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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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All sourcesNASA NTRSDOE OSTI
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 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↗
DOE OSTI2017

Modal characteristics of structures considering dynamic soil-structure interaction effects

The modal characteristics of structures are usually computed disregarding any interaction with the soil. Here, a finite element-perfectly matched layers model is presented to compute the modal characteristics of 2D and 3D coupled soil-structure systems while taking fully into account dynamic soil-structure interaction. The methodology can facilitate the interpretation of experimentally identified modal characteristics by assessing the importance of dynamic soil-structure interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Bell-Plesset effects in Rayleigh-Taylor instability of finite-thickness spherical and cylindrical shells

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining the “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A Robust and Efficient Implementation of LOBPCG

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. Here, we also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

VERA BWR progression problems

During the first phase of the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, the Virtual Environment for Reactor Applications (VERA) was developed with a focus on capabilities for high-fidelity, multiphysics simulation of pressurized water reactors (PWRs). During this development effort, a set of progression problems was created ranging from smaller pin cell calculations to larger 3D full-core calculations. These progression problems helped to guide the development of the software and served as benchmarks against which to test VERA. Since 2019, efforts have been made to extend the capabilities of VERA to model boiling water reactors (BWRs). Because BWR simulations come with many unique challenges, a set of BWR progression problems was developed to aid in this new effort. The BWR progression problems range from 2D lattice calculations to 3D mini-core problems, and reference neutronic solutions were computed using continuous-energy Monte Carlo codes. MPACT, one of the neutronics code in VERA, was benchmarked using the BWR progression problems. The code is capable of computing solutions to all problems. The eigenvalues computed by MPACT agree well with the Monte Carlo reference solutions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

Steady-State Thermal-Hydraulic Analysis and Bowing Reactivity Evaluation Methods Based on Neutron and Gamma Transport Calculations

With the advancement of computer technology, the variational nodal transport code VARIANT is now routinely used for sodium-cooled fast reactor (SFR) design analysis. In particular, VARIANT transport calculations are usually performed for whole core neutronics analyses and for fuel cycle analyses with REBUS-3. However, the steady-state thermal hydraulics analysis with the SE2-ANL coed and the assembly bowing reactivity calculation with the structural analysis with the NUBOW-3D code are still performed with the DIF3D finite difference diffusion theory code. Furthermore, the DIF3D diffusion calculation for these applications is performed with only six triangular meshes per hexagonal assembly, and the SE2-ANL code determines the pin power distributions approximately by assuming that the power distribution within an assembly is separable in the radial and axial directions. In order to overcome the limitations and to improve the accuracy of the existing methods, it was proposed to develop the relevant computational methods based on the transport calculations with the VARIANT and PROTEUS-SN codes. The objectives of this study are to develop a new heating calculation method based on the coupled neutron and gamma transport calculations with VARIANT, to implement the new heating calculation method into the SE2-ANL steady-state thermal-hydraulics analysis code with improved numerical algorithms and additional capabilities for automatic flow allocation calculations, and to develop a method to calculate bowing reactivity coefficients based on the VARIANT core solutions and the PROTEUS-SN assembly solutions, which can be used in NUBOW-3D calculations. A new, coupled neutron and gamma heating calculation procedure has been developed based on VARIANT transport calculations. In the new heating calculation procedure, the neutron flux distribution is first determined by solving an eigenvalue transport problem using the VARIANT transport code. Using the calculated neutron flux, the intra-nodal gamma source distributions are calculated to be consistent with the neutron flux distribution with the GAMSOR code. For this, the GAMSOR code has been updated to generate the intra-nodal gamma source distributions in the form of the VARSRC dataset of VARIANT. With this gamma source distribution, the gamma flux distribution is determined by solving a fixed source gamma transport problem using VARIANT again. With the neutron and gamma flux distributions, the heat generation rates are evaluated at individual fuel pins and assembly duct walls, without assuming separable axial and radial profiles for the intra-assembly power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Bounds on spectral gaps of Hyperbolic spin surfaces

We describe a method for constraining Laplacian and Dirac spectra of two dimensional compact orientable hyperbolic spin manifolds and orbifolds. The key ingredient is an infinite family of identities satisfied by the spectra. These spectral identities follow from the consistency between 1) the spectral decomposition of functions on the spin bundle into irreducible representations of SL(2,R) and 2) associativity of pointwise multiplication of functions. Applying semidefinite programming methods to our identities produces rigorous upper bounds on the Laplacian spectral gap as well as on the Dirac spectral gap conditioned on the former. In several examples, our bounds are nearly sharp; a numerical algorithm based on the Selberg trace formula shows that the [0;3,3,5] orbifold, a particular surface with signature [1;3], and the Bolza surface nearly saturate the bounds at genus 0, 1 and 2 respectively. Under additional assumptions on the number of harmonic spinors carried by the spin-surface, we obtain more restrictive bounds on the Laplacian spectral gap. In particular, these bounds apply to hyperelliptic surfaces. We also determine the set of Laplacian spectral gaps attained by all compact orientable two-dimensional hyperbolic spin orbifolds. We show that this set is upper bounded by 12.13798; this bound is nearly saturated by the [0;3,3,5] orbifold, whose first non-zero Laplacian eigenvalue is λ^(0)_1 ≈ 12.13623.

Spectral theory↗