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At least 1,459 records · Page 81
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Analysis of the shifted boundary method for the Stokes problem

The analysis of stability and accuracy of the shifted boundary method is developed for the Stokes flow equations. The key feature of the shifted boundary method, an embedded finite element method, is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary, and an appropriate modification (shifting) of the value of the boundary conditions. An inf–sup condition is proved for the variational formulation associated to the shifted boundary method and we derive, by way of Strang’s second lemma, an optimal error estimate in the natural SBM norm. Here we also derive an L 2 -error estimate for the velocity field, by means of an extension of the Aubin–Nitsche approach to embedded, non-consistent, mixed finite element methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Verification and Large Deformation Analysis Using the Reproducing Kernel Particle Method

The reproducing kernel particle method (RKPM) is a meshless method used to solve general boundary value problems using the principle of virtual work. RKPM corrects the kernel approximation by introducing reproducing conditions which force the method to be complete to arbritrary order polynomials selected by the user. Effort in recent years has led to the implementation of RKPM within the Sierra/SM physics software framework. The purpose of this report is to investigate convergence of RKPM for verification and validation purposes as well as to demonstrate the large deformation capability of RKPM in problems where the finite element method is known to experience difficulty. Results from analyses using RKPM are compared against finite element analysis. A host of issues associated with RKPM are identified and a number of potential improvements are discussed for future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman D_0 D 0 function, and the two-loop self-energy master integral M. We find that in low dimensions (d = 3), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions (d=5, 6, 9) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Metals and Quantum Materials with Spin-orbit Interactions by Quantum Monte Carlo methods

The key goals of this project were as follows: 1) Analysis and benchmarks of electron correlation effects recovered in the fixed-node approximation that is inherent to quantum Monte Carlo (QMC) method as applied to metallic states; 2) development of new algorithms for electron spin-degrees of freedom to be treated as explicit quantum variables; 3) designing electronic structure QMC algorithm for efficient evaluation of spin-orbit effects in systems with heavy atoms; 4) adapting the algorithm to complex wave functions and developing corresponding fixed-phase approximation; 5) design and testing of algorithm for valence-only non-local spin-orbit operators; 6) analysis of fixed-node vs fixed-phase errors and their comparisons. The key accomplishments: i) We carried out a systematic study of Li systems by the fixed-node diffusion Monte Carlo method. This involved Li atom, molecule, cluster and solid calculated by the full range of QMC methods including fixed-node QMC.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Multiscale convergence properties for spectral approximations of a model kinetic equation

Here in this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of the kinetic distribution and, as such, is accompanied by standard algebraic estimates of the form N -q , where N is the number of modes and q > 0 depends on the regularity of the solution. However, in the multiscale setting, the error estimate can be expressed in terms of the scaling parameter ϵ, which measures the ratio of the mean-free-path to the characteristic domain length. We show that, for isotropic initial conditions, the error in the spectral approximation is $\mathcal{O}$($ϵ^{N+1}$). More surprisingly, the coefficients of the expansion satisfy super convergence properties. In particular, the error of the ℓ th coefficient of the expansion scales like $\mathcal{O}$($ϵ^{2N}$ ) when ℓ = 0 and $\mathcal{O}$($ϵ^{2N+2-ℓ}$ ) for all 1 ≤ ℓ ≤ N. This result is significant, because the low-order coefficients correspond to physically relevant quantities of the underlying system. All the above estimates involve constants depending on N, the time t, and the initial condition. We investigate specifically the dependence on N, in order to assess whether increasing N actually yields an additional factor of ϵ in the error. Numerical tests will also be presented to support the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Validations of calibration-free measurements of electron temperature using double-pass Thomson scattering diagnostics from theoretical and experimental aspects

This paper evaluates the accuracy of electron temperature measurements and relative transmissivities of double-pass Thomson scattering diagnostics. The electron temperature (T{sub e}) is obtained from the ratio of signals from a double-pass scattering system, then relative transmissivities are calculated from the measured T{sub e} and intensity of the signals. How accurate the values are depends on the electron temperature (T{sub e}) and scattering angle (θ), and therefore the accuracy of the values was evaluated experimentally using the Large Helical Device (LHD) and the Tokyo spherical tokamak-2 (TST-2). Analyzing the data from the TST-2 indicates that a high T{sub e} and a large scattering angle (θ) yield accurate values. Indeed, the errors for scattering angle θ = 135° are approximately half of those for θ = 115°. The method of determining the T{sub e} in a wide T{sub e} range spanning over two orders of magnitude (0.01–1.5 keV) was validated using the experimental results of the LHD and TST-2. A simple method to provide relative transmissivities, which include inputs from collection optics, vacuum window, optical fibers, and polychromators, is also presented. The relative errors were less than approximately 10%. Numerical simulations also indicate that the T{sub e} measurements are valid under harsh radiation conditions. This method to obtain T{sub e} can be considered for the design of Thomson scattering systems where there is high-performance plasma that generates harsh radiation environments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals

We performed simulations for solid molecular hydrogen at high pressures (250 GPa ≤ P ≤ 500 GPa) along two isotherms at T = 200 K (phase III) and at T = 414 K (phase IV). At T = 200 K, we considered likely candidates for phase III, the C2c and Cmca12 structures, while at T = 414 K in phase IV, we studied the Pc48 structure. We employed both Coupled Electron-Ion Monte Carlo (CEIMC) and Path Integral Molecular Dynamics (PIMD). The latter is based on Density Functional Theory (DFT) with the van der Waals approximation (vdW-DF). The comparison between the two methods allows us to address the question of the accuracy of the exchange-correlation approximation of DFT for thermal and quantum protons without recurring to perturbation theories. In general, we find that atomic and molecular fluctuations in PIMD are larger than in CEIMC which suggests that the potential energy surface from vdW-DF is less structured than the one from quantum Monte Carlo. We find qualitatively different behaviors for systems prepared in the C2c structure for increasing pressure. Within PIMD, the C2c structure is dynamically partially stable for P ≤ 250 GPa only: it retains the symmetry of the molecular centers but not the molecular orientation; at intermediate pressures, it develops layered structures like Pbcn or Ibam and transforms to the metallic Cmca-4 structure at P ≥ 450 GPa. Instead, within CEIMC, the C2c structure is found to be dynamically stable at least up to 450 GPa; at increasing pressure, the molecular bond length increases and the nuclear correlation decreases. For the other two structures, the two methods are in qualitative agreement although quantitative differences remain. Finally, we discuss various structural properties and the electrical conductivity. Here, we find that these structures become conducting around 350 GPa but the metallic Drude-like behavior is reached only at around 500 GPa, consistent with recent experimental claims.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2012

ENERGY RELAXATION OF HELIUM ATOMS IN ASTROPHYSICAL GASES

We report accurate parameters describing energy relaxation of He atoms in atomic gases, important for astrophysics and atmospheric science. Collisional energy exchange between helium atoms and atomic constituents of the interstellar gas, heliosphere, and upper planetary atmosphere has been investigated. Energy transfer rates, number of collisions required for thermalization, energy distributions of recoil atoms, and other major parameters of energy relaxation for fast He atoms in thermal H, He, and O gases have been computed in a broad interval of energies from 10 meV to 10 keV. This energy interval is important for astrophysical applications involving the energy deposition of energetic atoms and ions into atmospheres of planets and exoplanets, atmospheric evolution, and analysis of non-equilibrium processes in the interstellar gas and heliosphere. Angular- and energy-dependent cross sections, required for an accurate description of the momentum-energy transfer, are obtained using ab initio interaction potentials and quantum mechanical calculations for scattering processes. Calculation methods used include partial wave analysis for collisional energies below 2 keV and the eikonal approximation at energies higher than 100 eV, keeping a significant energy region of overlap, 0.1-2 keV, between these two methods for their mutual verification. The partial wave method and the eikonal approximation excellently match results obtained with each other as well as experimental data, providing reliable cross sections in the astrophysically important interval of energies from 10 meV to 10 keV. Analytical formulae, interpolating obtained energy- and angular-dependent cross sections, are presented to simplify potential applications of the reported database. Thermalization of fast He atoms in the interstellar gas and energy relaxation of hot He and O atoms in the upper atmosphere of Mars are considered as illustrative examples of potential applications of the new database.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

THE EFFECTS OF EXPERIMENTAL CONDITIONS ON THE REFRACTIVE INDEX AND DENSITY OF LOW-TEMPERATURE ICES: SOLID CARBON DIOXIDE

We present the first study on the effects of the deposition technique on the measurements of the visible refractive index and the density of a low-temperature ice using solid carbon dioxide (CO{sub 2}) at 14–70 K as an example. While our measurements generally agree with previous studies that show a dependence of index and density on temperature below 50 K, we also find that the measured values depend on the method used to create each sample. Below 50 K, we find that the refractive index varied by as much as 4% and the density by as much as 16% at a single temperature depending on the deposition method. We also show that the Lorentz–Lorenz approximation is valid for solid CO{sub 2} across the full 14–70 K temperature range, regardless of the deposition method used. Since the refractive index and density are important in calculations of optical constants and infrared (IR) band strengths of materials, our results suggest that the deposition method must be considered in cases where n {sub vis} and ρ are not measured in the same experimental setup where the IR spectral measurements are made.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Structural and elastic anisotropy of crystals at high pressures and temperatures from quantum mechanical methods: The case of Mg{sub 2}SiO{sub 4} forsterite

We report accurate ab initio theoretical predictions of the elastic, seismic, and structural anisotropy of the orthorhombic Mg{sub 2}SiO{sub 4} forsterite crystal at high pressures (up to 20 GPa) and temperatures (up to its melting point, 2163 K), which constitute earth’s upper mantle conditions. Single-crystal elastic stiffness constants are evaluated up to 20 GPa and their first- and second-order pressure derivatives reported. Christoffel’s equation is solved at several pressures: directional seismic wave velocities and related properties (azimuthal and polarization seismic anisotropies) discussed. Thermal structural and average elastic properties, as computed within the quasi-harmonic approximation of the lattice potential, are predicted at high pressures and temperatures: directional thermal expansion coefficients, first- and second-order pressure derivatives of the isothermal bulk modulus, and P-V-T equation-of-state. The effect on computed properties of five different functionals, belonging to three different classes of approximations, of the density functional theory is explicitly investigated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

SU-E-T-74: A Simple Model of Dose Falloff for Highly Convergent SBRT Beams

Purpose: The purpose of this study was to create a simple model of dose falloff outside the target for a SBRT system employing a highly convergent beam geometry. With an estimate of the rate of reduction in dose away from a target of a given size, dose to tissues at a given distance from the target can be estimated. Our hypothesis is that dose at a given distance away from the edge of a target can be approximated using an inverse square model. Methods: With the GammaPod™ system used for this study, thirty-six rotating Co-60 beams with circular cross section converge at an isocenter and then diverge distal to the isocenter. Dose falloff beyond the target is mainly due to reduction in beam overlap, which in turn depends on projected area of all beams and projected beam area swept out during rotation. Beams also decrease in intensity beyond the isocenter. The GammaPod™ TPS calculates dose via superposition of Monte Carlo-generated kernels, each corresponding to the convergence of beams at an isocenter within a stereotactic breast cup. Results: The factors above yield a simple inverse square-based model that has been compared with TPS predictions and measurements for a variety of targets. Good agreement is seen considering the simple nature of the model. Fitting of the treatment planning and measured dose falloff data with a power law expression yields a negative exponent close to 2, confirming the inverse square nature of dose falloff. Conclusion: It is possible to apply a simple inverse square dose falloff model for SBRT or SRS systems such as the GammaPod which employ a highly-convergent beam geometry. This can be useful in estimating the “worst case scenario” for dose to critical organs at a known distance from the edge of the target volume. Authors are employees of Xcision Medical Systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

Here, we present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H 2 + in the singlet ungerade channels, and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multichannel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A Comparison of Electronic Structure Methods for Predicting the Hydrogenation Energies of Candidate Molecules for Hydrogen Storage

The development of novel energy materials and fuels is required to expand current available energy sources. Aiming to reach this goal, there is growing interest in using molecular hydrogen as an energy carrier due to its abundance and high energy density. Liquid organic hydrogen carriers (LOHCs) are a promising route to the large-scale storage and transport of hydrogen for use in the energy economy. The search for thermodynamically viable LOHC molecules for real world use has led to a set of constraints on the dehydrogenation enthalpy and the minimum gravimetric hydrogen capacity. These constraints allow one to formulate the search for an ideal LOHC candidate molecule as an optimization problem well suited to the strengths of machine learning and artificial intelligence computational approaches. A critical barrier to a large-scale, high-throughput screening of LOHC candidate molecules is the lack of reliable training data. Computational electronic structure methods including density functional theory, coupled cluster approximations, and diffusion Monte Carlo can be used to provide training data where experimental data are either unreliable or do not exist. In this work, we use these methods to calculate the dehydrogenation energies and enthalpies of candidate LOHC molecules.

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

Approximate singly excited states from a two-component Hartree-Fock reference

For many molecules, relaxing the spin symmetry constraint on the wave function results in the lowest energy mean-field solution. The two-component Hartree-Fock (2cHF) method relaxes all spin symmetry constraints, and the wave function is no longer an eigenfunction of the total spin, spin projection, or time-reversal symmetry operators. For ground state energies, 2cHF is a superior mean-field method for describing spin-frustrated molecules. For excited states, the utility of 2cHF is uncertain. Here, we implement the 2cHF extensions of two single-reference excited state methods, the two-component configuration interaction singles and time-dependent Hartree-Fock. We compare the results to the analogous methods based off of the unrestricted Hartree-Fock approximation, as well as the full configuration interaction for three small molecules with distinct 2cHF solutions, and discuss the nature of the 2cHF excited state solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Memory-Efficient Simulation of Frequency-Dependent Q

Memory-variable methods have been widely applied to approximate frequency-independent quality factor Q in numerical simulation of wave propagation. The frequency-independent model is often appropriate for frequencies up to about 1 Hz but at higher frequencies is inconsistent with some regional studies of seismic attenuation. We apply the memory-variable approach to frequency-dependent Q models that are constant below, and follow a power-law above, a chosen transition frequency. We present numerical results for the corresponding memory-variable relaxation times and weights, obtained by nonnegative least-squares fitting of the Q(f) function, for a range of exponent values; these times and weights can be scaled to an arbitrary transition frequency and a power-law prefactor, respectively. The resulting memory-variable formulation can be used with numerical wave-propagation solvers based on methods such as finite differences (FDs) or spectral elements and may be implemented in either conventional or coarse-grained form. In the coarse-grained approach, we fit effective Q for low-Q values (<200) using a nonlinear inversion technique and use an interpolation formula to find the corresponding weighting coefficients for arbitrary Q. A 3D staggered-grid FD implementation closely approximates the frequency–wavenumber solution to both a half-space and a layered model with a shallow dislocation source for Q as low as 20 over a bandwidth of two decades. We compare the effects of different power-law exponents using a finite-fault source model of the 2008 Mw 5.4 Chino Hills, California, earthquake and find that Q(f) models generally better fit the strong-motion data than the constant Q models for frequencies above 1 Hz.

Geochemistry & Geophysics↗