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At least 1,099 records · Page 61

Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.

97 MATHEMATICS AND COMPUTING↗

Scalable Statistical Analysis of Gaussian Models for Petascale Spatiotemporal Data (Final Technical Report)

Gaussian process models for spatial and spatiotemporal data are ubiquitous in scientific and engineering applications. Likelihood-based methods for fitting such models, which includes all Bayesian methods, have desirable statistical properties and are thus the methods of choice when feasible. However, calculating the likelihood function even once can be a challenge for N irregularly sited observations from such a process, requiring O(N 2 ) memory and O(N 3 ) complexity. Thus, there is a need for fast and accurate likelihood approximation even for N on the order of 10 5 , not to mention the 10 15 implied by petascale data. The main objective of this research was to develop computational tools for the statistical analysis of massive spatiotemporal datasets based on Gaussian process models. Another important objective was the development of appropriate statistical models for specific spatiotemporal processes arising in the physical sciences.

97 MATHEMATICS AND COMPUTING↗

Statistical properties of the interplanetary microscale fluctuations

Results are reported for a statistical study of short-period fluctuations in the interplanetary plasma velocity and magnetic field. The data base used consists of measurements of the interplanetary plasma and magnetic field by Pioneer 6 with a time resolution of 72 sec and by Mariner 5 with a resolution of 5 min. The analysis is conducted to characterize the parent population from which all individual microscale events on these time scales are drawn. The microscale changes are grouped according to their energy densities relative to the energy density of the background magnetic field, and it is found that each grouping exhibits certain statistical properties within the limits of observational uncertainty. It is noted that these statistical properties are purely observational and independent of any physical model which may be used to interpret them. The results are discussed in the context of MHD discontinuity theory for a thermally anisotropic plasma.

Belcher, J. W.↗

Sound radiation from randomly vibrating beams of finite circular cross section

The radiation of sound from vibrating cylindrical beams is analyzed based on the frequency of the beam vibrations and the physical characteristics of the beam and its surroundings. A statistical analysis of random beam vibrations allows this result to be independent of the boundary conditions at the ends of the beam. The acoustic power radiated by the beam can be determined from a knowledge of the frequency band vibration data without a knowledge of the individual modal vibration amplitudes. A practical example of the usefulness of this technique is provided by the application of the theoretical calculations to the prediction of the octave band acoustic power output of the picking sticks of an automatic textile loom. Calculations are made of the expected octave band sound pressure levels based on measured acceleration data. These theoretical levels are subsequently compared with actual sound pressure level measurements of loom noise.

Sutterlin, M. W.↗

Unbiased estimation of oceanic mean rainfall from satellite borne radiometer measurements

The statistical properties of the radar derived rainfall obtained during the GARP Atlantic Tropical Experiment (GATE) are used to derive quantitative estimates of the spatial and temporal sampling errors associated with estimating rainfall from brightness temperature measurements such as would be obtained from a satelliteborne microwave radiometer employing a practical size antenna aperture. A basis for a method of correcting the so called beam filling problem, i.e., for the effect of nonuniformity of rainfall over the radiometer beamwidth is provided. The method presented employs the statistical properties of the observations themselves without need for physical assumptions beyond those associated with the radiative transfer model. The simulation results presented offer a validation of the estimated accuracy that can be achieved and the graphs included permit evaluation of the effect of the antenna resolution on both the temporal and spatial sampling errors.

Mittal, M. C.↗

Statistical dependency in visual scanning

A method to identify statistical dependencies in the positions of eye fixations is developed and applied to eye movement data from subjects who viewed dynamic displays of air traffic and judged future relative position of aircraft. Analysis of approximately 23,000 fixations on points of interest on the display identified statistical dependencies in scanning that were independent of the physical placement of the points of interest. Identification of these dependencies is inconsistent with random-sampling-based theories used to model visual search and information seeking.

Ellis, Stephen R.↗

Cyclotron resonant scattering in gamma-ray bursts - Further analysis of GB880205

We have extended our previous work by exploring several plane-parallel slab geometries to model the formation of cyclotron line features. We calculated the Compton temperature T(C) as a function of column density Ne for each of the new geometries. We then fit the resulting spectra to GB880205 exactly as described in Wang et al. (1989). The results show that the addition of column depth below the photon source plane leads to a modest improvement in chi-squared which, although not statistically significant, is pleasing because these geometries are more physically realistic.

Freeman, P. E.↗

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

Molecular abundances and low-mass star formation. 1: Si- and S-bearing species toward IRAS 16293-2422

Results from millimeter and submillimeter spectral line surveys of the protobinary source Infrared Astronomical Satellite (IRAS) 16293-2422 are presented. Here we outline the abundances of silicon- and sulfur-containing species. A combination of rotation diagram and full statistical equilibrium/radiative transfer calculations is used to constrain the physical conditions toward IRAS 16293 and to construct its beam-averaged chemical composition over a 10 to 20 sec (1600 to 3200 AU) scale. The chemical complexity as judged by species such as SiO, OCS, and H2S, is intermediate between that of dark molecular clouds such as L134N and hot molecular cloud cores such as Orion KL. From the richness of the spectra compared to other young stellar objects of similar luminosity, it is clear that molecular abundances do not scale simply with mass; rather, the chemistry is a strong function of evolutionary state, i.e., age.

Blake, Geoffrey A.↗

Improved accuracy of radar WPMM estimated rainfall upon application of objective classification criteria

Application of the window probability matching method to radar and rain gauge data that have been objectively classified into different rain types resulted in distinctly different Z(sub e)-R relationships for the various classifications. These classification parameters, in addition to the range from the radar, are (a) the horizontal radial reflectivity gradients (dB/km); (b) the cloud depth, as scaled by the effective efficiency; (c) the brightband fraction within the radar field window; and (d) the height of the freezing level. Combining physical parameters to identify the type of precipitation and statistical relations most appropriate to the precipitation types results in considerable improvement of both point and areal rainfall measurements. A limiting factor in the assessment of the improved accuracy is the inherent variance between the true rain intensity at the radar measured volume and the rain intensity at the mouth of the rain guage. Therefore, a very dense rain gauge network is required to validate most of the suggested realized improvement. A rather small sample size is required to achieve a stable Z(sub e)-R relationship (standard deviation of 15% of R for a given Z(sub e)) -- about 200 mm of rainfall accumulated in all guages combined for each classification.

Rosenfeld, Daniel↗

Recent Advances on INSAR Temporal Decorrelation: Theory and Observations Using UAVSAR

We review our recent advances in understanding the role of temporal decorrelation in SAR interferometry and polarimetric SAR interferometry. We developed a physical model of temporal decorrelation based on Gaussian-statistic motion that varies along the vertical direction in forest canopies. Temporal decorrelation depends on structural parameters such as forest height, is sensitive to polarization and affects coherence amplitude and phase. A model of temporal-volume decorrelation valid for arbitrary spatial baseline is discussed. We tested the inversion of this model to estimate forest height from model simulations supported by JPL/UAVSAR data and lidar LVIS data. We found a general good agreement between forest height estimated from radar data and forest height estimated from lidar data.

polarimetric SAR interferometry↗

A Roundtrip Journey off the Career Track: Having a Successful Career Despite Your Best Efforts

Although career tracks in science and engineering are often depicted as straight and smooth, many contain detours, side journeys and interruptions. In the end, these detours not only influence who we are, they can make us better scientists and engineers. In this presentation, Dr. Ladbury tells the tale of how his detours took him to far-flung locations from the Himalayan mountains to the African Savannah and eventually back to a rewarding career in radiation physics.

Space Radiation↗

Colloids in Microgravity

Colloidal particles are important in a broad range of applications in technology and materials processing. Due to high sensitivity to thermal fluctuations, a suspension of colloidal particles is considered as an assembly of super-atoms in condensed matter physics. This feature provides an excellent experimental model in statistical mechanics for fundamental studies of microstructural evolution and phase transformation at the individual particle level. However, using colloids to probe three-dimensional phase transitions on Earth remains a challenge as they can be influenced by the gravity force causing the particles to sediment and the solvent to flow. To suppress the undesirable gravity effects, experiments on concentrated colloids were carried out in the International Space Station (ISS) Light Microscopy Module. We will present results of these experiments.

Colloids↗

Essay: Bob Siemann-SLC Days at SLAC

Bob Siemann was a great experimentalist and an excellent teacher.We will greatly miss him. Bob came to SLAC in early 1991 to work on the Stanford Linear Collider (SLC). The SLC was a challenging accelerator which began operating in the late 1980's but still had numerous obstacles to be overcome years into operation. One of the compounding difficulties was making reproducible measurements, since the stability of the collider was poor and the diagnostics were insufficient. Bob dove into this challenge and helped design experiments and diagnostics that provided further clarity. I first got to know Bob while I was still a graduate student, trying to finish my thesis and performing some experimental studies on the SLC, which, at the time, was proving to be very difficult. Most of my expertise had been in beam theory and simulation. Dealing with the real issues of the accelerator was challenging. Bob helped me understand the difference between systematic and statistical errors, and separate operational issues from the fundamental physics. His way of teaching was not to provide an explanation but to ask enough questions so that I could find the answer on my own - this was the best way to learn. I later asked Bob to be a reader on my thesis. As in all things, he took this role extremely seriously. He read through the draft and marked every page to the point where I was regretting my decision. However, his questions again helped me understand my own work better and greatly improved my thesis. Bob was also the de facto leader of an effort focused on the damping rings and the bunch compressors. He was great to work with. He made people think for themselves and refused to simply provide answers. He also worked hard himself, expressing real interest and curiosity. After the studies of the SLC damping rings identified a sawtooth instability due to the vacuum chamber impedance as a source of many downstream fluctuations, Bob took charge of upgrading the rings. As part of this program, I suggested an extensive upgrade that also replaced the dipoles with combined function magnets which might have reduced the horizontal emittance another factor of 3. Although he was extremely busy, Bob helped me develop the proposal and understand the magnetic limitations as well as the potential impacts on the beam dynamics. He helped me consider issues well beyond my initial scope. While the proposal never went anywhere and I think Bob had been aware that there was no funding to pursue the option, he saw that it would be a great learning experience for me and it was. In the early 1990's I had simulated a new regime for the beam-ion instability and, with Frank Zimmermann, I developed a model for the effect which was predicted to occur within the high current, low emittance bunch trains in future storage rings or linear colliders. I thought this was pretty good work but Bob convinced me that the next step had to be confirming the theory with measurements. Because the growth rate was inversely dependent on beam sizes and proportional to the vacuum pressure, measurements required significantly increasing the vacuum pressure in existing facilities. Most people discounted trying such an experiment, but with Bob's urging and suggestions and John Byrd's excitement, we managed to make the measurements at the Advanced Light Source (ALS) at Berkeley. By the mid-1990's Bob was completely focused on advanced acceleration concepts and I was not interacting with him as often. At the time, SLAC was putting together a large effort in designing and documenting a design for the Next Linear Collider (NLC) while constructing the NLC Test Accelerator. Bob was worried that a straightforward extrapolation of the microwave technology would be difficult to bring to fruition because of the cost. He wanted to focus on more cost-effective approaches that could enable future accelerators for high energy physics. As usual, he was correct. The experimental programs that he started in direct laser acceleration and plasma-wakefield acceleration have made great progress. He accomplished this with lots of hard work and by engaging the people around him, especially students and postdocs. In the process, he created a group of extremely talented people which has enabled these technologies to be developed to the point where it seems likely that they are viable and will offer two cost-effective approaches to high-gradient acceleration.

43 PARTICLE ACCELERATORS↗

A fingerprint based metric for measuring similarities of crystalline structures

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum mechanics as applied mathematical statistics

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using statistical modeling to predict and understand fusion experiments

Over 300 cryogenic layered direct-drive inertial confinement fusion implosions have been successfully executed on the OMEGA Laser System in the last decade. However, extracting sufficient understanding from these experiments to develop new designs or to identify or mitigate degradation sources remains challenging. Recently, a statistical modeling approach was developed to successfully design and predict improved implosion experiments on OMEGA. Here, we show that one-dimensional simulations can be used to predict the outcomes of systematically perturbed three-dimensional simulations and that this statistical modeling approach can be used to identify or rule out physical mechanisms for some of the degradation sources observed on the OMEGA Laser System for direct-drive cryogenic inertial confinement fusion. In this instance, we investigate the fusion yield dependencies on the ion temperature asymmetries and laser beam size observed in experiments by comparing with trends in three-dimensional synthetic simulation databases. Using the statistical model on these systematically perturbed simulations, we find that the statistically inferred dependency on the measured ion temperature asymmetries is well explained by imposed ℓ =1 modes. However, we find that the dependency on the laser beam size is only dominated by the illumination non-uniformity for some extreme cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Process-Structure-Property Modeling for Severe Plastic Deformation Processes Using Orientation Imaging Microscopy and Data-Driven Techniques

Machining is a severe plastic deformation process, wherein the workpiece material is subjected to high deformation rates and temperatures. During metal machining, the dynamic recrystallization mechanism causes grain refinement into the sub-micron range. In this study, we investigate the microstructure evolution of oxygen-free high conductivity copper (OFHC Cu) subject to a machining process where the cutting speed and rake angle are controlled to manipulate the process strain, strain rate, and temperatures. Microstructures of the deformed chips are quantified using orientation imaging microscopy and novel statistical descriptors that capture the morphology and local lattice misorientations generated during the several mechanistic stages of the dynamic recrystallization process. Mechanical properties of the resulting chips are quantified using spherical nanoindentation protocols. A multiple output Gaussian process regression model is used to simultaneously model the structure-property evolution, which differs from more common approaches that establish such relationships sequentially. This modeling strategy is particularly attractive since it can flexibly provide both structure and property uncertainty estimates. In addition, the statistical modeling framework allows for the inclusion of multi-fidelity data. The statistical metrics utilized serve as efficient microstructure descriptors, which retain the physics of the observed structures without having to introduce ad hoc microstructure feature definitions.

36 MATERIALS SCIENCE↗