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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Development of Tearing Instability in a Current Sheet Forming by Sheared Incompressible Flow

Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvenic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi et al. 1976; Rutherford 1973) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal MHD, a coordinate transformation reveals that the flow compresses and stretches perturbations. A multiple scale formulation describes how linear tearing mode theory (Furth et al. 1963; Coppi et al. 1976) can be applied to an equilibrium changing under flow, showing that tearing eigenfunctions grow slowly due to the flow and undergo exponential growth at a rate given by standard scalings with time dependence added. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Multigroup cross section generation capability in GRIFFIN

GRIFFIN is an advanced reactor multiphysics application built on the object-oriented simulation environment (MOOSE) and is jointly developed by Idaho National Laboratory and Argonne National Laboratory. The cross section application programming interface, originally developed for the PROTEUS code, has been integrated into GRIFFIN to prepare cross sections for thermal reactor applications with heterogeneous geometries. Additional improvements have been made by implementing an on-the-fly slowing down method, a double heterogeneity treatment capability, and updating the procedure to generate the fine multigroup library. The cross section preparation capability in GRIFFIN was verified for graphite-moderated TRISO fuel-based reactor benchmark problems: unit-cell problems of VHTR and EMPIRE micro reactor and HTTR assembly problems. Eigenvalues and multigroup cross sections of GRIFFIN agreed very well with those of the continuous-energy Monte Carlo code Serpent2 within 200 pcm in eigenvalue and 2% in cross sections. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Bethe-Salpeter Eigenvalue Solver Package (BSEPACK) v0.1

The BSEPACK contains a set of subroutines for solving the Bethe-Salpeter Eigenvalue (BSE) problem. This type of problem arises in this study of optical excitation of nanoscale materials. The BSE problem is a structured non-Hermitian eigenvalue problem. The BSEPACK software can be used to compute all or subset of eigenpairs of a BSE Hamiltonian. It can also be used to compute the optical absorption spectrum without computing BSE eigenvalues and eigenvectors explicitly. The package makes use of the ScaLAPACK, LAPACK and BLAS.

SHAO, MEIYUE↗
DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗
DOE OSTI2018

Systems of Functions Orthogonal Over the Domain and Their Application in Boundary-Value Problems of Mathematical Physics

We formulate a boundary-value problem for eigenvalues and eigenfunctions of the Helmholtz equation in a complex domain with the use of mutually conjugated complex variables. The obtained systems of functions are orthogonal in this domain and constructed by using the Bessel functions and powers of the conformal mappings of the analyzed domains onto a circle. The solutions of boundary-value problems for the principal equations of mathematical physics (hyperbolic, parabolic and elliptic types) are obtained in the form of the sums of series in the systems of functions orthogonal over the domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Second Moment Method for k -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasidiffusion. While this method has been shown to be comparable to quasidiffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to the belief that the resulting inhomogeneous source makes the problem ill posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasidiffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Finally, the results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Grand Unification of Quantum Algorithms

Quantum algorithms offer significant speed-ups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms have recently been tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW’19 paper on the QSVT [Gilyén et al., ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which the QSVT naturally emerges. Paralleling GSLW’19, we then employ the QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how the QSVT is a single framework comprising the three major quantum algorithms, suggesting a grand unification of quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Electronic structure with direct diagonalization on a D-wave quantum annealer

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A short proof of Weyl's law for fractional differential operators

We study spectral asymptotics for a large class of differential operators on an open subset of R{sup d} with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non-homogeneous symbols. Based on a sharp estimate for the sum of the eigenvalues we establish the first term of the semiclassical asymptotics. This generalizes Weyl's law for the Laplace operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Asymptotics of the Resonant Tunneling of High-Energy Electrons in Two-Dimensional Quantum Waveguides of Variable Cross-Section

A waveguide occupies a strip in ℝ{sup 2} having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

We describe a number of recently developed techniques for improving the performance of large-scalenuclear configuration interaction calculations on high performance parallel computers. We show thebenefit of using a preconditioned block iterative method to replace the Lanczos algorithm that hastraditionally been used to perform this type of computation. The rapid convergence of the block iterativemethod is achieved by a proper choice of starting guesses of the eigenvectors and the construction of aneffective preconditioner. These acceleration techniques take advantage of special structure of the nuclearconfiguration interaction problem which we discuss in detail. The use of a block method also allows usto improve the concurrency of the computation, and take advantage of the memory hierarchy of modernmicroprocessors to increase the arithmetic intensity of the computation relative to data movement. Wealso discuss the implementation details that are critical to achieving high performance on massivelyparallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to threetimes faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Shao, Meiyue↗
DOE OSTI2018

Study of excited quark propagator contributions in perturbative chiral quark model

In this work, masses of octet baryons are evaluated in the framework of the perturbative chiral quark model (PCQM) with considering both the ground and excited states in the quark propagator, in which a Cornell-like potential is first constructed by letting the predetermined ground state quark wavefunction satisfy Dirac equation, and the excited quark states are derived by resolving Dirac equation with the extracted PCQM potential numerically employing Generalized Eigenvalue & Eigenstate Problem method. The results on the octet baryon masses are found in good agreement with the experimental data, and the study reveals that the contributions of the excited quark states are considerably influential in the octet baryon masses as expected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps

As an analog to graphene, honeycomb photonic crystals (PhCs) have attracted a great deal of interest in recent years. The additional degrees of freedom in a honeycomb PhC are useful in designing and optimizing waveguides, can be used to control the symmetry of the system and to realize novel optical devices. In this paper, we present an efficient numerical method for analyzing two-dimensional honeycomb PhC waveguides. Our method is based on a special supercell that covers one period of the honeycomb PhC waveguide and the so-called Dirichlet-to-Neumann map of the supercell. The method gives rise to a linear eigenvalue value problem with relatively small matrices, and it is validated by comparing with previous works. As an application of the method, we calculate edge modes for a few different PhCs. For a honeycomb PhC with dielectric rods in air, we found an edge mode at the zigzag edge, without using special modified rods at the edge. For a honeycomb PhC with air holes, we found a new edge mode when the PhC is bounded by a perfectly electric conductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Coupled Neutron and Gamma Heating Calculation Based on VARIANT Nodal Transport Method

Accurate determination of temperature distributions in fuel pins and duct walls is essential for fuel-pin performance and assembly bowing analyses. Currently, the multi-assembly, sub-channel analysis code SE2-ANL is used in thermalhydraulic analysis of sodium cooled fast reactors (SFR). SE2- ANL is interfaced with the DIF3D/GAMSOR/DIF3D procedure for coupled neutron and gamma heating calculations, developed at Argonne National Laboratory (ANL). In this procedure, the neutron flux distribution is first calculated using the finite-difference diffusion theory option of the DIF3D code. Using the neutron flux solution, the GAMSOR code computes the gamma source distribution for the subsequent gamma flux calculation with DIF3D. However, in the current heating calculation scheme, the neutron and gamma flux calculations are limited to six triangular meshes per hexagonal assembly. In addition, the pin power distributions are estimated by assuming that the power distribution within an assembly is separable in the radial and axial directions. In each assembly, the axial power profile is obtained by averaging the power densities of six triangular meshes at each axial mesh interval. The radial power profile is evaluated at a single axial mesh (e.g., at the core mid-plane) by approximating the neutron and gamma flux distributions by a linear or quadratic polynomial of two variables x and y, depending on the polynomial order specified by the user. The coefficients of the linear and quadratic polynomials are determined by the least squares fit of six and 24 triangular mesh fluxes, respectively. Furthermore, the total heat generation rate in an assembly duct wall is simply determined by a user-specified fraction of the total gamma heating within that assembly. With the advancement of computer technology, the nodal transport theory code VARIANT is routinely used in core design analyses of SFR instead of DIF3D. It is therefore necessary to develop a new heating calculation procedure based on VARIANT neutron and gamma transport calculations. In this study, a new, coupled neutron and gamma heating calculation scheme has been developed to determine the pin power distributions more accurately by eliminating the aforementioned limitations of the current procedure. For this, the GAMSOR code has been extended to generate the intra-nodal gamma source distribution to be consistent with the trial functions of VARIANT. In the new heating calculation procedure, the neutron flux distribution is determined first by solving an eigenvalue transport problem using VARIANT. The obtained neutron flux is then used in GAMSOR to calculate the gamma source distribution. Using this gamma source distribution, the gamma flux distribution is determined by solving a fixed-source transport problem using VARIANT again. Using the computed neutron and gamma flux distributions, the power distribution in each fuel pin and duct wall is determined using a new utility code CURVE, which has been developed to evaluate the VARIANT flux solution at each fuel pin position and along the duct mid-wall. For each pin segment contained in a VARIANT node, the axial power shape is represented as a quadratic profile. The performance of the new heating calculation scheme based on VARIANT transport solutions has been tested against the existing method of SE2-ANL, using the ABR-1000 metal core design. The gamma source distribution and the assembly, fuel pin and duct wall power distributions were calculated and compared. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors

Here, we present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations and many-body localization studies of quantum spin chains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Consistent spatial expansion functions on hexagonal surfaces for use in radiation transport methods

Some of the radiation transport solvers that are based on expansion function methods in hexagonal geometry generally use projection techniques that transform the spatial dependence of the angular flux in hexagonal geometry to Cartesian geometry by mapping and then expanding in terms of expansion functions (e.g., Legendre polynomials). However, this approach usually requires a relatively higherorder expansion in space for accurate representation of the spatial distribution of the flux. To overcome this limitation, a set of consistent spatial expansion functions have been developed in hexagonal geometry in this paper. These functions satisfy the orthogonality condition on hexagonal surfaces and guarantee the conservation of currents after expansion regardless of the truncation order. The latter is an important property for preservation of neutron balance. The new spatial expansion method has been implemented into the coarse mesh radiation transport (COMET) code and tested in both the single assembly and the full core Advanced High Temperature Reactor (AHTR) benchmark problems. The eigenvalues and assembly-averaged and stripe-wise fission density distributions predicted by the new method with 2nd order spatial expansion functions were found to exhibit similar accuracy as those computed by the current mapping method with 4th order spatial expansion functions. This indicates that the angular fluxes in AHTRs can be predominantly represented by a low order expansion if the new spatial expansion functions are used. As a result, to maintain the same accuracy, the computational efficiency of COMET is improved significantly (2–5 times) by using the new spatial expansion method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC

In this work, we present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. Here we present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

97 MATHEMATICS AND COMPUTING↗