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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Uncoupling Electrokinetic Flow Solutions

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

58 GEOSCIENCES↗
DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Diagnostics for Undersampling and Clustering in Monte Carlo Criticality Calculations

For the past 40 years, it has been known from the theoretical work of Gelbard [1] and Brissenden [2] that the results from Monte Carlo (MC) criticality calculations are biased if the number of neutrons per generation is not sufficiently large. The computed k-effective eigenvalue will be lower than the actual eigenvalue, and the computed eigenfunction will be too low in high-importance regions and too high in low-importance regions. This difficulty is commonly called the undersampling problem for criticality calculations. The biases for undersampling were confirmed for practical, realistic problems with modern MC codes by Brown [3]. The solution to undersampling is simple - use a larger number of neutrons per generation to reduce the biases to levels that are negligible. Over the past few years, the OECD-NEA-WPNCS Expert Group on Advanced Monte Carlo Techniques (EGAMCT) [4,5,6] investigated an extreme form of undersampling called clustering. When the number of neutrons per generation is small, neutrons in successive generations tend to group together (cluster) due to correlations, and the clusters tend to migrate through the problem space. While the problems of undersampling and clustering are well known and well understood theoretically, there were no existing diagnostics for MC codes to determine whether a given calculation is using sufficient neutrons per generation to eliminate these problems. That is, no tools were available to diagnose biases due to undersampling or clustering. The tools described herein resolve this longstanding problem by providing 2 robust methods for detecting undersampling and clustering in MC criticality calculations. The diagnosis of undersampling and clustering is part of a larger effort to thoroughly overhaul the calculational methods for criticality problems, providing for automated sampling of the initial fission distribution, acceleration of the iteration convergence process, automated detection of convergence in the iterations and starting of the active tally cycles, and the diagnosis of undersampling. All of these new methods have been prototyped in a local modified version of mcnp6.2 [7] and tested on a variety of critical systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

An inexact regularized Newton framework with a worst-case iteration complexity of $ {\mathscr O}(\varepsilon^{-3/2}) $ for nonconvex optimization

Abstract An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes ${\mathscr O}(\varepsilon ^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive real number $\varepsilon $ and can take ${\mathscr O}(\varepsilon ^{-3})$ iterations to drive the leftmost eigenvalue of the Hessian of the objective above $-\varepsilon $. The proposed algorithm is a general framework that covers a wide range of techniques including quadratically and cubically regularized Newton methods, such as the Adaptive Regularization using Cubics (arc) method and the recently proposed Trust-Region Algorithm with Contractions and Expansions (trace). The generality of our method is achieved through the introduction of generic conditions that each trial step is required to satisfy, which in particular allows for inexact regularized Newton steps to be used. These conditions center around a new subproblem that can be approximately solved to obtain trial steps that satisfy the conditions. A new instance of the framework, distinct from arc and trace, is described that may be viewed as a hybrid between quadratically and cubically regularized Newton methods. Numerical results demonstrate that our hybrid algorithm outperforms a cubically regularized Newton method.

Mathematics↗
DOE OSTI2014

Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well

This paper is a direct offspring of the work of Garbaczewski and Stephanovich [“Lévy flights and nonlocal quantum dynamics,” J. Math. Phys. 54, 072103 (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions were made with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deepening finite wells. The employed numerical methodology (algorithm based on the Strang splitting method) has been tested for an exemplary Cauchy oscillator problem, whose analytic solution is available. An impact of the inherent spatial nonlocality of motion generators upon computer-assisted outcomes (potentially defective, in view of various cutoffs), i.e., detailed eigenvalues and shapes of eigenfunctions, has been analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

GW and Bethe-Salpeter study of small water clusters

We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H{sub 2}O){sub n} water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green’s function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G{sub 0}W{sub 0}@PBE or G{sub 0}W{sub 0}@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G{sub 0}W{sub 0} description of the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G{sub 0}W{sub 0} and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Electronic structure and metallization of cubic GdH{sub 3} under pressure: Ab initio many-body GW calculations

The electronic structures of the cubic GdH{sub 3} are extensively investigated using the ab initio many-body GW calculations treating the Gd 4f electrons either in the core (4f-core) or in the valence states (4f-val). Different degrees of quasiparticle (QP) self-consistent calculations with the different starting points are used to correct the failures of the GGA/GGA + U/HSE03 calculations. In the 4f-core case, GGA + G{sub 0}W{sub 0} calculations give a fundamental band gap of 1.72 eV, while GGA+ GW{sub 0} or GGA + GW calculations present a larger band gap. In the 4f-val case, the nonlocal exchange-correlation (xc) functional HSE03 can account much better for the strong localization of the 4f states than the semilocal or Hubbard U corrected xc functional in the Kohn–Sham equation. We show that the fundamental gap of the antiferromagnetic (AFM) or ferromagnetic (FM) GdH{sub 3} can be opened up by solving the QP equation with improved starting point of eigenvalues and wave functions given by HSE03. The HSE03 + G{sub 0}W{sub 0} calculations present a fundamental band gap of 2.73 eV in the AFM configuration, and the results of the corresponding GW{sub 0} and GW calculations are 2.89 and 3.03 eV, respectively. In general, for the cubic structure, the fundamental gap from G{sub 0}W{sub 0} calculations in the 4f-core case is the closest to the real result. By G{sub 0}W{sub 0} calculations in the 4f-core case, we find that H or Gd defects can strongly affect the band structure, especially the H defects. We explain the mechanism in terms of the possible electron correlation on the hydrogen site. Under compression, the insulator-to-metal transition in the cubic GdH{sub 3} occurs around 40 GPa, which might be a satisfied prediction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Process tomography for unitary quantum channels

We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary channel acting on a d-level quantum system can be uniquely identified among all other channels (unitary or otherwise) with only O(d{sup 2}) interactive observables, as opposed to the O(d{sup 4}) required for tomography of arbitrary channels. This result generalizes to the problem of identifying channels with at most q Kraus operators, and slight improvements can be obtained if we wish to identify such a channel only among unital channels or among other channels with q Kraus operators. These results are proven via explicit construction of large subspaces of Hermitian matrices with various conditions on rank, eigenvalues, and partial trace. Our constructions are built upon various forms of totally nonsingular matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

THE BEHAVIOR OF TRANSVERSE WAVES IN NONUNIFORM SOLAR FLUX TUBES. I. COMPARISON OF IDEAL AND RESISTIVE RESULTS

Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics

We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local well-posedness, in the Hadamard sense, of the Cauchy problem. Our regularity assumptions are very minimal. As an application, we apply our results to systems of ideal and viscous relativistic fluids, where the theory of strongly hyperbolic equations has been systematically used to study several systems of physical interest.

Mathematics↗
DOE OSTI2019

Quantum computation of nanosheets in a background magnetic field for external control of nanosystems

We ran quantum simulations on lattices of interacting fermions in a background magnetic field [1]. We created discretized Hamiltonian matrices for each system and pre-processed them so that they could be read by the quantum simulator implemented in IBM's Qiskit package [2]. The simulator uses the variational quantum eigensolver (VQE) algorithm [3] to approximate the ground state energy of the input Hamiltonian, which is then compared to the classically-calculated exact value. This classical evaluation is possible because the systems studied are still within the grasp of classical computers. We also investigated ways to simplify the system before the pre-processing step. We found that in almost all cases these simplifications made our quantum calculations converge to better answers using simpler starting conditions. We are exploring other ways to interface with IBM's quantum computing software so that we no longer need to explicitly define the Hamiltonian matrices for our systems, a problem which will itself soon become intractable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Efficiency and accuracy of the perturbation response coefficient generation method for whole core comet calculations in BWR and CANDU configurations

The coarse mesh transport method (COMET) is a highly accurate and efficient computational tool which predicts whole-core neutronics behaviors for heterogeneous reactor cores via a pre-computed eigenvalue-dependent response coefficient (function) library. Recently, a high order perturbation method was developed to significantly improve the efficiency of the library generation method. In that work, the method's accuracy and efficiency was tested in a small PWR benchmark problem. This paper extends the application of the perturbation method to include problems typical of the other water reactor cores such as BWR and CANDU bundles. It is found that the response coefficients predicted by the perturbation method for typical BWR bundles agree very well with those directly computed by the Monte Carlo method. The average and maximum relative errors in the surface-to-surface response coefficients are 0.02%-0.05% and 0.06%-0.25%, respectively. For CANDU bundles, the corresponding quantities are 0.01%-0.05% and 0.04% -0.15%. It is concluded that the perturbation method is highly accurate and efficient with a wide range of applicability. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2013

Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations

The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Prediction on Underestimation of Statistical Uncertainty in Monte Carlo Eigenvalue Calculation for Two-dimensional Heterogeneous Color Set Geometry

In a Monte Carlo calculation, statistical uncertainty is inevitably included in the result. The statistical uncertainty is commonly estimated by the central limit theorem without considering correlation among generations. The statistical uncertainty is usually expected to decrease at the inverse square root of the number of neutron histories. However, in a Monte Carlo eigenvalue calculation in a large geometry whose dominance ratio is close to unity, the central limit theorem would not be valid and thus the statistical uncertainty of fission source distribution can be significantly underestimated when inter-cycle correlation is not appropriately taken into account. The true statistical uncertainty can be calculated by statistical processing of the results obtained by multiple Monte Carlo runs using different initial random seeds, but this approach has a drawback of large calculation cost. Therefore, prediction of true statistical uncertainty by alternate approach is desirable. One of the solutions for this issue is an evaluation method of statistical uncertainty based on the eigenfunction expansion and the Autoregressive model (AR model). In this method, the true statistical uncertainty is theoretically derived by applying the AR model to behavior of expansion coefficients of eigenfunction in fission source distribution during cycles. Underestimation ratio of statistical uncertainty of fission source distribution can be predicted by this method. Note that the underestimation ratio of statistical uncertainty is defined by the ratio of estimated error by a Monte Carlo calculation to the true statistical error. In the previous study, the proposed method was verified in a simple condition such as one energy group, one dimensional homogeneous slab geometry. Contributions of this summary are as follows. Firstly, expression of the noise term that is appeared in the AR model is theoretically derived. Secondly, prediction on underestimation ratio of statistical uncertainty is carried out in a more general case, i.e., flux of each fuel cell in 2 x 2 heterogeneous assembly geometry taken from the C5G7 benchmark problem. Through the present study, applicability of the theoretical prediction for underestimation of statistical uncertainty in practical problems will be verified. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

On quark-antiquark approximation in light front QCD with zero gluon modes

We consider a transition to the light front Hamiltonian from theories quantized on spacelike planes approaching to the light front. In this approach we preserve the dynamics of zero mode present in the theories near the light front. We make the limit transition differently for zero and nonzero modes. This leads to the appearance of some phenomenological parameter which can be used to describe vacuum effects. Also we use a lattice gauge invariant regularization in transverse coordinate space. As an illustration of our scheme we consider the quark-antiquark bound states problem in 2+1 dimensions. We construct basis states in the light front Fock space and provide detailed computations of the Hamiltonian matrix in this basis. These steps allow us to construct the matrix eigenvalue equation. In conclusion we discuss the nuances of obtained results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Sodium-Cooled Fast Reactor Reference Plant Model

This report details the progress of Idaho National Laboratory (INL) in creating a reference plant multiphysics model for the Advanced Burner Test Reactor (ABTR). This model was developed under Task 13 of the U.S. Nuclear Regulatory Commission project “Development and Modeling Support for Advanced Non-Light Water Reactors,” and is an extension of the reference plant model developed in Task 4b, which was improved upon in the following ways. (1) The discrete ordinates method was used in lieu of the super-homogenization (SPH)-corrected diffusion approximation in order to better capture the anisotropic scattering contribution and the neutron leakage change due to thermal expansion. (2) The novel neutronic spatial discretization approach, termed the ring-heterogeneous (RH) approximation, was conceptualized and introduced to capture the differential expansion of the materials in the core. This new technique proved capable of preserving fission rates and maintaining the eigenvalue within 2.5% and 266 pcm with 9 neutron energy groups, respectively. Separating the different materials in the core enables the differential expansion of materials to be explicitly accounted for, eliminating the need for problem-specific cross-section functionalization techniques. (3) The SAM model for the core and system thermal-hydraulics analysis was updated to include 61 channels instead of just four representative ones. This enables users to obtain improved spatial resolution for sodium temperature and density scalar fields. (4) All the mesh files were created via the Multiphysics Object-Oriented Simulation Environment (MOOSE) Reactor module, eliminating all reliance on external tools for mesh creation. (5) Finally, the fuel axial expansion now leverages the HT9 and UPuZr material properties that have been validated against experimental data. The reference plant model was used to perform a full-core unprotected loss of flow (ULOF) transient calculation, including neutronics, thermal and mechanical feedback mechanisms. Future work will be devoted to further enhancements of the model. Potential improvements to the model include the addition of the control rod driveline expansion feedback and the upgrading of the support plate model so as to explicitly include 3D effects. Additionally, a Nuclear Energy Advanced Modeling and Simulation funded parallel effort has completely automated the creation of the ring-heterogeneous (RH) mesh from the fully heterogeneous (FH) geometry, thus maximizing user friendliness for the sodium fast reactor sodium-cooled fast reactor (SFR) workflow and will be incorporated in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗