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Unified collision operator demonstrated for both radiation transport and PIC-DSMC. A side-by-side comparison between the DSMC method and the radiation transport method was conducted for photon attenuation in the atmosphere over 2 kilometers in physical distance with a reduction of photon density of six orders of magnitude. Both DSMC and traditional radiation transport agreed with theory to two digits. This indicates that PIC-DSMC operators can be unified with the radiation transport collision operators into a single code base and that physics kernels can remain unique to the actual collision pairs. This simulation example provides an initial validation of the unified collision theory approach that will later be implemented into EMPIRE.

54 ENVIRONMENTAL SCIENCES↗

Validation of Actuator Line and Actuator Disk Models with Filtered Lifting Line Corrections Implemented in Nalu-Wind Large Eddy Simulations of the Atmospheric Boundary Layer

Turbine generator power from simulations using Actuator Line Models and Actuator Disk Models with a Filtered Lifting Line Correction are compared to field data of a V27 turbine. Preliminary results of the wake characteristics are also presented. Turbine quantities of interest from traditional ALM and ADM with the Gaussian kernel (..epsilon..) set at the optimum value for matching power production and that resolve the kernel at all mesh sizes are also presented. The atmospheric boundary layer is simulated using Nalu-Wind, a Large Eddy Simulation code which is part of the ExaWind code suite. The effect of mesh resolution on quantities of interest is also examined.

Actuator Disk Models↗

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization. We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TH-A-18C-09: Ultra-Fast Monte Carlo Simulation for Cone Beam CT Imaging of Brain Trauma

Purpose: Application of cone-beam CT (CBCT) to low-contrast soft tissue imaging, such as in detection of traumatic brain injury, is challenged by high levels of scatter. A fast, accurate scatter correction method based on Monte Carlo (MC) estimation is developed for application in high-quality CBCT imaging of acute brain injury. Methods: The correction involves MC scatter estimation executed on an NVIDIA GTX 780 GPU (MC-GPU), with baseline simulation speed of ~1e7 photons/sec. MC-GPU is accelerated by a novel, GPU-optimized implementation of variance reduction (VR) techniques (forced detection and photon splitting). The number of simulated tracks and projections is reduced for additional speed-up. Residual noise is removed and the missing scatter projections are estimated via kernel smoothing (KS) in projection plane and across gantry angles. The method is assessed using CBCT images of a head phantom presenting a realistic simulation of fresh intracranial hemorrhage (100 kVp, 180 mAs, 720 projections, source-detector distance 700 mm, source-axis distance 480 mm). Results: For a fixed run-time of ~1 sec/projection, GPU-optimized VR reduces the noise in MC-GPU scatter estimates by a factor of 4. For scatter correction, MC-GPU with VR is executed with 4-fold angular downsampling and 1e5 photons/projection, yielding 3.5 minute run-time per scan, and de-noised with optimized KS. Corrected CBCT images demonstrate uniformity improvement of 18 HU and contrast improvement of 26 HU compared to no correction, and a 52% increase in contrast-tonoise ratio in simulated hemorrhage compared to “oracle” constant fraction correction. Conclusion: Acceleration of MC-GPU achieved through GPU-optimized variance reduction and kernel smoothing yields an efficient (<5 min/scan) and accurate scatter correction that does not rely on additional hardware or simplifying assumptions about the scatter distribution. The method is undergoing implementation in a novel CBCT dedicated to brain trauma imaging at the point of care in sports and military applications. Research grant from Carestream Health. JY is an employee of Carestream Health.

60 APPLIED LIFE SCIENCES↗

Application of activity pencil beam algorithm using measured distribution data of positron emitter nuclei for therapeutic SOBP proton beam

Purpose: Recently, much research on imaging the clinical proton-irradiated volume using positron emitter nuclei based on target nuclear fragment reaction has been carried out. The purpose of this study is to develop an activity pencil beam (APB) algorithm for a simulation system for proton-activated positron-emitting imaging in clinical proton therapy using spread-out Bragg peak (SOBP) beams.Methods: The target nuclei of activity distribution calculations are {sup 12}C nuclei, {sup 16}O nuclei, and {sup 40}Ca nuclei, which are the main elements in a human body. Depth activity distributions with SOBP beam irradiations were obtained from the material information of ridge filter (RF) and depth activity distributions of compounds of the three target nuclei measured by BOLPs-RGp (beam ON-LINE PET system mounted on a rotating gantry port) with mono-energetic Bragg peak (MONO) beam irradiations. The calculated data of depth activity distributions with SOBP beam irradiations were sorted in terms of kind of nucleus, energy of proton beam, SOBP width, and thickness of fine degrader (FD), which were verified. The calculated depth activity distributions with SOBP beam irradiations were compared with the measured ones. APB kernels were made from the calculated depth activity distributions with SOBP beam irradiations to construct a simulation system using the APB algorithm for SOBP beams.Results: The depth activity distributions were prepared using the material information of RF and the measured depth activity distributions with MONO beam irradiations for clinical therapy using SOBP beams. With the SOBP width widening, the distal fall-offs of depth activity distributions and the difference from the depth dose distributions were large. The shapes of the calculated depth activity distributions nearly agreed with those of the measured ones upon comparison between the two. The APB kernels of SOBP beams were prepared by making use of the data on depth activity distributions with SOBP beam irradiations that were made from the depth activity distributions with MONO beam irradiations and sorted in terms of energy, SOBP width, and thickness of FD. The data on APB kernels of SOBP beams were determined as installment data for the simulation system using the APB algorithm for SOBP beam irradiations.Conclusions: A method of obtaining the depth activity distributions and the APB algorithm for clinical use of SOBP beams have been developed. It is suggested that the simulation system for imaging the clinical irradiated volume with the APB algorithm can be used in clinical proton therapy using SOBP beams by preparing and investigating the data on APB kernels of SOBP beams.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies

The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. Here, the stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincaré constant, and other parameters. In the nonlinear setting, the bounds quantify in different L p norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.

97 MATHEMATICS AND COMPUTING↗

Real-space inversion and super-resolution of ultrafast scattering

Ultrafast scattering using x-rays or electrons is an emerging method to obtain structure dynamics at the atomic lengthscales and timescales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector range and the probe energy. So, as a result, the time-resolved signal interpretation is mostly done in reciprocal space and relies on modeling and simulations of specific structures and processes. Here, we introduce a model-free approach to directly resolve scattering signals in real space, surpassing the diffraction limit, using scattering kernels and signal priors that naturally arise from the measurement constraints. We demonstrate the approach on simulated and experimental data, recover multiple atomic motions at sub-angstrom resolutions, and discuss the recovery accuracy and resolution limits versus signal fidelity. The approach offers a robust path to obtain high-resolution real-space information of atomic-scale structure dynamics using current time-resolved x-ray or electron scattering sources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gaussian kernel density functions for compositional quantification in atom probe tomography

Highlights: • A methodology for compositional quantification from atom probe tomography is proposed. • A probability density function p(x) given discrete data points is constructed. • Each atom approximated by a Gaussian function with a particular smoothing parameter. • Density Kernel functions are used to find the optimum smoothing parameter. • The method is validated by using simulated data of semiconductor materials. - Abstract: Atom probe tomography (APT) has the ability to identify the nature and position of single atoms in a material with an almost 3D atomic resolution. However, the quantification of the material composition requires an appropriate treatment of the discrete APT data. When the amount of atoms selected to quantify the composition is relatively small, the spatial resolution is enhanced but the statistical error worsens. Conversely, the increase in the number of atoms considered reduces the spatial resolution, but improving the statistics. We have developed a methodology to reach an optimum equilibrium between the positional and the statistical error in an unsupervised form using Gaussian Kernel density functions. The validity of the method has been tested using APT simulated data of semiconductor materials. It has been proved that the chemical quantification in these materials requires the appropriate selection of the smoothing parameter, obtained without user intervention. In addition, the results have been compared to the usual techniques for composition measurement from APT data (voxelization and proximity histograms), showing better precision for high spatial resolution. This work supplies a data driven methodology based in Gaussian Kernel density functions for the accurate quantification of the composition from APT data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling of thermal and kinetic processes in non-equilibrium plasma ignition applied to a lean combustion engine

In recent years novel ignition systems have been developed to enable stable and efficient engine operations with lean mixtures. Among them, radio-frequency corona ignition systems create discharges that involve a much wider region compared to traditional spark, and produce non equilibrium plasma with high levels of active radicals and excited species. These devices considerably increase the early flame growth speed and extend stable operating limits. With the aim of expanding the knowledge on high efficiency lean-burn SI engines, this paper investigates and compares the combustion development generated by spark and corona ignitions through computational fluid dynamics, within the Reynolds-Averaged Navier-Stokes framework for turbulence modeling. In order to simultaneously take thermal and chemical effects into account, the Perfectly Stirred Reactor combustion model is used. Experimental data are also collected for validation in an optical access engine, for different mixture levels, from stoichiometric to very lean. Furthermore, the faster burn rate generated by the corona system in the initial stage of the combustion is well predicted by the simulations, in all the relative air-fuel ratio conditions. Remarkably, as the mixture becomes lean, simulations are able to capture the non-linear transition from fast to slow kernel growth, before a self-sustainable flame propagation is established. This correlates very well with the measured engine cyclic variability and the corresponding steep change in the duration of the flame kernel formation. Ultimately, this study highlights the important role of the atomic oxygen, as active radical, in promoting and enhancing the combustion initiated by a corona discharge, in addition to the volumetric ignition effect. By contrast, the validated simulations allow to explain that the high-temperature thermal plasma generated in a traditional spark discharge is insensitive to kinetic aspects.

42 ENGINEERING↗

Nonparametric probability density estimation by optimization theoretic techniques

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Scott, D. W.↗

Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel

We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.

97 MATHEMATICS AND COMPUTING↗

On the measurement of shape: With applications to lunar regolith

With the renewed commitment from NASA and other commercial entities for a presence on the Moon, the importance of understanding the characteristics of lunar regolith and how to utilize it have become the target of increasing scrutiny. Much of what is known about lunar regolith was collected during and immediately after the Apollo program, however, analytical techniques and instrumentation have advanced in leaps and bounds in the subsequent decades. Specifically, dynamic image analysis systems have advanced to the point that millions of particles can have morphological characteristics automatically determined in relatively short time frames. Particle morphological data was collected on several lunar samples and a pair of widely used regolith simulants to ascertain the accuracy of these simulants and to explore statistical analysis methods of these large datasets. It is found that these morphology datasets can vary widely depending on the particle size of the particles, and simple averaging of the data skews the results heavily towards the numerically abundant size ranges, the fines. Different reporting methods are suggested to ameliorate these problems. When applied to the lunar regolith, the particles are noted to be less morphologically complex than initially suspected. Compared to the lunar material, the simulants are found to contain some more morphological variability and angular grains. Such difference is likely due to the wildly different comminution processes that these different powder systems are subjected to.

2D shape↗

Liquid–Vapor Phase Equilibrium in Molten Aluminum Chloride (AlCl 3 ) Enabled by Machine Learning Interatomic Potentials

Molten salts are promising candidates in numerous clean energy applications, where knowledge of thermophysical properties and vapor pressure across their operating temperature ranges is critical for safe operations. Due to challenges in evaluating these properties using experimental methods, fast and scalable molecular simulations are essential to complement the experimental data. In this study, we developed machine learning interatomic potentials (MLIP) to study the AlCl 3 molten salt across varied thermodynamic conditions (T = 473–613 K and P = 2.7–23.4 bar), which allowed us to predict temperature-surface tension correlations and liquid–vapor phase diagram from direct simulations of two-phase coexistence in this molten salt. Two MLIP architectures, a Kernel-based potential and neural network interatomic potential (NNIP), were considered to benchmark their performance for AlCl 3 molten salt using experimental structure and density values. The NNIP potential employed in two-phase equilibrium simulations yields the critical temperature and critical density of AlCl 3 that are within 10 K (∼3%) and 0.03 g/cm 3 (∼7%) of the reported experimental values. An accurate correlation between temperature and viscosities is obtained as well. In doing so, we report that the inclusion of low-density configurations in their training is critical to more accurately represent the AlCl 3 system across a wide phase-space. The MLIP trained using PBE-D3 functional in the ab initio molecular dynamics (AIMD) simulations (120 atoms) also showed close agreement with experimentally determined molten salt structure comprising Al 2 Cl 6 dimers, as validated using Raman spectra and neutron structure factor. Furthermore, the PBE-D3 as well as its trained MLIP showed better liquid density and temperature correlation for AlCl 3 system when compared to several other density functionals explored in this work. Overall, the demonstrated approach to predict temperature correlations for liquid and vapor densities in this study can be employed to screen nuclear reactors-relevant compositions, helping to mitigate safety concerns.

Ab initio molecular dynamics↗

Machine-Learning of Nonlocal Kernels for Anomalous Subsurface Transport from Breakthrough Curves

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport in various subsurface applications, their application is hindered by computational challenges. Simpler nonlocal models characterized by integrable kernels and finite interaction length represent a computationally feasible alternative to fractional models; yet, the informed choice of their kernel functions still remains an open problem. We propose a general data-driven framework for the discovery of optimal kernels on the basis of very small and sparse data sets in the context of anomalous subsurface transport. Using spatially sparse breakthrough curves recovered from fine-scale particle-density simulations, we learn the best coarse-scale nonlocal model using a nonlocal operator regression technique. Predictions of the breakthrough curves obtained using the optimal nonlocal model show good agreement with fine-scale simulation results even at locations and time intervals different from the ones used to train the kernel, confirming the excellent generalization properties of the proposed algorithm. A comparison with trained classical models and with black-box deep neural networks confirms the superiority of the predictive capability of the proposed model.

97 MATHEMATICS AND COMPUTING↗

Gluon transverse-momentum-dependent distributions from large-momentum effective theory

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the $\overline{MS}$ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for the extraction of gluon TMDPDFs from lattice simulations, and have the potential to greatly facilitate perturbative calculations of the hard matching kernel.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗

Evaluating cloud feedbacks and rapid responses in the ACCESS model

A cloud feedback diagnostic package is implemented in the Australian Community Climate and Earth-System Simulator General Circulation Model, based on the methodology of “cloud radiative kernels.” Using separate increased sea surface temperature and CO 2 experiments, both the “rapid response” cloud contribution to forcing and temperature-mediated cloud feedbacks are analyzed. Under increased temperature and CO 2 changes, temperature-mediated cloud radiative feedback dominates over the rapid response in the final radiative response. Cloud feedback is positive in both long and short wave, with short wave dominating global values. Contributing most to this are low to mid-level clouds, of medium-to-high optical thickness. As a means of illustration of the methodology, a number of key parameters related to clouds, precipitation, and convection that are typically used in “tuning” in the model are modified. These changes result in substantial impacts on the model's current climate, but only modest changes to rapid response and feedbacks occur globally, regionally, and as a function of cloud optical thickness and height. This limited set of experiments shows that cloud adjustments and feedbacks in this model are robust under these changes, lending confidence that both model climate change projections and the conclusions of attribution studies are not overly sensitive to such parameterization tuning. Of course, a considerably larger set of experiments would be needed to demonstrate that feedbacks and rapid response are robust under the wider set of tuning adjustments commonly undertaken.

54 ENVIRONMENTAL SCIENCES↗