polarization techniques will be developed to enhance signal/noise ratios in order to be able to detect low concentrations of the introduced species. The required lifetimes for atomic hydrogen and other species can only be realized at low temperatures to avoid recombination of atoms before use as a fuel.
Palasezski, Bryan↗
The Frequency Detuning Correction and the Asymmetry of Line Shapes: The Far Wings of H2O-H2O
A far-wing line shape theory which satisfies the detailed balance principle is applied to the H2O-H2O system. Within this formalism, two line shapes are introduced, corresponding to band-averages over the positive and negative resonance lines, respectively. Using the coordinate representation, the two line shapes can be obtained by evaluating 11-dimensional integrations whose integrands are a product of two factors. One depends on the interaction between the two molecules and is easy to evaluate. The other contains the density matrix of the system and is expressed as a product of two 3-dimensional distributions associated with the density matrices of the absorber and the perturber molecule, respectively. If most of the populated states are included in the averaging process, to obtain these distributions requires extensive computer CPU time, but only have to be computed once for a given temperature. The 11-dimensional integrations are evaluated using the Monte Carlo method, and in order to reduce the variance, the integration variables are chosen such that the sensitivity of the integrands on them is clearly distinguished.
Ma, Q.↗
Carbon Nanomaterials as Reinforcements for Composites
Carbon nanomaterials including fellerenes, nanotubes (CNT) and nanofibers have been proposed for many applications. One of applications is to use the carbon nanomaterials as reinforcements for composites, especially for polymer matrices. Carbon nanotubes is a good reinforcement for lightweight composite applications due to its low mass density and high Young's modulus. Two obscures need to overcome for carbon nanotubes as reinforcements in composites, which are large quantity production and functioning the nanotubes. This presentation will discuss the carbon nanotube growth by chemical vapor deposition. In order to reduce the cost of producing carbon nanotubes as well as preventing the sliding problems, carbon nanotubes were also synthesized on carbon fibers. The synthesis process and characterization results of nanotubes and nanotubes/fibers will be discussed in the presentation.
Zhu, Shen↗
Maturation of bone and dentin matrices in rats flown on the Soviet biosatellite Cosmos 1887
We have studied the chemistry, hydroxyapatite crystal size, and maturational changes in bone and dentin from rats exposed to microgravity for 12 days in a Soviet biosatellite (Cosmos 1887). Bone ash was reduced in vertebrae (L5) but not in the non-weight-bearing calvaria or mandibles. All tissues had a relatively normal percentage composition of Ca, P, and Mg. Nevertheless, flight rat calvaria and vertebral tissues tended to exhibit lower Ca/P and higher Ca/Mg ratios that any of their weight-matched controls groups, and gradient density analysis (calvaria) indicated a strong shift to the fractions lower specific gravity that was commensurate with impaired rates of matrix-mineral maturation. X-ray diffraction data were confirmatory. Bone hydroxyapatite crystal growth in the mandibles of flight rats was preferentially altered in such a way as to reduce their size (C-axis dimension). But in the mandibular diastemal region devoid of muscle attachments, flight rat bone and dentin were normal with respect to the Ca, P, Mg, and Zn concentrations and Ca/P and Ca/Mg ratios of age-matched controls. These observations affirm the concept that while microgravity most adversely affects the maturation of newly formed matrix and mineral moieties in weight-bearing bone, such effects occur throughout the skeleton.
NASA Experiment Number COS 1887-33↗
Designing Lightweight Neutron Absorbing Composites Using a Comprehensive Absorber Areal Density Metric
Efforts to lightweight neutron absorbing composites are limited by incomplete understandings of the interaction between absorbing particles and their matrices. In this study, analytical models and a more physically representative simulation evaluated the penalty to neutron absorbing performance due to neutron channeling between large absorbing particles. Models and simulation agreed that B 4 C particles smaller than 100μm and especially those smaller than 10μm did not cause excessive neutron channeling. A more comprehensive neutron absorbing composite design metric – boron-10 equivalent areal density, which considers the particle size penalty and the matrix contribution to absorptivity – was introduced and used to estimate lightweighting via matrix substitution. Calculations using this new metric showed that a non-absorbing Mg matrix reduced mass by up to 35% over Al, constrained by the difference in mass density, while an absorbing Mg–Li matrix reduced mass by up to 60%, exceeding the difference in mass densities alone. Measurement of apparent absorber areal density through two experimental techniques – foil activation and direct counting – validated estimated absorber areal density as a neutron absorbing composite design metric. This updated understanding of the particle size penalty, newly introduced design metric, and experimental validation demonstrate a path to lightweight neutron absorbing composites.
Radiation shielding↗
Experiment K-6-05. The maturaton of bone and dentin matrices in rats flown on Cosmos 1887
The chemistry, hydroxyapatite crystal size, and maturation of the bone and dentin is characterized in rats exposed to microgravity for 12.5d in a Soviet Biosatellite (Cosmos-1887). Calvarial and vertebral bone ash was subnormal, but contained a normal percent composition of Ca, P, and Mg. These tissues varied from the norm by having lower Ca/P and higher Ca/Mg ratios than any of their age-matched controls (Vivarium and Synchronous Groups). Gradient density analyses (calvaria) indicated a strong shift to the lower sp.gr. fractions which was commensurate with impaired rates of matrix-mineral maturation. X-ray diffraction data were confirmatory. Bone hydroxyapatite crystal growth in Flight rats was preferentially altered in a way to reduce the dimension of their C-axis. Flight rat dentin was normal with respect to age-matched control Ca, P, Mg, and Zn concentrations and their Ca/P and Ca/Mg ratios. These observations affirm the concept that microgravity adversely affects the maturation of newly formed matrix and mineral moieties in bone.
Simmons, D.↗
An investigation of adhesive/adherend and fiber/matrix interactions. Part B: SEM/ESCA analysis of fracture surfaces
Adhesion was studied with emphasis on the characterization of surface oxide layers, the analysis of fracture surfaces, and the interaction of matrices and fibers. A number of surface features of the fractured lap shear samples were noted in the SEM photomicrographs including the beta phase alloy of the Ti 6-4 adherend, the imprint of the adherend on the adhesive failure surface, increased void density for high temperature samples, and the alumina filler particles. Interfacial failure of some of the fractured lap shear samples is invariably characterized by the appearance of an ESCA oxygen photopeak at 530.3 eV assigned to the surface oxide layer of Ti 6-4 adherend. The effect of grit blasting on carbon fiber composites is evident in the SEM analysis. A high surface fluorine concentration on the composite surface is reduced some ten fold by grit blasting.
Beck, B.↗
High-Performance SiC/SiC Ceramic Composite Systems Developed for 1315 C (2400 F) Engine Components
As structural materials for hot-section components in advanced aerospace and land-based gas turbine engines, silicon carbide (SiC) ceramic matrix composites reinforced by high performance SiC fibers offer a variety of performance advantages over current bill-of-materials, such as nickel-based superalloys. These advantages are based on the SiC/SiC composites displaying higher temperature capability for a given structural load, lower density (approximately 30- to 50-percent metal density), and lower thermal expansion. These properties should, in turn, result in many important engine benefits, such as reduced component cooling air requirements, simpler component design, reduced support structure weight, improved fuel efficiency, reduced emissions, higher blade frequencies, reduced blade clearances, and higher thrust. Under the NASA Ultra-Efficient Engine Technology (UEET) Project, much progress has been made at the NASA Glenn Research Center in identifying and optimizing two highperformance SiC/SiC composite systems. The table compares typical properties of oxide/oxide panels and SiC/SiC panels formed by the random stacking of balanced 0 degrees/90 degrees fabric pieces reinforced by the indicated fiber types. The Glenn SiC/SiC systems A and B (shaded area of the table) were reinforced by the Sylramic-iBN SiC fiber, which was produced at Glenn by thermal treatment of the commercial Sylramic SiC fiber (Dow Corning, Midland, MI; ref. 2). The treatment process (1) removes boron from the Sylramic fiber, thereby improving fiber creep, rupture, and oxidation resistance and (2) allows the boron to react with nitrogen to form a thin in situ grown BN coating on the fiber surface, thereby providing an oxidation-resistant buffer layer between contacting fibers in the fabric and the final composite. The fabric stacks for all SiC/SiC panels were provided to GE Power Systems Composites for chemical vapor infiltration of Glenn designed BN fiber coatings and conventional SiC matrices. Composite panels with system B were heat treated at Glenn, and the pores that remained open were filled by silicon melt infiltration (MI). Panels with system A and the other SiC/SiC systems were not heat treated, and remaining open pores in these systems were filled with SiC slurry and silicon MI.
DiCarlo, James A.↗
Snow Microphysical Retrieval from the NASA D3R Radar During ICE-POP 2018
A method is developed to use both polarimetric and dual-frequency radar measurements to retrieve microphysical properties of falling snow. It is applied to the Ku- and Ka-band measurements of the NASA dual-polarization, dual-frequency Doppler radar (D3R) obtained during the International Collaborative Experiments for PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign and incorporates the Atmospheric Radiative Transfer Simulator (ARTS) microwave singles cattering property database for oriented particles. The retrieval uses optimal estimation to solve for several parameters that describe the particle size distribution (PSD), relative contribution of pristine, aggregate, and rimed ice species, and the orientation distribution along an entire radial simultaneously. Examination of Jacobian matrices and averaging kernels shows that the dual-wavelength ratio (DWR) measurements provide information regarding the characteristic particle size, and to a lesser extent, the rime fraction and shape parameter of the size distribution, whereas the polarimetric measurements provide information regarding the mass fraction of pristine particles and their characteristic size and orientation distribution. Thus, by combining the dual-frequency and polarimetric measurements, some ambiguities can be resolved that should allow a better determination of the PSD and bulk microphysical properties (e.g., snowfall rate) than can be retrieved from single-frequency polarimetric measurements or dual-frequency, single-polarization measurements. The D3R ICE-POP retrievals were validated using Precipitation Imaging Package (PIP) and Pluvio weighing gauge measurements taken nearby at the May Hills ground site. The PIP measures the snow PSD directly, and its measurements can be used to derived the snowfall rate (volumetric and water equivalent), mean volume-weighted particle size, and effective density, as well as particle aspect ratio and orientation. Four retrieval experiments were performed to evaluate the utility of different measurement combinations: Kuonly, DWR-only, Ku-pol, and All-obs. In terms of correlation, the volumetric snowfall rate (r D 0:95) and snow water equivalent rate (r D 0:92) were best retrieved by the Ku-pol method, while the DWR-only method had the lowest magnitude bias for these parameters (-31% and -8 %, respectively). The methods that incorporated DWR also had the best correlation to particle size (r D 0:74 and r D 0:71 for DWR-only and All-obs, respectively), although none of the methods retrieved density particularly well (r D 0:43 for Allobs). The ability of the measurements to retrieve mean aspect ratio was also inconclusive, although the polarimetric methods (Ku-pol and All-obs) had reduced biases and mean absolute error (MAE) relative to the Ku-only and DWR-only methods. The significant biases in particle size and snowfall rate appeared to be related to biases in the measured DWR, emphasizing the need for accurate DWR measurements and frequent calibration in future D3R deployments.
S Joseph Munchak↗
Silica/Polymer and Silica/Polymer/Fiber Composite Aerogels
Aerogels that consist, variously, of neat silica/polymer alloys and silica/polymer alloy matrices reinforced with fibers have been developed as materials for flexible thermal-insulation blankets. In comparison with prior aerogel blankets, these aerogel blankets are more durable and less dusty. These blankets are also better able to resist and recover from compression . an important advantage in that maintenance of thickness is essential to maintenance of high thermal-insulation performance. These blankets are especially suitable as core materials for vacuum- insulated panels and vacuum-insulated boxes of advanced, nearly seamless design. (Inasmuch as heat leakage at seams is much greater than heat leakage elsewhere through such structures, advanced designs for high insulation performance should provide for minimization of the sizes and numbers of seams.) A silica/polymer aerogel of the present type could be characterized, somewhat more precisely, as consisting of multiply bonded, linear polymer reinforcements within a silica aerogel matrix. Thus far, several different polymethacrylates (PMAs) have been incorporated into aerogel networks to increase resistance to crushing and to improve other mechanical properties while minimally affecting thermal conductivity and density. The polymethacrylate phases are strongly linked into the silica aerogel networks in these materials. Unlike in other organic/inorganic blended aerogels, the inorganic and organic phases are chemically bonded to each other, by both covalent and hydrogen bonds. In the process for making a silica/polymer alloy aerogel, the covalent bonds are introduced by prepolymerization of the methacrylate monomer with trimethoxysilylpropylmethacrylate, which serves as a phase cross-linker in that it contains both organic and inorganic monomer functional groups and hence acts as a connector between the organic and inorganic phases. Hydrogen bonds are formed between the silanol groups of the inorganic phase and the carboxyl groups of the organic phase. The polymerization process has been adapted to create interpenetrating PMA and silica-gel networks from monomers and prevent any phase separations that could otherwise be caused by an overgrowth of either phase. Typically, the resulting PMA/silica aerogel, without or with fiber reinforcement, has a density and a thermal conductivity similar to those of pure silica aerogels. However, the PMA enhances mechanical properties. Specifically, flexural strength at rupture is increased to 102 psi (=0.7 MPa), about 50 times the flexural strength of typical pure silica aerogels. Resistance to compression is also increased: Applied pressure of 17.5 psi (=0.12 MPa) was found to reduce the thicknesses of several composite PMA/silica aerogels by only about 10 percent.
Ou, Danny↗