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At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Rigorous Computation of Diffusion Coefficients for Expanding Maps

For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a theoretical algorithm, our approximation scheme is shown to give quadratic exponential convergence to the diffusion coefficient. The method for converting this rapid convergence into explicit high precision rigorous bounds is illustrated in the setting of Lanford’s map x↦2x+(1/2)x(1−x) (mod 1).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Density-functional theory of material design: fundamentals and applications-I

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article, we start with an introduction to Schrödinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schrödinger equation is discussed. The resulting Hartree and Hartree–Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas–Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern DFT by discussing Hohenberg–Kohn theorems that form its foundations. We then go on to discuss Kohn–Sham (KS) formulation of DFT in its exact form. Next, local density approximation (LDA) is introduced and solutions of KS equation for some representative systems, obtained using the LDA, are presented. We end part-I of the review describing the contents of part-II.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Assessing the distinguishable cluster approximation based on the triple bond-breaking in the nitrogen molecule

Obtaining the correct potential energy curves for the dissociation of multiple bonds is a challenging problem for ab initio methods which are affected by the choice of a spin-restricted reference function. Coupled cluster (CC) methods such as CCSD (coupled cluster singles and doubles model) and CCSD(T) (CCSD + perturbative triples) correctly predict the geometry and properties at equilibrium but the process of bond dissociation, particularly when more than one bond is simultaneously broken, is much more complicated. New modifications of CC theory suggest that the deleterious role of the reference function can be diminished, provided a particular subset of terms is retained in the CC equations. The Distinguishable Cluster (DC) approach of Kats and Manby [J. Chem. Phys. 139, 021102 (2013)], seemingly overcomes the deficiencies for some bond-dissociation problems and might be of use in quasi-degenerate situations in general. DC along with other approximate coupled cluster methods such as ACCD (approximate coupled cluster doubles), ACP-D45, ACP-D14, 2CC, and pCCSD(α, β) (all defined in text) falls under a category of methods that are basically obtained by the deletion of some quadratic terms in the double excitation amplitude equation for CCD/CCSD (coupled cluster doubles model/coupled cluster singles and doubles model). Here these approximate methods, particularly those based on the DC approach, are studied in detail for the nitrogen molecule bond-breaking. The N{sub 2} problem is further addressed with conventional single reference methods but based on spatial symmetry-broken restricted Hartree–Fock (HF) solutions to assess the use of these references for correlated calculations in the situation where CC methods using fully symmetry adapted SCF solutions fail. The distinguishable cluster method is generalized: 1) to different orbitals for different spins (unrestricted HF based DCD and DCSD), 2) by adding triples correction perturbatively (DCSD(T)) and iteratively (DCSDT-n), and 3) via an excited state approximation through the equation of motion (EOM) approach (EOM-DCD, EOM-DCSD). The EOM-CC method is used to identify lower-energy CC solutions to overcome singularities in the CC potential energy curves. It is also shown that UHF based CC and DC methods behave very similarly in bond-breaking of N{sub 2}, and that using spatially broken but spin preserving SCF references makes the CCSD solutions better than those for DCSD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Demonstration of Full Core Reactor Depletion with MPACT

MPACT is a three-dimensional (3-D) whole core transport code capable of generating sub-pin level power distributions. This feature is accomplished by obtaining the integral transport solutions to the heterogeneous reactor problem in which the actual detailed geometrical configuration of fuel components such as the pellet and cladding is modelled explicitly.. The cross section data needed for the neutron transport calculation are obtained directly from a multigroup microscopic cross section library similar to those used in lattice physics codes. Hence MPACT involves neither a priori homogenization nor group condensation for the core spatial solution. The integral transport solution is obtained by means of the method of characteristics (MOC) that employs discrete ray tracing. Since the direct application of the 3-D MOC capability in MPACT to 3-D core configuration requires considerable amounts of memory and computing time for practical reactor applications, an alternative approximate 3-D solution method was implemented in MPACT based on a 2D-1D approach which employs planar MOC solutions in the framework of the 3-D coarse mesh finite difference (CMFD) formulation. The axial coupling is resolved by one-dimensional (1-D) diffusion solutions and the planar and axial problems are coupled through the transverse leakage. The use of a lower order 1-D solution in the axial direction is justified by the fact that most heterogeneity in the core occurs in the radial direction rather than the axial. However, it is possible to use one of the higher order methods in MPACT such as the 1-D SN kernel if improved solution accuracy is desired. The CMFD formulation which originally served as an efficient nodal formulation is used in MPACT to accelerate the whole core transport calculation. The basic mesh in the CMFD formulation is a pin cell which is much coarser than the flat source regions defined for MOC calculations. The concept of dynamic homogenization of group constants for the pin cells provides the basis of the CMFD formulation in whole core transport calculation. The intra-cell flux distribution determined from the MOC calculation is used to generate the homogenized cell constants while the MOC cell surface averaged currents are used to determine the radial nodal coupling coefficients. This dynamic implementation of the equivalence theory formulation ensures the same transport solution is obtained with CMFD as the one obtained using unaccelerated MOC calculations alone. The ability of MPACT to predict the Hot, Zero Power (HZP) condition of a reactor was reported in CASL-U-2014-0045-000. The purpose of this report is to demonstrate the capability of MPACT to simulate the operation of a reactor at Hot, Full Power (HFP) conditions during normal operation throughout a full operating cycle. The time scale for a reactor burnup cycle is typically one to two years and therefore short time phenomena such as the effect of delayed neutrons can be neglected. Instead the time dependence can be treated quasi-statically using the depletion algorithm presented in CASL-U-2013-0276-001. The full power operation requires thermal hydraulic feedback to be present during the entire simulation which will utilize the work in CASL-U-2014-0051-000. However, due to the significant computational burden of the coupled physics simulation, a simplified thermal hydraulic model is used for the analysis reported here which is principally intended to demonstrate the full core neutronics depletion. In addition to the thermal hydraulic feedback, the effect of Boron 10 depletion should be modeled in cases where major boron additions are not performed for extended periods of time. Each of these capabilities will be described in the following sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree–Fock exchange matrix. Here, we call this new scheme the “approximate pair coefficient” (APC) method and we show that it performs quite well for the test systems presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods can improve the convergence behavior and efficiency of JFNK method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Nuclear Shell Structure in Semi-Realistic Mean-Field Approach

By applying the Hartree-Fock calculations with the newly developed methods and interactions, spherical shell structure of medium-mass nuclei is investigated, with paying special attention to the magicity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Cluster truncated Wigner approximation in strongly interacting systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Frozen-Orbital and Downfolding Calculations with Auxiliary-Field Quantum Monte Carlo

We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings, compared to fully correlating all of the electrons. While the many-body wave function is never explicit in AFQMC, its random walkers are Slater determinants, whose orbitals may be expressed in terms of any one-particle orbital basis. It is therefore straightforward to partition the full N-particle Hilbert space into active and inactive parts to implement the frozen-orbital method. In the frozen-core approximation, for example, the core electrons can be eliminated in the correlated part of the calculations, greatly increasing the computational efficiency, especially for heavy atoms. Scalar relativistic effects are easily included using the Douglas–Kroll–Hess theory. Using this method, we obtain a way to effectively eliminate the error due to single-projector, norm-conserving pseudopotentials in AFQMC. We also illustrate a generalization of the frozen-orbital approach that downfolds high-energy basis states to a physically relevant low-energy sector, which allows a systematic approach to produce realistic model Hamiltonians to further increase efficiency for extended systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Noncommutative FRW Universe

In this work, we present several solutions to noncommutative cosmology using the WKB approximation in noncommutative quantum cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Multiple scattering of surface waves by cavities in a half-space

Scattering of surface waves from multiple two-dimensional cavities at the surface of a homogenous, isotropic, linearly elastic half-space is analyzed in this work. For the case of multiple cavities, the scattered field is shown to be equivalent to the total radiation from the distributions of tractions, calculated from the incident wave, over the surfaces of the cavities. The multiple-scattering model is obtained from known single-scattering calculation for a cavity by the use of the self-consistent method. The second order approximation to the multiple-scattering problem by a random distribution of cavities is then considered and solved analytically. The vertical displacement at some distance from the cavities is calculated and verified by the solution of the same problem obtained by the boundary element method (BEM). The analytical and BEM results are graphically displayed and show good agreement when the depths of the cavities are small compared to the wavelength.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Construction of approximate invariants for non-integrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

TU-F-CAMPUS-I-05: Parameterization of the Noise Power Spectrum in X-Ray Computed Tomography

Purpose: The purpose of this work was to develop a method so that the noise power spectrum (NPS) can be approximated for arbitrary levels of mAs, from a single determination in CT. Methods: The NPS is factorized into 2 components, 1) a parameterized function representing the 1D normalized spatial frequency distribution and 2) a function to scale the magnitude of 1) for arbitrary values of mAs. The 1D NPS, normalized by image variance (NNPS), was determined for 2 FBP reconstruction kernels (smoothing and edge enhancing) for 400 mAs. The NNPS were fit to the parameterized function and a scaling function was established to approximate the image variance at arbitrary values of mAs. Using the root mean square error normalized by the maximum value (NRMSE), the NPS approximated with the factorization method was compared to the NPS determined at 5 different mAs levels. Results: The factorization resulted in a set of 7 coefficients that can be used to approximate the 1D NPS, for arbitrary levels of mAs, for the convolution kernels studied in this work. The approximated NPS (factorization) agreed well with the determined NPS for all mAs levels. The greatest NRMSE was 0.02 and was observed for the edge enhancing kernel. Conclusion: The proposed factorization method has been demonstrated as applicable for FBP reconstruction. It can be used to approximate the 1D NPS for arbitrary levels of mAs, from a single NPS determination. Furthermore, approximations of the 1D NPS can conveniently be distributed since the factorization method only used 7 coefficients in the approximation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗
DOE OSTI2019

Reconstructing high-dimensional Hilbert-valued functions via compressed sensing

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based `1 regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Dexter, Nick↗
DOE OSTI2016

First-principles studies of the atomic, elastic and vibrational properties of BaNbO{sub 3}

We have employed the ab initio pseudopotential method, within a generalized gradient approximation of the density functional theory, a linear response approach, to determine atomic, elastic and lattice dynamical properties of the BaNbO{sub 3}. The obtained structural and elastic parameter are in good agreement with previous experimental and theoretical results. The analysis of B/G ratio indicates that BaNbO{sub 3} is a ductile material. The calculated lattice dynamical properties compared with phonon spectrum of the similar structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Radiation image reconstruction and uncertainty quantification using a Gaussian process prior

We propose a complete framework for Bayesian image reconstruction and uncertainty quantification based on a Gaussian process prior (GPP) to overcome limitations of maximum likelihood expectation maximization (ML-EM) image reconstruction algorithm. The prior distribution is constructed with a zero-mean Gaussian process (GP) with a choice of a covariance function, and a link function is used to map the Gaussian process to an image. Unlike many other maximum a posteriori approaches, our method offers highly interpretable hyperparamters that are selected automatically with the empirical Bayes method. Furthermore, the GP covariance function can be modified to incorporate a priori structural priors, enabling multi-modality imaging or contextual data fusion. Lastly, we illustrate that our approach lends itself to Bayesian uncertainty quantification techniques, such as the preconditioned Crank–Nicolson method and the Laplace approximation. The proposed framework is general and can be employed in most radiation image reconstruction problems, and we demonstrate it with simulated free-moving single detector radiation source imaging scenarios. We compare the reconstruction results from GPP and ML-EM, and show that the proposed method can significantly improve the image quality over ML-EM, all the while providing greater understanding of the source distribution via the uncertainty quantification capability. Furthermore, significant improvement of the image quality by incorporating a structural prior is illustrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Compton scattering of an X-ray photon by an open-shell atom

A nonrelativistic quantum theory for the nonresonant Compton scattering of an X-ray photon by a free many-electron atom with an open shell in the ground state has been constructed in the single-configuration Hartree-Fock approximation outside the impulse approximation widely used in the literature. The transition to an atom with closed shells reproduces the results obtained previously in [6, 7]. The results of a test calculation for atoms with open (Ti, Fe) and closed (Zn) 3d core shells are presented. The effects of the radial relaxation of one-electron states in the field of core vacancies have been taken into account. The results of the calculation agree well with the experimental results [15, 16]. It has been established that the results of the impulse approximation in the investigated X-ray photon energy ranges disagree with those of our theory not only quantitatively but also qualitatively. In particular, the impulse approximation near the elastic (Thomson and Rayleigh) scattering line leads to a gross overestimation of the contributions from the deep atomic shells involved in the inelastic photon scattering only virtually to the scattering probability. The presented theory is general in character and its applicability to a particular element of the Mendeleev table with an open core shell or to a many-electron atomic ion is limited only by the requirement that the nonrelativistic Hartree-Fock approximation be properly used in describing the scattering-state wave functions.

74 ATOMIC AND MOLECULAR PHYSICS↗