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DOE OSTI2025

Microscopic calculations with noniterative finite amplitude methods and the application to neutron radiative captures and inelastic scatterings

We derive the fully self-consistent quasiparticle random-phase approximation (QRPA) equations with noniterative finite amplitude methods and calculate the transition strengths of giant resonances. Then, we apply the QRPA results to both neutron radiative capture calculations based on the statistical Hauser-Feshbach theory and inelastic scattering calculations based on distorted-wave Born approximation (DWBA). We compare the calculated results with available experimental data and demonstrate how our approach can reproduce giant resonances and various nuclear reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Basis convergence of range-separated density-functional theory

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

A new approach to the generalization of Planck’s law of black-body radiation

Highlights: A new approximation approach to generalized Planck’s radiation law has been developed. Average energy of radiation derived using the nonextensive partition function. The spectral energy density and spectral radiance have been computed. The present approach has been compared with approximate schemes and the exact method. Deviations of present approach and AA and FA schemes from exact result computed. -- Abstract: In this study, Planck’s law of black-body radiation has been modified within the framework of nonextensive statistical mechanics. The average energy of radiation has been derived by introducing the nonextensive partition function in the statistical relation of internal energy. The spectral energy density and spectral radiance have also been computed. The derived expression has been compared with the earlier developed approximate schemes (i.e. asymptotic approach and factorization approach) and with the recently obtained exact result. We utilize the exact and approximate Stefan–Boltzmann laws in order to compare with the new approach introduced here.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

The Simons Observatory: validation of reconstructed power spectra from simulated filtered maps for the small aperture telescope survey

We present a transfer function-based method to estimate angular power spectra from filtered maps for cosmic microwave background (CMB) surveys. This is especially relevant for experiments targeting the faint primordial gravitational wave signatures in CMB polarisation at large scales, such as the Simons Observatory (SO) small aperture telescopes. While timestreams can be filtered to mitigate the contamination from low-frequency noise, usual methods that calculate the mode coupling at individual multipoles can be challenging for experiments covering large sky areas or reaching few-arcminute resolution. The method we present here, although approximate, is more practical and faster for larger data volumes. We validate it through the use of simulated observations approximating the first year of SO data, going from half-wave plate-modulated timestreams to maps, and using simulations to estimate the mixing of polarisation modes induced by an example of time-domain filtering. We show its performance through an example null test and with an end-to-end pipeline that performs inference on cosmological parameters, including the tensor-to-scalar ratio r. The performance demonstration uses simulated observations at multiple frequency bands. We find that the method can recover unbiased parameters for our simulated noise levels.

CMBR experiments↗

DOE OSTI2016

Iterative algorithms for processing experimental data

The need to solve linear and nonlinear integral equations arise, e.g., in recovering plasma parameters from the data of multichannel diagnostics. The paper presents an iterative method for solving integral equations with a singularity at the upper limit of integration. The method consists in constructing successive approximations and calculating the integral by quadrature formulas in each integration interval. An example of application of the iterative algorithm to numerically solve an integral equation similar to those arising in recovering the plasma density profile from reflectometry data is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculations show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Effect of mechanical strain on electronic properties of bulk MoS{sub 2}

Ab-initio density functional theory based calculations of electronic properties of bulk and monolayer Molybdenum di-Sulfide (MoS{sub 2}) have been performed using all electron Full Potential Linearised Augmentad Plane Wave (FPLAPW) method using Elk code. We have used Generalised Gradient Approximation (GGA) for exchange and correlation functionals and performed calculaitons of Lattice parameters, Density Of States (DOS) and Band Structure (BS). Band structure calculations revealed that bulk MoS{sub 2} has indirect band gap of 0.97 eV and mono-layer MoS{sub 2} has direct band gap which has increased to 1.71 eV. These are in better agreement with experimental values as compared with the other calculations using pseudo-potential code. The effect of mechanical strain on the electronic properties of bulk MoS{sub 2} has also been studied. For the different values of compressive strain (varying from 2% to 8% in steps of 2%) along the c-axis, the corresponding DOS and BS are obtained. We observed that the band gap decreases by about 15% for every 2% increase in strain along the c-axis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Low to intermediate energy elastic electron scattering from dichloromethane (CH 2 Cl 2 )

We report a theoretical-experimental investigation of electron scattering by dichloromethane (CH 2 Cl 2 ) in the low- and intermediate energy ranges. Experimental elastic differential cross sections (DCS), in the incident electron energy range of 0.5–800 eV and scattering angle range of 10°–130°, were measured using a crossed beam relative flow technique. Integral and momentum-transfer cross sections were determined from the experimental DCS. Theoretical elastic differential, integral, and momentum-transfer, as well as grand-total, and total absorption cross sections were also calculated for impact energies ranging from 0.5 to 500 eV. A complex optical Hartree–Fock potential represented the electron-target interaction and a single-center expansion method combined with a Padé approximation was used to solve the scattering equations. Three resonances: a 2 A 1 C–Cl k σ * resonance centered at about 3.5 eV, a 2 B 2 C–Cl k σ * resonance centered at about 5 eV and a broad 2 A 1 C–H k σ * resonance at about 10 eV were detected in our calculation. Further calculations of DCS were performed at an intermediate energy range of 50–800 eV, using the independent-atom model in which the atomic complex optical potential and partial-wave method were used to obtain atomic scattering amplitudes. In conclusion, comparisons of our experimental and theoretical data with very recent experimental and theoretical results are made.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2015

First principle investigation of structural and electronic properties of bulk ZnSe

Electronic and structural properties of ZnSe are investigated using plane-wave self-consistent field method within the framework of density functional theory. The pseudopotential method within the local density approximation is used for the exchange-correlation potential. The equilibrium lattice parameter, static bulk modulus and its pressure derivative are calculated. The electronic band structure, partial density of states and density of states are also obtained. The results are compared with available theoretical calculations and experimental results.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Automated discovery and construction of surface phase diagrams using machine learning

Surface phase diagrams are necessary for understanding surface chemistry in electrochemical catalysis, where a range of adsorbates and coverages exist at varying applied potentials. These diagrams are typically constructed using intuition, which risks missing complex coverages and configurations at potentials of interest. More accurate cluster expansion methods are often difficult to implement quickly for new surfaces. We adopt a machine learning approach to rectify both issues. Using a Gaussian process regression model, the free energy of all possible adsorbate coverages for surfaces is predicted for a finite number of adsorption sites. Our result demonstrates a rational, simple, and systematic approach for generating accurate free-energy diagrams with reduced computational resources. Finally, the Pourbaix diagram for the IrO 2 (110) surface (with nine coverages from fully hydrogenated to fully oxygenated surfaces) is reconstructed using just 20 electronic structure relaxations, compared to approximately 90 using typical search methods. Similar efficiency is demonstrated for the MoS 2 surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Stability of fissile solution systems - 14614

A Dynamic System Simulation (DSS) has been developed for aqueous homogenous reactors (AHR) and subcritical accelerator-driven system employing fissile solution fuel. These models are comprised of coupled non-linear differential equations describing the neutronics, thermal hydraulic and radiolytic gas behavior in the time domain. Models of specific historic AHR, SUPO (Super Power), KEWB (Kinetics Experiment Water Boiler), and SILENE exhibit close agreement with experimental data in all operating modes including steady-state, ramp and step reactivity insertions. The set of non-linear equations have been utilized to generate a generic transfer function for this class of systems. Output from specific DSS models operating at steady-state is then utilized as input parameters into a transfer function specific to each. Traditional Bode amplitude and phase, Nyquist and Nichols plots, are then generated to examine stability. Results for SUPO and a generic accelerator-driven system suggest these systems are unconditionally stable in the linear approximation. This treatment offers a method to examine the physics and time-based evolution of a critical excursion in a fissile solution system and provides a means to examine the severity of the consequence. This approach provides insight into the characteristics of such and even and sensitivity to materials involved and configuration of the physical system. (authors)

42 ENGINEERING↗

DOE OSTI2016

THE MIRA–TITAN UNIVERSE: PRECISION PREDICTIONS FOR DARK ENERGY SURVEYS

Large-scale simulations of cosmic structure formation play an important role in interpreting cosmological observations at high precision. The simulations must cover a parameter range beyond the standard six cosmological parameters and need to be run at high mass and force resolution. A key simulation-based task is the generation of accurate theoretical predictions for observables using a finite number of simulation runs, via the method of emulation. Using a new sampling technique, we explore an eight-dimensional parameter space including massive neutrinos and a variable equation of state of dark energy. We construct trial emulators using two surrogate models (the linear power spectrum and an approximate halo mass function). The new sampling method allows us to build precision emulators from just 26 cosmological models and to systematically increase the emulator accuracy by adding new sets of simulations in a prescribed way. Emulator fidelity can now be continuously improved as new observational data sets become available and higher accuracy is required. Finally, using one ΛCDM cosmology as an example, we study the demands imposed on a simulation campaign to achieve the required statistics and accuracy when building emulators for investigations of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A Procedure for Evaluating Modified Pulsed-Neutron- Source Experiments in Subcritical Nuclear Reactors

A theoretical interpretation of the modified pulsed-neutron-source experiments of Sjöstrand, Gozani, and Garelis and Russell is given using exact steady-state Boltzmann equations. Here, interpretation is based on a phenomenological description of the experiments and is patterned after work done on the Garelis-Russell method by Corngold. The basic approximation made is that the fundamental prompt-mode decay constant is much larger than any delayed-neutron precursor decay constant. The theoretical interpretation allows the reactivities measured by the above three modified pulsed-source techniques to be easily calculated and compared to more conventional definitions of reactivity. The calculations can be performed by any standard source-iteration code that has been modified to solve the inhomogeneous problem. Experiments were performed on the Cornell University Critical Assembly and interpreted with the aid of the above theory. Calculations and experiments agree to within 20%. Sjöstrand's method is found to give the best result for this reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Data-scarce surrogate modeling of shock-induced pore collapse process

Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Modeling of column apparatuses: A review

This paper presents a review of the modeling method on the base of the physical approximations of the mechanics of continua, which have been developed for processes in column apparatuses. This method includes diffusion type of model for modeling of mass transfer with chemical reaction in column apparatuses with and without circulation zones. The diffusion type of model is used for modeling of scale effect in column apparatuses too. The study concluded that the proposal method is possibility for investigation the influence of radial non uniformity of the velocity distribution on the process efficiency, influence of zones breadths on the mass transfer efficiency in the column. The method of the column apparatuses modeling can be used for modeling of physical and chemical absorption, chemical adsorption, homogeneous and heterogeneous (catalytic) chemical reactions, airlift reactors for chemical and photochemical reactions.

42 ENGINEERING↗

DOE OSTI2022

Determination of asymptotic normalization coefficients for the channel 16 O→ α+ 12 C: excited state 16 O(0 + ; 6.05 MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗