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NASA NTRS1995

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

Killen, K.↗

NASA NTRS1994

A PV view of the zonal mean distribution of temperature and wind in the extratropical troposphere

The dependence of the temperature and wind distribution of the zonal mean flow in the extratropical troposphere on the gradient of pontential vorticity along isentropes is examined. The extratropics here refer to the region outside the Hadley circulation. Of particular interest is whether the distribution of temperature and wind corresponding to a constant potential vorticity (PV) along isentropes resembles the observed, and the implications of PV homogenization along isentropes for the role of the tropics. With the assumption that PV is homogenized along isentropes, it is found that the temperature distribution in the extratropical troposphere may be determined by a linear, first-order partial differential equation. When the observed surface temperature distribution and tropical lapse rate are used as the boundary conditions, the solution of the equation is close to the observed temperature distribution except in the upper troposphere adjacent to the Hadley circulation, where the troposphere with no PV gradient is considerably colder. Consequently, the jet is also stronger. It is also found that the meridional distribution of the balanced zonal wind is very sensitive to the meridional distribution of the tropopause temperature. The result may suggest that the requirement of the global momentum balance has no practical role in determining the extratropical temperature distribution. The authors further investigated the sensitivity of the extratropical troposphere with constant PV along isentropes to changes in conditions at the tropical boundary (the edge of the Hadley circulation). It is found that the temperature and wind distributions in the extratropical troposphere are sensitive to the vertical distribution of PV at the tropical boundary. With a surface distribution of temperature that decreases linearly with latitude, the jet maximum occurs at the tropical boundary and moves with it. The overall pattern of wind distribution is not sensitive to the change of the position of the tropical boundary. Finally, the temperature and wind distributions of an extratropical troposphere with a finite PV gradient are calculated. It is found that the larger the isentropic PV gradient, the warmer the troposphere and the weaker the jet.

Sun, De-Zheng↗

DOE OSTI2023

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Data-Driven Generic Turbines for Distributed Wind Modeling, Optimization, and Economic Studies

As distributed energy resources (DER) become less expensive and more popular, utilities, project developers, and customers have an increasing need to model the performance of existing and proposed DER systems. Distributed wind has been shown to have widespread economic potential but is often represented by a simplified model in - or excluded from - DER modeling tools and studies. There is often no economic imperative to extend models and studies to give full consideration to distributed wind. We present a set of data-driven generic turbines derived from 16 years of annual distributed wind market survey data. The proposed methodology can be used to derive generic turbines from separate or updated data sets. Finally, a mixed-integer linear programming approach to optimal distributed wind project sizing is used to demonstrate the generic turbine models. Combined, these models and methods can reduce barriers to considering distributed wind in modeling tools and studies.

Reiman, Andrew P.↗

NASA NTRS1989

Thin-plate spline quadrature of geodetic integrals

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman↗

NASA NTRS2005

Boundary-Layer Receptivity and Integrated Transition Prediction

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Chang, Chau-Lyan↗

NASA NTRS1989

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗

DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Improved Evaluation of Large Network Matrices for Linear Power Flow Within Optimization Problems: Preprint

This work discusses methods for evaluating the Power Transfer Distribution Factor (PTDF) and Line Outage Distribution Factor (LODF) matrices by employing sparse linear algebra for large-scale computing applications. These matrices are critical in many power systems applications, such as the Unit Commitment Problem (UC), pre- and post-contingency power flow analysis, and transmission expansion. These matrices are typically dense, which means they require a significant amount of time and memory to be computed for large networks. However, by analyzing the structure of the matrices and their computation method, it is possible to use reduced memory methods based on sparse matrix operations. This paper shows that sparse linear algebra algorithms are faster and require less memory and time than traditional dense approaches. Additionally, we explore the effect of matrix sparsification by eliminating trailing digits on power flow calculations.

ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1985

Proton dosimeter design for distributed body organs

A simple dosimeter design has been developed by NASA to monitor the space proton dose (in rads) to a distributed body organ as a linear combination of ion chambers with varying wall thickness. Estimated doses are given for ion chambers of thickness 2, 3, 4, and 5 g/sq cm. The analytical equation used to calculate the dose distribution factor is also given.

Wilson, J. W.↗

NASA NTRS1983

Stability of electron distributions within the earth's bow shock

The present examination of the linear Vlasov stability of a class of electron velocity distributions modeling those observed within the earth's bow shock is restricted to electrostatic waves propagating parallel to the ambient magnetic field B. Two instabilities are identified as driven by free energy in the direction parallel to B: an ion acoustic wave with real frequency below the ion plasma frequency, and an electron acoustic wave whose real frequency is several times the ion plasma frequency. Unstable wave characteristics are in accord with the trend of the observed electrostatic waves toward polarization parallel to the magnetic field. The instabilities identified may contribute to electron dissipation in collisionless shocks.

Thomsen, M. F.↗

NASA NTRS1993

Quasi-linear regime of gravitational instability: Implication to density-velocity relation

The well known linear relation between density and peculiar velocity distributions is a powerful tool for studying the large-scale structure in the Universe. Potentially it can test the gravitational instability theory and measure Omega. At present it is used in both ways: the velocity is reconstructed, provided the density is given, and vice versa. Reconstructing the density from the velocity field usually makes use of the Zel'dovich approximation. However, the standard linear approximation in Eulerian space is used when the velocity is reconstructed from the density distribution. I show that the linearized Zel'dovich approximation, in other words the linear approximation in the Lagrangian space, is more accurate for reconstructing velocity. In principle, a simple iteration technique can recover both the density and velocity distributions in Lagrangian space, but its practical application may need an additional study.

Shandarin, Sergei F.↗

NASA NTRS1975

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Mukhopadhyay, A. K.↗

DOE OSTI2021

Parallel String Graph Construction and Transitive Reduction for De Novo Genome Assembly

One of the most computationally intensive tasks in computational biology is de novo genome assembly, the decoding of the sequence of an unknown genome from redundant and erroneous short sequences. A common assembly paradigm identifies overlapping sequences, simplifies their layout, and creates consensus. Despite many algorithms developed in the literature, the efficient assembly of large genomes is still an open problem. In this work, we introduce new distributed-memory parallel algorithms for overlap detection and layout simplification steps of de novo genome assembly, and implement them in the diBELLA 2D pipeline. Our distributed memory algorithms for both overlap detection and layout simplification are based on linear-algebra operations over semirings using 2D distributed sparse matrices. Our layout step consists of performing a transitive reduction from the overlap graph to a string graph. We provide a detailed communication analysis of the main stages of our new algorithms. diBELLA 2D achieves near linear scaling with over 80% parallel efficiency for the human genome, reducing the runtime for overlap detection by 1.2-1.3× for the human genome and 1.5-1.9× for C.elegans compared to the state-of-the-art. Our transitive reduction algorithm outperforms an existing distributed-memory implementation by 10.5-13.3× for the human genome and 18-29× for the C. elegans. Our work paves the way for efficient de novo assembly of large genomes using long reads in distributed memory.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1979

The source of electrostatic fluctuations in the solar-wind

Solar wind electron and ion distribution functions measured simultaneously with or close to times of intense electrostatic fluctuations are subjected to a linear Vlasov stability analysis. Although all distributions tested were found to be stable, the analysis suggests that the ion beam instability is the most likely source of the fluctuations.

Lemons, D. S.↗

NASA NTRS1987

Linear and nonlinear dynamic instability of rotating polytropes

A three-dimensional hydrodynamic computer program is used to study the growth of nonaxisymmetric structures in rapidly rotating, self-gravitating polytropes. Models with polytropic index n = 0.8, 1.0, 1.3, 1.5, and 1.8 are studied. The initially axisymmetric equilibria are constructed by the Ostriker-Mark self-consistent-field method. The nonaxisymmetric pattern that develops out of low-amplitude random noise is a two-armed spiral with a well-defined pattern speed and growth rate which closely match properties of the toroidal mode predicted from the linear, second-order tensor-virial equation. A Fourier analysis of each polytrope's azimuthal density distribution shows that, even in the linear amplitude regime, higher-order angular patterns also develop exponentially in time. The higher-order patterns ultimately move in synchronization with the broad two-armed spiral, creating a narrow two-armed spiral. As the polytropic index is decreased, a more open and centrally more barlike pattern develops.

Williams, Harold A.↗

NASA NTRS2023

Parameter Dependencies of Early-Stage Tangential Discontinuity-Driven Foreshock Bubbles in Local Hybrid Simulations

Foreshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere-ionosphere system. In the kinetic formation model, foreshock ions interact with the discontinuity by performing partial gyrations to generate currents that change the magnetic field topology around the discontinuity. However, how different foreshock ion properties affect the growth of the field variations is not well understood. Therefore, we use 2-D local hybrid simulations to study the effects of different foreshock ion distributions and properties on the growth of tangential discontinuity (TD)-driven FBs. We discover that for a gyrophase-bunched distribution with an initial phase where the guiding center is on the other side of the TD, the foreshock ions gyrate together across the TD, causing more foreshock ions to cross the TD and leading to a faster expansion of the structure than for a Maxwellian distribution. A ring distribution also yields higher expansion speeds because of the higher projected velocity into the new perpendicular direction. For Maxwellian distributions, there are positive and linear correlations of the FB expansion speeds with the initial foreshock ion densities, thermal speeds, parallel speeds, and sine of the TD magnetic shear angles. These parameter dependencies grow in strength as the structures evolve with time. The foreshock ion distributions and properties that lead to stronger currents produce more significant magnetic field variations and higher expansion speeds. Our study helps quantify the formation and expansion of FBs to forecast their space weather effects and contribution to shock acceleration.

Andrew Vu↗