Device for generating ellipses over an arbitrary pair of conjugate diameters
Adjustable rotor device for generating ellipses over arbitrary pair of conjugate diameters
ROTOR SYSTEM↗
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Novel solutions to low-frequency problems with geometrically designed beam-waveguide systems
The poor low-frequency performance of geometrically designed beam-waveguide (BWG) antennas is shown to be caused by the diffraction phase centers being far from the geometrical optics mirror focus, resulting in substantial spillover and defocusing loss. Two novel solutions are proposed: (1) reposition the mirrors to focus low frequencies and redesign the high frequencies to utilize the new mirror positions, and (2) redesign the input feed system to provide an optimum solution for the low frequency. A novel use of the conjugate phase-matching technique is utilized to design the optimum low-frequency feed system, and the new feed system has been implemented in the JPL research and development BWG as part of a dual S-/X-band (2.3 GHz/8.45 GHz) feed system. The new S-band feed system is shown to perform significantly better than the original geometrically designed system.
Imbriale, W. A.↗
Predicting Flow in Fracture Networks With Quantum Algorithms
Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.
58 GEOSCIENCES↗
Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Studies of the Effects of Actuator Errors on the HCIT/PIAA Contrast Performance
The High Contrast Imaging Testbed Phase Induced Amplitude Apodization (HCIT/PIAA) coronagraph system at JPL relies on an Electric-Field Conjugation (EFC) wavefront correction algorithm to obtain the required high contrast. This algorithm works with one deformable mirror (DM) to estimate the electric-field to be controlled, and with one or multiple DM's to create a "dark-hole" in the image plane. We have investigated the effects of DM actuator errors on the efficiency of the EFC algorithm. The structural design of the optical system as well as the parameters of various optical elements used in the analysis are drawn from those of the HCIT/PIAA system that have been and will be implemented with one or two DM's. The simulation takes into account the surface errors of various optical elements. In this paper, we report our findings in the case of narrowband wavelength light.
PIAA↗
Constraint treatment techniques and parallel algorithms for multibody dynamic analysis
Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.
Chiou, Jin-Chern↗
Two-dimensional radiative transfer in cloudy atmospheres - The spherical harmonic spatial grid method
A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.
Evans, K. F.↗
Introduction: Photons and Ground-Based
A Conference on Measurement Techniques for Solar and Space Physics was held on 20-24 April 2015 in Boulder, Colorado, at the National Center for Atmospheric Research Center Green Campus. The present volume collects together the conference papers for photons and ground-based categories. This gathering of over 200 scientists and instrumentalists was born out of the desire to collect in one place the latest experiment and instrument technologies required for advancement of scientific knowledge in the disciplines of solar and space physics. The two goals for this conference and the subsequent publication of its content are (a) to describe measurement techniques and technology development needed to advance high priority science in the fields of solar and space physics; and (b) to provide a survey or reference of techniques for in situ measurement and remote sensing of space plasmas. Towards this end, our goal has always been inspired by the two 1998 Geophysical Monographs (Nos. 102 and 103) entitled, "Measurement Techniques in Space Plasmas" (particles and fields) [Pfaff et al., 1998a, 1998b], which have served as a reference and resource for advanced students, engineers, and scientists who wish to learn the fundamentals of measurement techniques and technology in this field. Those monographs were the product of an American Geophysical Union Chapman Conference that took place in Santa Fe, NM, in 1995: "Measurement Techniques in Space Plasmas-What Works, What Doesn't." Two decades later, we believe that it is appropriate to revisit this subject, in light of recent advances in technology, research platforms, and analysis techniques. Moreover, we now include direct measurements of neutral gases in the upper atmosphere, optical imaging techniques, and remote observations in space and on the ground. Accordingly, the workshop was organized among four areas of measurement techniques: particles, fields, photons, and ground-based. This two-set volume is largely composed of the content of that workshop. Special attention is given to those techniques and technologies that demonstrate promise of significant advancement in measurements that will enable the highest priority science as described in the 2012 National Research Council Decadal Survey [Baker and Zurbuchen et al., 2013]. Additionally, a broad tutorial survey of the current technologies is provided to serve as reference material and as a basis from which advanced and innovative ideas can be discussed and pursued. Included are instrumentation and techniques to observe the solar environment from its interior to its outer atmosphere, the heliosphere out to the interstellar regions, in geospace, and other planetary magnetospheres and atmospheres. To make significant progress in priority science as expressed in the National Research Council solar and space physics decadal survey and recent NASA Heliophysics roadmaps, identification of enabling new measurement techniques and technologies to be developed is required. Also, it is valuable to the community and future scientists and engineers to have a complete survey of the techniques and technologies used by the practitioners of solar and space physics. As with the 1995 conference and subsequent 1998 publication, it is incumbent on the community to identify those measurements that are particularly challenging and still require new techniques to be identified and tested to enable the necessary accuracy and resolution of certain parameters to be achieved. The following is a partial list of the measurement technique categories that are featured in these special publications: Particles; Thermal plasma to MeV energetic particles, neutral gas properties including winds, density, temperature, and composition, and enhanced neutral atom imaging; Fields; DC electric and magnetic fields, plasma waves, and electron drift instruments from which the plasma velocity information provides a measure of the DC electric field; Photons; Instruments sensitive from the near-infrared to X-rays; Contributions of techniques and technology for optical design, optical components, sensors, material selection for cameras, telescopes, and spectrographs; Ground based; Remote sensing methods for solar and geospace activity and space weather. The focus includes solar observatories, all-sky cameras, lidars, and ionosphere thermosphere mesosphere observatory systems such as radars, ionosondes, GPS receivers, magnetometers, conjugate observations, and airborne campaigns. The present volume collects together the papers for photons and ground-based categories. The companion volume collects together the papers for particles and fields categories. It is recognized that there are measurement techniques that overlap among the four categories. For example, use of microchannel plate detectors is used in photon and particle measurement techniques or the observation of visible photons and magnetic fields in space and on the ground share common technologies. Therefore, the reader should consider the entire collection of papers as they seek to understand particular applications. We hope that these volumes will be as valuable as a reference for our community as the earlier 1998 volumes have been.
Spann, James↗
On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices
Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
Freund, Roland↗
Multivariable Hermite polynomials and phase-space dynamics
The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.
Dattoli, G.↗
Analysis of the DFP/AFCS Systems for Compensating Gravity Distortions on the 70-Meter Antenna
This paper presents the theoretical computations showing the expected performances for both systems. The basic analysis tool is a Physical Optics reflector analysis code that was ported to a parallel computer for faster execution times. There are several steps involved in computing the RF performance of the various systems. 1 . A model of the RF distortions of the main reflector is required. This model is based upon measured holography maps of the 70-meter antenna obtained at 3 elevation angles. The holography maps are then processed (using an appropriate gravity mechanical model of the dish) to provide surface distortion maps at all elevation angles. 2. From the surface distortion maps, ray optics is used to determine the theoretical shape of the DFP that will exactly phase compensate the distortions. 3. From the theoretical shape and a NASTRAN mechanical model of the plate, the actuator positions that generate a surface that provides the best RMS fit to the theoretical model are selected. Using the actuator positions and the NASTRAN model provides an accurate description of the actual mirror shape. 4. Starting from the mechanical drawings of the feed, a computed RF feed pattern is generated. This pattern is expanded into a set of spherical wave modes so that a complete near field analysis of the reflector system can be obtained. 5. For the array feed, the excitation coefficients that provide the maximum gain are computed using a phase conjugate technique. The basic experimental geometry consisted of a dual shaped 70-meter antenna system; a refocusing ellipse, a DFP and an array feed system. To provide physical insight to the systems performance, focal plane field plots are presented at several elevations. Curves of predicted performance are shown for the DFP system, monopulse tracking system, AFCS and combined DFP/AFCS system. The calculated results show that the combined DFP/AFCS system is capable of recovering the majority of the gain lost due to gravity distortion.
Imbriale, William A.↗
Design Principles for Resonant Wave Energy Converters: Benchmarking Power Capture and Flow
Control co-design (CCD) in Wave Energy Converters (WECs) integrates the controller, power take-off (PTO), and buoy models during system design to optimize power output. Using the bi-conjugate impedance matching principle, this study models the PTO as a two-port network, revealing impedance matching conditions at the input and output ports as a function of the buoy, PTO, and controller. Here, this study examines the pairing of a flywheel-type pitch resonator PTO within a given buoy constrained by limited space and ballast capacity. The results show that physical constraints imposed by the buoy affect PTO performance. While controller tuning achieves optimal output impedance matching and flywheel inertia is maximized within the buoy's limitations, the PTO's input impedance remains smaller than the complex conjugate of the buoy's intrinsic impedance. This mismatch limits the PTO's ability to generate sufficient reaction torque, particularly outside the resonance frequency, resulting in narrow-band power transfer. The findings emphasize the need for PTO design modifications to improve input power transfer. Pendulum-based PTO mechanisms are proposed as alternatives to couple with multiple buoy motion modes and improve wave-to-wire efficiency while respecting system constraints.
Control Co-Design↗
Multigrid Methods for Fully Implicit Oil Reservoir Simulation
In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.
Molenaar, J.↗
On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices
The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.
Fischer, Bernd↗
GMRES acceleration of computational fluid dynamics codes
The generalized minimal residual algorithm (GMRES) is a conjugate-gradient like method that applies directly to nonsymmetric linear systems of equations. In this paper, GMRES is modified to handle nonlinear equations characteristic of computational fluid dynamics. Attention is devoted to the concept of preconditioning and the role it plays in assuring rapid convergence. A formulation is developed that allows GMRES to be preconditioned by the solution procedures already built into existing computer codes. Examples are provided that demonstrate the ability of GMRES to greatly improve the robustness and rate of convergence of current state-of-the-art fluid dynamics codes. Theoretical aspects of GMRES are presented that explain why it works. Finally, the advantage GMRES enjoys over related methods such as conjugate gradients are discussed.
Wigton, L. B.↗
Numerical Modeling of the Chilldown of Cryogenic Transfer Lines Using a Sinda/GFSSP Integrated Solver
An important first step in cryogenic propellant loading is the chilldown of transfer lines. During the chilldown of the transfer line, the flow is two-phase and unsteady, with solid to fluid heat transfer and therefore a coupled thermo-fluid analysis is necessary to model the system. This paper describes a numerical model of pipe chilldown that utilizes the Sinda/GFSSP Conjugate Integrator (SGCI). SGCI is a new analysis tool developed at NASA's Marshall Space Flight Center (MSFC). SGCI facilitates the solution of thermofluid problems in interconnected solid-fluid systems. The solid component of the system is modeled in MSC Patran and translated into an MSC Sinda thermal network model. The fluid component is modeled in GFSSP, the Generalized Fluid System Simulation Program. GFSSP is a general network flow solver developed at NASA/MSFC. GFSSP uses a finite-volume approach to model fluid systems that can include phase change, multiple species, fluid transients, and heat transfer to simple solid networks. SGCI combines the GFSSP Fortran code with the Sinda input file and compiles the integrated model. Sinda solves for the temperatures of the solid network, while GFSSP simultaneously solves the fluid network for pressure, temperature, and flow rate. The two networks are coupled by convection heat transfer from the solid wall to the cryogenic fluid. The model presented here is based on a series of experiments conducted in 1966 by the National Bureau of Standards (NBS). A vacuum-jacketed, 200 ft copper transfer line was chilled by liquid nitrogen and liquid hydrogen. The predictions of transient temperature profiles and chilldown time of the integrated Sinda/GFSSP model will be compared to the experimental measurements.
LeClair, Andre↗
M-step preconditioned conjugate gradient methods
Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.
Adams, L.↗
Objectives and design of the Echo 6 electron beam experiment - Large ionospheric perturbations and energetic particle patterns
The data from the March 30, 1983 launching of Echo 6 are presented. Echo 6 contained duplex accelerators and a system of four throw away detectors to detect and analyze conjugate electron echoes. The model used to calculate the proper trajectory of the rocket and the reason for not detecting echoes are discussed. The components of the plasma diagnostic package which was used to study the electron beam interactions with the ionospheric plasma, and the functions of the two controllable electron guns and the two sets of orthogonal electric probes are described. The signal-mode potentials between each probe and the plasma diagnostic payload are investigated. The signals produced by the gun pulses are analyzed and the interpretation of the electric field probe response is examined.
Winckler, J. R.↗