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At least 811 records · Page 45

Transformation of two and three-dimensional regions by elliptic systems

Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.

Mastin, C. Wayne↗

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions

We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.

97 MATHEMATICS AND COMPUTING↗

A spin-wave magnetometer with a positive feedback

In this work, we demonstrate experimentally the operation of a spin-wave magnetometer integrated into a circuit with a positive feedback. The circuit consists of the passive magnetic and active electric parts. The magnetic part includes a sensing element, which is a magnetic cross junction made of Y 3 Fe 2 (FeO 4 ) 3 . The electric part includes a non-linear amplifier and a phase shifter. The electric and magnetic parts are connected via micrometer size antennae. Spin waves are excited by two of these antennae while the output inductive voltage produced by the interfering spin waves is detected by the third antenna. Spin waves propagating in the orthogonal arms of the cross can accumulate significantly different phase shifts, depending on the direction and the strength of the external magnetic field. The output inductive voltage reaches its maximum in the case of constructive spin wave interference. The positive feedback provides further signal amplification. It appears possible to enhance the response function, compared to the passive circuits without a feedback, by a factor of ×100 without an increase in the noise level. The experimental data show a prominent response to the external magnetic field variation, exceeding 5 x 10 3 V/T. The intrinsic noise spectral density of the device can be as low as 10 -16 V 2 /Hz. The estimated sensitivity of the prototype device is 2 x 10 -12 T/√Hz at room temperature. We argue that spin-wave magnetometers can potentially be as sensitive as SQUIDs while operating at room temperature.

36 MATERIALS SCIENCE↗

The influence of temperature induced phase transition on the energy storage density of anti-ferroelectric ceramics

Anti-ferroelectric (AFE) composite ceramics of (Pb{sub 0.858}Ba{sub 0.1}La{sub 0.02}Y{sub 0.008})(Zr{sub 0.65}Sn{sub 0.3}Ti{sub 0.05})O{sub 3}-(Pb{sub 0.97}La{sub 0.02})(Zr{sub 0.9}Sn{sub 0.05} Ti{sub 0.05})O{sub 3} (PBLYZST-PLZST) were fabricated by the conventional solid-state sintering process (CS), the glass-aided sintering (GAS), and the spark plasma sintering (SPS), respectively. The influence of the temperature induced phase transition on the phase structure, hysteresis loops, and energy storage properties of the composite ceramics were investigated in detail. The measured results of X-ray diffraction demonstrate that the composite ceramics exhibit the perovskite phases and small amounts of non-functional pyrochlore phases. Compared with the CS process, the GAS and SPS processes are proven more helpful to suppress the diffusion behaviors between the PBLYZST and PLZST phases according to the field emission scanning electron microscopy, thereby being able to improve the contribution of PBLYZST phase to the temperature stability of the orthogonal AFE phase. When the ambient temperature rises from 25 °C to 125 °C, CS and GAS samples have undergone a phase transition from orthorhombic AFE phase to tetragonal AFE phase, which results in a sharp decline in the energy storage density. However, the phase transition temperature of SPS samples is higher than 125 °C, and the energy storage density only slightly decreases due to the disorder of material microstructure caused by the high temperature. As a result, the SPS composite ceramics obtain a recoverable high energy storage density of 6.46 J/cm{sup 3} and the excellent temperature stability of the energy storage density of 1.16 × 10{sup −2} J/°C·cm{sup 3}, which is 1.29 × 10{sup −2} J/°C·cm{sup 3} lower than that of CS samples and about 0.43 times as that of GAS samples.

36 MATERIALS SCIENCE↗

Floquet operator dynamics and orthogonal polynomials on the unit circle

Operator spreading under stroboscopic time evolution under a unitary is studied. An operator Krylov space is constructed and mapped to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parametrizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC under persistent m-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the Z 3 clock model. The numerically obtained Krylov angles of the Z 3 clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.

Floquet systems↗

AERCam Autonomy: Intelligent Software Architecture for Robotic Free Flying Nanosatellite Inspection Vehicles

The NASA Johnson Space Center has developed a nanosatellite-class Free Flyer intended for future external inspection and remote viewing of human spacecraft. The Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam) technology demonstration unit has been integrated into the approximate form and function of a flight system. The spherical Mini AERCam Free Flyer is 7.5 inches in diameter and weighs approximately 10 pounds, yet it incorporates significant additional capabilities compared to the 35-pound, 14-inch diameter AERCam Sprint that flew as a Shuttle flight experiment in 1997. Mini AERCam hosts a full suite of miniaturized avionics, instrumentation, communications, navigation, power, propulsion, and imaging subsystems, including digital video cameras and a high resolution still image camera. The vehicle is designed for either remotely piloted operations or supervised autonomous operations, including automatic stationkeeping, point-to-point maneuvering, and waypoint tracking. The Mini AERCam Free Flyer is accompanied by a sophisticated control station for command and control, as well as a docking system for automated deployment, docking, and recharge at a parent spacecraft. Free Flyer functional testing has been conducted successfully on both an airbearing table and in a six-degree-of-freedom closed-loop orbital simulation with avionics hardware in the loop. Mini AERCam aims to provide beneficial on-orbit views that cannot be obtained from fixed cameras, cameras on robotic manipulators, or cameras carried by crewmembers during extravehicular activities (EVA s). On Shuttle or International Space Station (ISS), for example, Mini AERCam could support external robotic operations by supplying orthogonal views to the intravehicular activity (IVA) robotic operator, supply views of EVA operations to IVA and/or ground crews monitoring the EVA, and carry out independent visual inspections of areas of interest around the spacecraft. To enable these future benefits with minimal impact on IVA operators and ground controllers, the Mini AERCam system architecture incorporates intelligent systems attributes that support various autonomous capabilities. 1) A robust command sequencer enables task-level command scripting. Command scripting is employed for operations such as automatic inspection scans over a region of interest, and operator-hands-off automated docking. 2) A system manager built on the same expert-system software as the command sequencer provides detection and smart-response capability for potential system-level anomalies, like loss of communications between the Free Flyer and control station. 3) An AERCam dynamics manager provides nominal and off-nominal management of guidance, navigation, and control (GN&C) functions. It is employed for safe trajectory monitoring, contingency maneuvering, and related roles. This paper will describe these architectural components of Mini AERCam autonomy, as well as the interaction of these elements with a human operator during supervised autonomous control.

Fredrickson, Steven E.↗

Model for the electrical conductivity in dense plasma mixtures

A new density functional theory, average atom based model for the electrical conductivity of dense plasmas with a mixture of ion species, containing no adjustable parameters, is presented herein. The model takes the temperature, mass density and relative abundances of the species as input. It takes into account partial ionization, ionic structure, and core-valence orthogonality, and uses quantum mechanical calculations of cross sections. Comparison to an existing high fidelity but computationally expensive method reveals good agreement. The new model is computationally efficient and can reach high temperatures. A new mixing rule is also presented that gives reasonably accurate conductivities for high temperature plasma mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Programs for computing abscissas and weights for classical and nonclassical Gaussian quadrature formulas

Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.

Desmarais, R. N.↗

Effects of volume averaging on the line spectra of vertical velocity from multiple-Doppler radar observations

Calculations of the ratio of the true one-dimensional spectrum of vertical velocity and that measured with multiple-Doppler radar beams are presented. It was assumed that the effects of pulse volume averaging and objective analysis routines is replacement of a point measurement with a volume integral. A u and v estimate was assumed to be feasible when orthogonal radars are not available. Also, the target fluid was configured as having an infinite vertical dimension, zero vertical velocity at the top and bottom, and having homogeneous and isotropic turbulence with a Kolmogorov energy spectrum. The ratio obtained indicated that equal resolutions among radars yields a monotonically decreasing, wavenumber-dependent response function. A gain of 0.95 was demonstrated in an experimental situation with 40 levels. Possible errors introduced when using unequal resolution radars were discussed. Finally, it was found that, for some flows, the extent of attenuation depends on the number of vertical levels resolvable by the radars.

Gal-Chen, T.↗

Embedding potentials for excited states of embedded species

Frozen-Density-Embedding Theory (FDET) is a formalism to obtain the upper bound of the ground-state energy of the total system and the corresponding embedded wavefunction by means of Euler-Lagrange equations [T. A. Wesolowski, Phys. Rev. A 77(1), 012504 (2008)]. FDET provides the expression for the embedding potential as a functional of the electron density of the embedded species, electron density of the environment, and the field generated by other charges in the environment. Under certain conditions, FDET leads to the exact ground-state energy and density of the whole system. Following Perdew-Levy theorem on stationary states of the ground-state energy functional, the other-than-ground-state stationary states of the FDET energy functional correspond to excited states. In the present work, we analyze such use of other-than-ground-state embedded wavefunctions obtained in practical calculations, i.e., when the FDET embedding potential is approximated. Three computational approaches based on FDET, that assure self-consistent excitation energy and embedded wavefunction dealing with the issue of orthogonality of embedded wavefunctions for different states in a different manner, are proposed and discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large eddy simulation of flow through an axisymmetric sudden expansion

Here, this study aims at investigating the inlet flow conditions of flow through an axisymmetric sudden expansion with an expansion ratio of 2.0. A series of large eddy simulations with the WALE model were conducted for different inlet Reynolds numbers ( Re) and turbulence intensities ($u_{rms}/\bar{U}_m$). The reattachment length, defined as the length measured downstream of the expansion where the flow direction is reversed adjacent to the wall ( Lr), was measured for each case. For widely studied inlet turbulence intensity values (TI), the simulation results are in good agreement with the experimental and numerical results reported in the literature. Parametric studies revealed that turbulence intensity affects the critical Reynolds number, marking the transition between the laminar and transition regions and the reattachment length. The critical Reynolds number was found to decrease with increasing turbulence intensity. A correlation expression is proposed. Additional analysis with proper orthogonal decomposition was performed to enhance the understanding of complex flow structures downstream of the expansion. Finally, an overall correlation expression for the reattachment length was obtained for 500 ≤ Re ≤15 000 and 0.2 ≤ TI (%) ≤ 20. For a given turbulence intensity, the reattachment length can be expressed for laminar and turbulent regions as a function of the Reynolds number. The reattachment length in the transition region can be expressed as a fractional average of reattachment lengths for laminar and turbulent flows.

99 GENERAL AND MISCELLANEOUS↗

Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations

The one-loop quark contribution to the QCD effective potential for the homogeneous Abelian gluon field in the presence of an external strong electromagnetic field is evaluated. The structure of extrema of the potential as a function of the angles between chromoelectric, chromomagnetic, and electromagnetic fields is analyzed. In this setup, the electromagnetic field is considered as an external one while the gluon field represents domain structured nonperturbative gluon configurations related to the QCD vacuum in the confinement phase. Two particularly interesting gluon configurations, (anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric fields, are discussed specifically. Within this simplified framework it is shown that the strong electromagnetic fields can play a catalyzing role for a deconfinement transition. At the qualitative level, the present consideration can be seen as a highly simplified study of an impact of the electromagnetic fields generated in relativistic heavy ion collisions on the strongly interacting hadronic matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗

Fission matrix capability for MCNP, Part I - Theory

The theory underlying the fission matrix method is derived using a rigorous Green's function approach. The method is then used to investigate fundamental properties of the transport equation for a continuous-energy physics treatment. We provide evidence that an infinite set of discrete, real eigenvalues and eigenfunctions exist for the continuous-energy problem, and that the eigenvalue spectrum converges smoothly as the spatial mesh for the fission matrix is refined. We also derive equations for the adjoint solution. We show that if the mesh is sufficiently refined so that both forward and adjoint solutions are valid, then the adjoint fission matrix is identical to the transpose of the forward matrix. While the energy-dependent transport equation is strictly bi-orthogonal, we provide surprising results that the forward modes are very nearly self-adjoint for a variety of continuous-energy problems. A companion paper (Part II - Applications) describes the initial experience and results from implementing this fission matrix capability into the MCNP Monte Carlo code. (authors)

97 MATHEMATICS AND COMPUTING↗

Attitude stability of spinning flexible spacecraft

The stability of spinning flexible satellites in a force-free environment was analyzed. The satellite was modeled as a rigid core having attached to it a flexible appendage idealized as a collection of particles (point masses) interconnected by springs. Both Liapunov and Routh-Hurwitz stability procedures are used. In the former, the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, is used as a testing function. Equations of motion are written using the hybrid coordinate formulation, which readily accepts a modal coordinate transformation ultimately allowing truncation to a level amenable to literal stability analysis. Closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane containing the system center of mass and orthogonal to the spin axis. The effects of spin on flexible bodies are discussed by considering a very elementary particle model. Control of passively unstable spacecraft is briefly considered.

Likins, P. W.↗

Habitat Demonstration Unit (HDU) Vertical Cylinder Habitat

NASA's Constellation Architecture Team defined an outpost scenario optimized for intensive mobility that uses small, highly mobile pressurized rovers supported by portable habitat modules that can be carried between locations of interest on the lunar surface. A compact vertical cylinder characterizes the habitat concept, where the large diameter maximizes usable flat floor area optimized for a gravity environment and allows for efficient internal layout. The module was sized to fit into payload fairings for the Constellation Ares V launch vehicle, and optimized for surface transport carried by the All-Terrain Hex-Limbed Extra-Terrestrial Explorer (ATHLETE) mobility system. Launch and other loads are carried through the barrel to a top and bottom truss that interfaces with a structural support unit (SSU). The SSU contains self-leveling feet and docking interfaces for Tri-ATHLETE grasping and heavy lift. A pressurized module needed to be created that was appropriate for the lunar environment, could be easily relocated to new locations, and could be docked together in multiples for expanding pressurized volume in a lunar outpost. It was determined that horizontally oriented pressure vessels did not optimize floor area, which takes advantage of the gravity vector for full use. Hybrid hard-inflatable habitats added an unproven degree of complexity that may eventually be worked out. Other versions of vertically oriented pressure vessels were either too big, bulky, or did not optimize floor area. The purpose of the HDU vertical habitat module is to provide pressurized units that can be docked together in a modular way for lunar outpost pressurized volume expansion, and allow for other vehicles, rovers, and modules to be attached to the outpost to allow for IVA (intra-vehicular activity) transfer between them. The module is a vertically oriented cylinder with a large radius to allow for maximal floor area and use of volume. The modular, 5- m-diameter HDU vertical habitat module consists of a 2-m-high barrel with 0.6-mhigh end domes forming the 56-cubicmeter pressure vessel, and a 19-squaremeter floor area. The module has up to four docking ports located orthogonally from each other around the perimeter, and up to one docking port each on the top or bottom end domes. In addition, the module has mounting trusses top and bottom for equipment, and to allow docking with the ATHLETE mobility system. Novel or unique features of the HDU vertical habitat module include the nodelike function with multiple pressure hatches for docking with other versions of itself and other modules and vehicles; the capacity to be carried by an ATHLETE mobility system; and the ability to attach inflatable 'attic' domes to the top for additional pressurized volume.

Howe, Alan↗

Analysis of the multipactor effect in circular waveguides excited by two orthogonal polarization waves

Circular waveguides, either employed as resonant cavities or as irises connecting adjacent guides, are widely present in many passive components used in different applications (i.e., particle accelerators and satellite subsystems). In this paper, we present the study of the multipactor effect in circular waveguides considering the coexistence of the two polarizations of the fundamental TE{sub 11} circular waveguide mode. For a better understanding of the problem, only low multipactor orders have been explored as a function of the polarization ellipse eccentricity. Special attention has been paid to the linear and circular polarizations, but other more general configurations have also been explored.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

GeN-ROM—An OpenFOAM®-based multiphysics reduced-order modeling framework for the analysis of Molten Salt Reactors

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM® and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeN-Foam, a similarly OpenFOAM®-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 – 10 5 .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗