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NASA NTRS1992

Angle-dependent Green's functions for relativistic Compton reflection

Using analytic methods, we derived the first-order Green's functions, in terms of the observing angle, for the reflected spectra after a single Compton scattering of relativistic photons by a plane-parallel semiinfinite medium of cold electrons. We also calculated the total Green's functions for incident photons of 511 keV, using Monte Carlo methods. We show that both the first-order and total Green's functions have strong angular dependences and that the first-order Green's functions play a dominant role in determining the properties of the total reflected spectra.

Hua, Xin-Min↗

DOE OSTI2025

Machine-learning-informed scattering correlation analysis of sheared colloids

We have carried out theoretical analysis, Monte Carlo simulations and machine-learning analysis to quantify microscopic rearrangements of dilute dispersions of spherical colloidal particles from coherent scattering intensity. Both monodisperse and polydisperse dispersions of colloids were created and underwent a rearrangement consisting of an affine simple shear and non-affine rearrangement using the Monte Carlo method. We calculated the coherent scattering intensity of the dispersions and the correlation function of intensity before and after the rearrangement and generated a large data set of angular correlation functions for varying system parameters, including number density, polydispersity, shear strain and non-affine rearrangement. Singular value decomposition of the data set shows the feasibility of machine-learning inversion from the correlation function for the polydispersity, shear strain and non-affine rearrangement using only three parameters. A Gaussian process regressor is then trained on the data set and can retrieve the affine shear strain, non-affine rearrangement and polydispersity with relative errors of 3%, 1% and 6%, respectively. Altogether, our model provides a framework for quantitative studies of both steady and non-steady microscopic dynamics of colloidal dispersions using coherent scattering methods.

Gaussian process regression↗

NASA NTRS1992

Reflectance of broken cloud fields - Simulation and parameterization

The transfer of solar irradiance in plane parallel and broken cloud fields is simulated using a Monte Carlo method. The angular distribution pattern of radiances exiting the cloud layer is studied with varying cloud geometries, optical thicknesses, cloudiness, and solar zenith angles. A rather large anisotropy of the reflected flux is found, usually increasing with solar zenith angle and with patterns that strongly depend on cloud geometry. The main features are (1) a local maximum of reflected intensity in the forward direction for all cases, (2) a limb darkening for the plane parallel case, and (3) a limb brightening and a local maximum of reflected intensity in the backward direction for broken clouds. A parameterization for the azimuth-average reflectance function is developed. It reproduces the Monte Carlo simulation with a reasonable accuracy and illustrates that, when azimuthally averaged, the reflectance function is dominated by side viewing and intercloud shadowing effects.

Breon, Francois-Marie↗

DOE OSTI2023

Tensor renormalization group study of 3D principal chiral model

We study the three-dimensional SU(2) principal chiral model using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based on the character expansion of the Boltzmann weight. We compare the average action obtained using these two tensor network algorithms and confirm that the resulting critical coupling and exponent are comparable with the recent estimations from the Monte Carlo methods.

Unmuth-Yockey, Judah↗

DOE OSTI2023

Tensor renormalization group study of 3D principal chiral model

We study the three-dimensional $SU(2)$ principal chiral model (PCM) using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based on the character expansion of the Boltzmann weight. We compare the average action obtained using these two tensor network algorithms and confirm that the resulting critical coupling and exponent are comparable with the recent estimations from the Monte Carlo methods.

Akiyama, Shinichiro↗

DOE OSTI2026

Monte Carlo Simulations of Crystal Defects in Open Ensembles

Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian Monte Carlo method that samples energy-biased gradual transformations. In conclusion, the method enables free energy calculations for nonideal point defects and the direct prediction of finite-temperature interface structures.

Grain boundaries↗

DOE OSTI2021

Monte Carlo MP2-F12 for Noncovalent Interactions: The C 60 Dimer

A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green’s functions in real space and imaginary time. Furthermore, these integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol –1 for the C 60 dimer at the center distance of 9.748 Å.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Radiation Transport Models in Space: from Supernovae to Cells

Humans embarking on deep space exploration missions will encounter persistent exposure to galactic cosmic rays (GCR) - an energetic and highly complex radiation field that is unlike anything found on Earth. Exposure to such radiation fields is attributed to various adverse health effects, including cancer, cardiovascular disease, and cognitive impairment and is identified by NASA as one of the five main hazards of human spaceflight. It is therefore critical to be able to fully characterize the exposure received by humans behind shielding in space and project consequent health risks. A wide variety of computational models have been developed over the years to help meet this requirement. In this talk, an overview of the GCR environment in deep space is provided. Methods of propagating GCR fields through the shielding that protects humans in space are described along with simulation tools used to assess biological damage at the cellular scale. Finally, the NASA cancer risk model is briefly described, and risk projections are provided for various mission scenarios. Radiation transport models and solution methods pervade many aspects of this talk. For example, the GCR spectrum impinging on spacecraft is determined by solving the Fokker-Planck transport equation to propagate cosmic rays (believed to originate from supernovae) from the edge of the heliosphere to the vicinity of Earth. The Boltzmann transport equation is solved to transport this GCR spectrum through shielding and human tissue. Monte Carlo methods are used to simulate the transport of low energy electrons that dominate biological damage at the cellular scale. Progress and challenges in each of these areas will be highlighted.

Tony C. Slaba↗

DOE OSTI2023

Attractive Su-Schrieffer-Heeger-Hubbard model on a square lattice away from half-filling

The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron tunneling, is a paradigmatic electron-phonon model that hosts an antiferromagnetic order to bond order transition at half-filling. In the presence of a repulsive Hubbard interaction, the antiferromagnetic phase is enhanced, but the phase transition remains first order. Here, we explore the physics of the SSH model with an attractive Hubbard interaction, which hosts an interesting interplay among charge order, s-wave pairing, and bond order. Using the numerically exact determinant quantum Monte Carlo method, we show that both charge order, present at weak electron-phonon coupling, and bond order, at large coupling, give way to s-wave pairing when the system is doped. Lastly, we demonstrate that the SSH electron-phonon interaction competes with the attractive Hubbard interaction and reduces the s-wave pairing correlation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Neutron (and other Particle) Transport at LANL: An Overview [Presentation]

For decades, Los Alamos National Laboratory has been at the forefront of neutron transport methods research and code development. One such code is PARTISN, the LANL parallel time-dependent discrete ordinate neutron transport code. In this presentation, we describe the various research efforts currently underway by the PARTISN and other code teams. Some examples of current research are a block automated mesh refinement scheme, the application of tensor trains to the discretized neutron transport equation, and GPU code porting. The block automated mesh refinement scheme uses cross section information to refine and coarsen the solution mesh to improve time to solution and reduce memory. The tensor train approach expresses discretized transport operators as tensor products of vectors and matrices to compress the size of linear systems being solved by transport codes. Rather than relying on matrix-free methods such as the transport sweep, we have access to an operator that can be inverted, reshaped, or manipulated algebraically. Finally, we describe how PARTISN is used, what problems we are looking to solve, and what the future holds for neutron transport at LANL. In addition to this, we briefly describe the various research efforts in other particle transport teams using both deterministic and Monte Carlo methods. In the presentation, we list possible opportunities for collaboration between the laboratory and faculty and students.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗

NASA NTRS1972

Low-energy electron transport with the method of discrete ordinates

The one-dimensional discrete ordinates code ANISN was adapted to transport low energy (a few MeV) electrons. Calculated results obtained with ANISN were compared with experimental data for transmitted electron energy and angular distribution data for electrons normally incident on aluminum slabs of various thicknesses. The calculated and experimental results are in good agreement for a thin slab (0.2 of the electron range), but not for the thicker slabs (0.6 of the electron range). Calculated results obtained with ANISN were also compared with results obtained using Monte Carlo methods.

Bartine, D. E.↗

NASA NTRS1982

Transport processes on the lunar surface - Comparison of model calculations with radionuclides data

Descriptions are given of the experimental methods used in determining Al-26 and Mn-53 activities and of the possible improvements that can be expected in the near future. The results obtained for the seven lunar core sections where both Al-26 and Mn-53 are measured with good depth definition are discussed. It is then shown how meteoritic impacts and the secondary effects they induce modify the Al-26 and Mn-53 activities in a core. Using a Monte Carlo method, 150 possible depositional histories for a core are generated; from these the resulting activity profiles for both Al-26 and Mn-53 are computed, using several possible SCR energy spectra. These model-generated profiles are then compared with the experimental profiles in the seven cores, and plausible scenarios for the depositional history of each of the cores are tentatively inferred.

Langevin, Y.↗

DOE OSTI2020

Monte Carlo simulations for understanding the transport properties of metallic nanowires

We report the conductance calculation of metallic nanowires of different metals under the application of a tensile force. The elongation induced by the tensile force was simulated by means of the canonical Monte Carlo method combined with the embedded atom method to compute the energy of the system. We studied nanowires composed of Ag, Au, Pt and Cu. The conductance was calculated by means of the Landauer formula and the non-equilibrium Green function formalism. As previously verified experimentally and using other simulation techniques, the conductance is quantized. In addition to this, we have found that there is a strong correlation between the magnitude of the conductance and the width of the nanowire at its thinnest point. Conductance histograms were analyzed for all the different metals.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗

NASA NTRS2012

The Effect of Systematic Error in Forced Oscillation Testing

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods.

Williams, Brianne Y.↗

DOE OSTI2021

Xenon Trapping in Metal-Supported Silica Nanocages

Xenon (Xe) is a valuable and scarce noble gas used in various applications, including lighting, electronics, and anesthetics, among many others. It is also a volatile byproduct of the nuclear fission of uranium. In this work, a novel material architecture consisting of silicate nanocages in contact with a metal surface and an approach for trapping single Xe atoms in these cages is presented. The trapping is done at low Xe pressures and temperatures between 400 and 600 K, and the process is monitored in situ using synchrotron-based ambient pressure X-ray photoelectron spectroscopy. Release of the Xe from the cages occurs only when heating to temperatures above 750 K. A model that explains the experimental trapping kinetics is proposed and tested using Monte Carlo methods. Density functional theory calculations show activation energies for Xe exiting the cages consistent with experiments. This work can have significant implications in various fields, including Xe production, nuclear power, nuclear waste remediation, and nonproliferation of nuclear weapons. The results are also expected to apply to argon, krypton, and radon, opening an even more comprehensive range of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Optimized Viewing Techniques to Minimize Radiation Damage From X-ray Imaging Systems

X-ray inspection of ball grid arrays (BGAs) is typically performed at one or more viewing angles to examine adhesion sites for errors such as voids, joint cracking, or head-in-pillow. During this inspection process, the cir cuit board assembly is subject to ionizing radiation exposure, which can cause trapped charge within oxide layers of semiconductor devices. Some x-ray machines allow for programmable inspection routines, which could be used to optimize radiation exposure to semiconductor components. Using Monte Carlo methods, x-ray inspection of a BGA was simulated to determine a range of acceptable viewing angles. Dose rates to circuit board components were estimated at each inspection angle to determine the view resulting in optimized radiation exposure. Results showed that for each BGA, the maximum unobstructed viewing times without exceeding a 5 Gy dose limit to a single part ranged from 82 to 94 minutes. Using a radiation cost function method, optimized viewing across all components was found. Here, it was observed that for a consistent dose limit applied to silicon-based components, performing inspection with BGAs facing the x-ray source was optimal. A third method was applied, assigning individual dose limits based on empirical data from the NASA Goddard Space Flight Center radiation database. This method showed that optimized viewing maximizes the distance between the radiation source and highly sensitive components. It was also observed that cumulative effects from viewing two BGAs will influence viewing angles, causing the optimal view of one BGA to exist nearly 180° from the other.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗