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DOE OSTI2020

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗

DOE OSTI2023

Determination of single crystal thermal expansion in Uranium-6wt%Niobium shape memory alloy using in-situ diffraction and modeling of textured polycrystalline samples

In-situ neutron diffraction and ex-situ dilatometry experiments were performed on a chemically banded, quenched uranium-6wt% niobium shape memory alloy to study the impact of deformation-(detwinning-) induced texture on the evolution of thermally induced strains (and associated stresses). Thermal heating and cooling cycles between 5K and 473K were performed in-situ with neutron diffraction, and the lattice strain evolution is reported for the observed monoclinic α" phase. Comparisons between the measured diffraction strains and macroscopic dilatometry experiments reveal relationships between micro- and macro-level thermal expansion. Softening of the texture during heating suggests that twin boundary motion can accommodate the large internal thermal strains which are approximately 2% greater than that typically observed during the 175K heating interval used to age more randomly oriented polycrystalline material. Assuming weak constraint of neighboring grains in randomly textured polycrystals, the single crystal thermal expansion tensor is extracted from measurements of lattice strains over the range 5K to 473K. Predictions of polycrystalline thermal expansion, based upon this single crystal thermal expansion tensor, are shown to compare favorably with bulk thermal expansion observations of the as quenched microstructure. However, such a lower-bound estimate is insufficient to explain all aspects of the behavior of the textured material, where the matrix is not isotropic. In conclusion, it is hypothesized that relaxation processes which occur within the quenched microstructure during heating are responsible for the distinct thermal expansion behavior observed during the initial heating cycle compared to cooling and subsequent cycling.

36 MATERIALS SCIENCE↗

DOE OSTI2024

High-temperature structure, elasticity, and thermal expansion of ε-ZrH 1.8

Zirconium hydride is a promising candidate material for nuclear microreactor applications as a solid-state moderator component, owing to its favorable neutronics properties and good thermal stability over other metal hydrides. Here, in the present work, the crystal structure, thermal expansion, and elastic properties of the hydrogen-rich ε phase hydride were measured at elevated temperatures in the range 300–900 K. Samples were prepared by direct hydriding Zircaloy-4 metal – a nuclear-grade zirconium alloy. Room-temperature lattice parameters agree well with those reported from literature for unalloyed zirconium hydride and fall within an observed quadratic H-content dependence. The coefficients of thermal expansion, determined from lattice expansion and dilatometry, agree well within our work but were about 30 % lower than those reported by others for unalloyed hydrides. Density functional theory-based molecular dynamics simulations were used to compare with thermal expansion and elasticity measurements. Results showed lattice parameter temperature dependence and slope of thermal expansion align with those from measurements. Based on diffraction scans at select temperatures, ε phase remained stable in air up to at least 770 K. Likewise, dilatometry showed smooth thermal expansion up to the thermal decomposition temperature around 950 K. The precise decomposition temperature was not determined via diffraction due to sparse scanning. The complete elastic property measurements were gathered for ε-phase Ziracloy-4 hydride for the first time. Young's modulus was lower compared to the metal and δ hydride phases. High-temperature elasticity measurements were limited to <350 K due to acoustic dissipation effects.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Effect of Alkali-Silica Reaction Expansion Rate and Confinement on Concrete Degradation

Alkali-silica reaction (ASR) is a major deterioration mechanism that affects the durability of concrete structures. As the slow rate of ASR development and the restrained expansion in field concrete might affect the development of ASR damage, an experimental program was performed to investigate the effects of the rate of ASR expansion and confinement on the degradation of mechanical properties of concretes. Literature data on the degradation of mechanical properties of concretes with ASR expansion were collected and analyzed to investigate the influence of the rate of ASR expansion and confinement on the degradation trends. Degradation of mechanical properties was found to be significantly influenced by the rate of ASR expansion and slightly affected by confinements. The slow rate of ASR expansion seems to be beneficial in limiting concrete degradation. The effects of confinement seem to be related to the direction of restraint and crack orientations.

36 MATERIALS SCIENCE↗

NASA NTRS2013

The Thermal Expansion of Ring Particles and the Secular Orbital Evolution of Rings Around Planets and Asteroids

The thermal expansion and contraction of ring particles orbiting a planet or asteroid can cause secular orbit evolution. This effect, called here the thermal expansion effect, depends on ring particles entering and exiting the shadow of the body they orbit. A particle cools off in the shadow and heats up again in the sunshine, suffering thermal contraction and expansion. The changing cross-section it presents to solar radiation pressure plus time lags due to thermal inertia lead to a net along-track force. The effect causes outward drift for rocky particles. For the equatorial orbits considered here, the thermal expansion effect is larger than Poynting-Robertson drag in the inner solar system for particles in the size range approx. 0.001 - 0.02 m. This leads to a net increase in the semimajor axis from the two opposing effects at rates ranging from approx. 0.1 R per million years for Mars to approx. 1 R per million years for Mercury, for distances approx. 2R from the body, where R is the body's radius. Asteroid 243 Ida has approx. 10 R per million years, while a hypothetical Near-Earth Asteroid (NEA) can have faster rates of approx. 0.5 R per thousand years, due chiefly to its small radius compared to the planets. The thermal expansion effect weakens greatly at Jupiter and is overwhelmed by Poynting-Robertson for icy particles orbiting Saturn. Meteoroids in eccentric orbits about the Sun also suffer the thermal expansion effect, but with only approx. 0.0003e2 AU change in semimajor axis over a million years for a 2 m meteoroid orbiting between Mercury and Earth.

Ring particles↗

DOE OSTI2021

Continuous NF-κB pathway inhibition promotes expansion of human phenotypical hematopoietic stem/progenitor cells through metabolism regulation

Highlights: • Small molecular inhibition of NF-κB pathway efficiently expands human HSPCs. • NF-κB inhibition with TPCA-1 improves the self-renewal potential and biological function maintenance of expanded CD34{sup +} cells. • NF-κB pathway inhibition reprograms metabolism and enhances glycolysis. • Continuous NF-κB inhibition is required in the culture process to facilitate primitive HSC maintenance. Hematopoietic stem/progenitor cells (HSPCs) ex vivo expansion is critical in facilitating their widespread clinical application. NF-κB pathway is implicated in the energy homeostasis and metabolic adaptation. To explore the effect of NF-κB pathway on the ex vivo HSPC expansion and metabolism, the 50 nM–1 μM inhibitor of NF-κB pathway TPCA-1 was used to expand cord blood derived CD34{sup +} cells in serum-free culture. The expansion folds, function, mitochondrial profile and metabolism of HSPCs were determined. After 10 days of culture with 100 nM TPCA-1, the expansion of total cells CD34{sup +}CD38{sup −} cells and CD34{sup +}CD38{sup −}CD45RA{sup −}CD90{sup +}CD49f{sup +} cells were significantly increased compared to the cytokine priming alone. Notably, TPCA-1 treatment generated ~ 2-fold greater percentage of CD34{sup +}EPCR{sup +} and CD34{sup +}CD38{sup −}CD45RA{sup −}CD90{sup +}CD49f{sup +} cells compared to cytokine only conditions. Moreover, TPCA-1 expanded CD34{sup +} cells displayed enhanced serial colonies forming potential and secondary expansion capability. NF-κB inhibition increased the expression of self-renewal related genes, while downregulated the expression of mitochondrial biogenesis regulator (Pgc1α) and mitochondrial chaperones and proteases (ClpP, Hsp10, Hsp60). Mitochondrial mass and membrane potential were markedly decreased with TPCA-1 treatment, leading to the reduced mitochondrial reactive oxygen species (ROS) level in HSPCs. NF-κB inhibition displayed augmented glycolysis rate with compromising mitochondrial metabolism. This study demonstrated that NF-κB pathway inhibition improved glycolysis and limited ROS production that promoted the ex vivo expansion and maintenance of functional HSPCs.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Parallel expansion of a fuel pellet plasmoid

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.

Physics↗

DOE OSTI2021

Synergistic Coupling of CO2 and H2O during Expansion of Clays in Supercritical CO2-CH4 Fluid Mixtures

A combination of in operando IR and XRD methods were used to investigate the interaction of variably hydrated supercritical CO2-CH4 fluids with Na/NH4/Cs substituted montmorillonites. Comparing the behavior of Na-clay exposed to CH4 versus CO2 dominant fluid phases demonstrated that CO2 disrupts the H-bond network of intercalated H2O. At relatively low potentials of H2O, CO2 facilitates H2O intercalation and expansion of the interlayer region of the Na-clay. In contrast, CO2 inhibited H2O intercalation but promoted expansion of the Cs-clay. The NH4-clay displayed intermediated behavior. Methane likely intercalated the clays but opportunistically, filling unoccupied space after CO2 and H2O actively expanded the interlayer region. By comparing and contrasting the behavior of the Cs and NH4 clays to the Na Clay we conclude that, whereas H2O is required for initial Na-clay expansion, CO2 synergistically facilitated expansion and hydration of Na-clay by mixing with H2O (the entropic contribution) and participating in the outer solvation sphere of Na (the enthalpic contribution). In contrast, CO2 can directly solvate interlayer Cs and NH4 and cause expansion in the absence of H2O; nonetheless, H2O and CO2 also act synergistically to facilitate expansion of the Cs and NH4 clays at low H2O concentrations.

Loring, John S.↗

DOE OSTI2020

Negative thermal expansion and the role of hybridization in perovskite-type PbTiO 3 -Bi(Cu 0.5 Ti 0.5) O 3

PbTiO 3 -BiMeO 3 ferroelectrics have attracted much attention due to not only their extremely large polarization and piezoelectricity but also their controllable thermal expansion. In this study, we present a new binary system of (1 - x)PbTiO 3 -xBi(Cu 0.5 Ti 0.5 )O 3 possessing large tetragonality and enhanced spontaneous polarization. Interestingly, a combination of near zero thermal expansion and negative thermal expansion over a temperature range of RT to T C (~550 °C) has been observed in tetragonal 0.85PbTiO 3 -0.15Bi(Cu 0.5 Ti 0.5 )O 3 . The comprehensive structure analysis addressed that the abnormal thermal expansion is coupled to the spontaneous volume ferroelectrostriction. Moreover, the chemical bonding investigation by a maximum entropy method further attests that the covalent hybridization of Pb/Bi–O bonds plays a vital role in the improved ferroelectricity and interacts with thermal vibration to dominate the crossover from positive to negative thermal expansion. fINALLY, The present studies would give direct evidence to verify the theoretical calculations and could be extended to reveal the nature of thermal expansion in ferroelectrics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

High Throughput Coefficient Thermal Expansion Testing Utilizing Digital Image Correlation

Dr. Fitzgerald, a postdoc at Sandia National Laboratories, works in a materials of mechanics group characterizing material properties of ductile materials. Her presentation focuses specifically on increasing throughput of coefficient of thermal expansion (CTE) measurements with the use of optical strain measurements, called digital image correlation (DIC). Currently, the coefficient of thermal expansion is found through a time intensive process called dilatometry. There are multiple types of dilatometers. One type, a double push rod mechanical dilatometer, uses and LVDT to measure the expansion of a specimen in one direction. It uses a reference material with known properties to determine the CTE of the specimen in question. Testing about 500 samples using the double push rod mechanical dilatometer would take about 2 years if testing Monday through Friday, because the reference material needs to be at a constant temperature and heating must done slowly to ensure no thermal gradients across the rod. A second type, scissors type dilatometer, pinches a sample using a “scissor-like” appendage that also uses a LVDT to measure thermal expansion as the sample is heated. Finally, laser dilatometry, was created to provide a non-contact means to measure thermal expansion. This process greatly reduces the time required to setup a measurement but is still only able to measure one sample at a time. The time required to test 500 samples gets reduced to 3.5 weeks. Additionally, to measure expansion in different directions, multiple lasers must be used. Dr. Fitzgerald solved this conundrum by using an optical measurement technique called digital image correlation to create strain maps in multiple orientations as well as measuring multiple samples at once. Using this technique, Dr. Fitzgerald can test 500 samples, conservatively, in 2 days.

36 MATERIALS SCIENCE↗

NASA NTRS1978

A critical examination of expansion tunnel performance

An experimental study of the performance of the expansion tunnel for various test gases and range of quiescent acceleration section and nozzle pressure, nozzle geometric area ratio, and nozzle axial station has been performed. Flow diagnostics used to examine expansion tunnel flow characteristics were time histories and profiles of pitot pressure and axial component of flow velocity. The purpose of this study was to determine experimentally what limitations might restrict predicted operational flexibility and the advantages and disadvantages of this mode of operation as compared to the expansion tube. Results are presented which demonstrate the expansion tunnel offers several advantages over the expansion tube, but the severity of the disadvantages of the tunnel makes the expansion tube mode of operation the more desirable for performing hypersonic-hypervelocity aerothermodynamic studies of proposed entry configurations.

Miller, C. G.↗

NASA NTRS1985

A study of plasma expansion phenomena in laboratory generated plasma wakes - Preliminary results

The plasma expansion into the wake of a large rectangular plate immersed in a single-ion, collisionless, streaming plasma has been investigated in the laboratory. Several characteristics of the process involved in 'plasma expansion into vacuum' that have been predicted theoretically were observed, including the creation and motion of a rarefaction wave disturbance; the creation and motion of an expansion front; and the acceleration of ions into the wake at speeds above the ion-acoustic speed. The expansion was limited to early times; i.e., a few ion plasma periods, by the combination of plasma drift speed and vacuum chamber size. This prevented detailed comparison with self-similar theory, but results are in good agreement with numerical simulations and other laboratory experiments for the early time expansion. The conclusion is that the plasma expansion process is the dominant wake filling mechanism in the near wake of a body, whose potential is approximately the plasma space potential.

Wright, K. H., Jr.↗

NASA NTRS1987

Thermal expansion of selected graphite-reinforced polyimide-, epoxy-, and glass-matrix composites

The thermal expansion of continuous carbon-fiber reinforced composites with epoxy-, polyimide-, and borosilicate glass-matrices has been measured and compared. The expansion of a rubber-toughened epoxy-matrix/P75S carbon-fiber composite was very different from the expansion of two different single-phase epoxy-matrix/P75S composites, although all three had the same stacking sequence. Reasonable agreement was obtained between measured thermal expansion data and results from classical laminate theory. Microdamage in the graphite/polyimide laminate, induced by 250 cycles between -156 and 121 C, caused a 53 percent decrease in the coefficient of thermal expansion. The thermal expansion of the graphite/glass laminate was not changed after 100 thermal cycles from -129 to 38 C; however, a residual strain of about 10 x 10 to the -6 was observed for the laminate tested.

Tompkins, S. S.↗

NASA NTRS1988

Expansion tube test time predictions

The interaction of an interface between two gases and strong expansion is investigated and the effect on flow in an expansion tube is examined. Two mechanisms for the unsteady Pitot-pressure fluctuations found in the test section of an expansion tube are proposed. The first mechanism depends on the Rayleigh-Taylor instability of the driver-test gas interface in the presence of a strong expansion. The second mechanism depends on the reflection of the strong expansion from the interface. Predictions compare favorably with experimental results. The theory is expected to be independent of the absolute values of the initial expansion tube filling pressures.

Gourlay, Christopher M.↗

NASA NTRS1988

The driver in flares and coronal mass ejections: Magnetic expansion

Chromospheric filaments, and hence the sheared magnetic fields that they trace, are observed to erupt in flares and coronal mass ejections. In the eruption, the filament-traced field is seen to expand in volume. For frozen-in magnetic field and isotropic expansion, the magnetic energy in a flux tube decreases as the flux tube expands. The amount of expansion of the magnetic field and the corresponding decrease in magnetic energy in a filament-eruption flare and/or coronal mass ejection can be estimated to order of magnitude from the observed expansion of the erupting filament. This evaluation for filament-eruption events in which the filament expansion is clearly displayed gives decreases in magnetic energy of the order of the total energy of the accompanying flare and/or coronal mass ejection. This simple expanding flux tube model can also fit the observed acceleration of coronal mass ejections, if it is assumed that the increase in mechanical energy of the mass ejection comes from the magnetic energy decrease in the expansion. These results encourage the view that magnetic expansion such as seen in filament eruptions drives both the plasma particle energization in flares and the bulk mass motion in coronal mass ejections.

Moore, Ronald L.↗

NASA NTRS1989

Rocket nozzle expansion ratio analysis for dual-fuel earth-to-orbit vehicles

Results are reported from a recent study of the effects of Space Shuttle Main Engine expansion ratio modifications, in the cases of both single-stage and two-stage systems. Two-position nozzles were employed; after varying the lower expansion ratio while the higher was held constant at 120, the lower expansion ratio was held constant at 40 or 60 while the higher expansion ratio was varied. The expansion ratios for minimum vehicle dry mass are different for single-stage and two-stage systems. For two-stage systems, a single expansion ratio of 77.5 provides a lower dry mass than any two-position nozzle.

Martin, James A.↗

NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗

NASA NTRS1993

Expansion-based passive ranging

A new technique of passive ranging which is based on utilizing the image-plane expansion experienced by every object as its distance from the sensor decreases is described. This technique belongs in the feature/object-based family. The motion and shape of a small window, assumed to be fully contained inside the boundaries of some object, is approximated by an affine transformation. The parameters of the transformation matrix are derived by initially comparing successive images, and progressively increasing the image time separation so as to achieve much larger triangulation baseline than currently possible. Depth is directly derived from the expansion part of the transformation. To a first approximation, image-plane expansion is independent of image-plane location with respect to the focus of expansion (FOE) and of platform maneuvers. Thus, an expansion-based method has the potential of providing a reliable range in the difficult image area around the FOE. In areas far from the FOE the shift parameters of the affine transformation can provide more accurate depth information than the expansion alone, and can thus be used similarly to the way they were used in conjunction with the Inertial Navigation Unit (INU) and Kalman filtering. However, the performance of a shift-based algorithm, when the shifts are derived from the affine transformation, would be much improved compared to current algorithms because the shifts - as well as the other parameters - can be obtained between widely separated images. Thus, the main advantage of this new approach is that, allowing the tracked window to expand and rotate, in addition to moving laterally, enables one to correlate images over a very long time span which, in turn, translates into a large spatial baseline - resulting in a proportionately higher depth accuracy.

Barniv, Yair↗