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DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗

NASA NTRS1972

Martian doublet craters.

A large number of Mars craters are nearly tangential to other craters. They occur in clusters or as isolated crater doublets. Results of probability calculations and a Monte Carlo cratering simulation model show conclusively that many of the Mars craters could not have resulted from random single-body impact. The possibility that these craters are calderas is considered possible only if calderas on Mars form by mechanisms different from those on earth. However, clusters and doublets could be caused by meteoroid breakup resulting from stresses induced in the meteoroid by the gravitational field of Mars. It is concluded that, under certain conditions, doublets should be produced on Mars as a direct result of breakup of an impacting meteoroid. The impact process can yield nonrandom crater distributions that should be observed in different degrees of development on different planetary surfaces.

Oberbeck, V. R.↗

NASA NTRS1987

Weak solar fields and their connection to the solar cycle

Videomagnetograph observations of the weak solar magnetic fields are discussed. Intranetwork (IN) elements are found to emerge in bipolar form, but to flow in a random pattern rather than toward the network elements. Merging of IN fields is found to be more important than the ephemeral regions as a source of new network elements. Arguments for and against the hypothesis that all solar fields are intrinsically strong are considered. It is noted that reconnection and merging of magnetic fields take place continually under the conditions presently examined.

Zirin, Harold↗

DOE OSTI2017

INFLUENCE OF THE GALACTIC GRAVITATIONAL FIELD ON THE POSITIONAL ACCURACY OF EXTRAGALACTIC SOURCES

We investigate the influence of random variations of the Galactic gravitational field on the apparent celestial positions of extragalactic sources. The basic statistical characteristics of a stochastic process (first-order moments, an autocorrelation function and a power spectral density) are used to describe a light ray deflection in a gravitational field of randomly moving point masses as a function of the source coordinates. We map a 2D distribution of the standard deviation of the angular shifts in positions of distant sources (including reference sources of the International Celestial Reference Frame) with respect to their true positions. For different Galactic matter distributions the standard deviation of the offset angle can reach several tens of μ as (microarcsecond) toward the Galactic center, decreasing down to 4–6 μ as at high galactic latitudes. The conditional standard deviation (“jitter”) of 2.5 μ as is reached within 10 years at high galactic latitudes and within a few months toward the inner part of the Galaxy. The photometric microlensing events are not expected to be disturbed by astrometric random variations anywhere except the inner part of the Galaxy as the Einstein–Chvolson times are typically much shorter than the jittering timescale. While a jitter of a single reference source can be up to dozens of μ as over some reasonable observational time, using a sample of reference sources would reduce the error in relative astrometry. The obtained results can be used for estimating the physical upper limits on the time-dependent accuracy of astrometric measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Metalearners for estimating heterogeneous treatment effects using machine learning

There is growing interest in estimating and analyzing heterogeneous treatment effects in experimental and observational studies. We describe a number of metaalgorithms that can take advantage of any supervised learning or regression method in machine learning and statistics to estimate the conditional average treatment effect (CATE) function. Metaalgorithms build on base algorithms—such as random forests (RFs), Bayesian additive regression trees (BARTs), or neural networks—to estimate the CATE, a function that the base algorithms are not designed to estimate directly. We introduce a metaalgorithm, the X-learner, that is provably efficient when the number of units in one treatment group is much larger than in the other and can exploit structural properties of the CATE function. For example, if the CATE function is linear and the response functions in treatment and control are Lipschitz-continuous, the X-learner can still achieve the parametric rate under regularity conditions. We then introduce versions of the X-learner that use RF and BART as base learners. In extensive simulation studies, the X-learner performs favorably, although none of the metalearners is uniformly the best. In two persuasion field experiments from political science, we demonstrate how our X-learner can be used to target treatment regimes and to shed light on underlying mechanisms. A software package is provided that implements our methods.

42 ENGINEERING↗

DOE OSTI2023

Large Eddy Simulation of Convective Heat Transfer in a Random Pebble Bed Using the Spectral Element Method

The development of fluoride-cooled high-temperature reactors has drastically increased the demand for an in-depth understanding of the heat transfer (HT) in packed beds cooled by liquid salts. The complex flow fields and space-dependent porosity found in a pebble bed require a detailed understanding to ensure the proper cooling of the reactor core during normal and accident conditions. As detailed experimental data are complicated to obtain for these configurations, high-fidelity simulation such as large eddy simulation and direct numerical simulation (DNS) can be employed to create a high-resolution heat transfer numerical database that can assist in addressing industrial-driven issues associated with the heat transfer behavior of fluoride-cooled high-temperature reactors. In this paper, we performed a series of large eddy simulation using computational fluid dynamics (CFD) code NekRS to investigate the heat transfer for a bed of 1741 pebbles. Further, the characteristics of the flow, such as average, rms, and time series of velocity and temperature, have been analyzed. Porous media averages have also been performed. The simulation results show a good agreement between non-conjugate heat transfer and conjugate heat transfer. The generated data will be used to benchmark heat transfer modeling methods and local maxima/minima of heat transfer parameters. It will also be used for supporting convective heat transfer quantification for Kairos Power and benchmarking lower fidelity models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Randomization in Characterizing the Subsurface

Current methods for characterizing Earth’s subsurface, such as standard inverse techniques, are not sufficiently accurate to meet the needs of modern applications in the fields of energy exploration, environmental management, and global security. While increasing the quantity of field measurements and robustness of the applied data-/model-analysis methods can improve accuracy, such approaches can be computationally impractical for large data sets and complex site conditions. Thus, there is a need to develop economically-feasible and robust computational methods while maintaining accuracy. For example, in-field drilling for geothermal operations may yield high failure rates, resulting in unacceptably high costs; errors and/or large uncertainties in the estimated subsurface characteristics are the main impediment to the successful siting of an in-field well. This problem is not uniquely geothermal. Accurate characterization of uncertain subsurface properties is also essential for monitoring storage of carbon dioxide, estimating pathways of subsurface contaminant transport, and supervising ground-based nuclear-explosion tests.

58 GEOSCIENCES↗

DOE OSTI2024

Equilibrium Dynamics of Infinite-Range Quantum Spin Glasses in a Field

We determine the low-energy spectrum and Parisi replica-symmetry-breaking function for the spin-glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ( h ) fields. We show that, for all h , the spin-glass state has full replica symmetry breaking and the local spin spectrum is gapless, with a spectral density that vanishes linearly with frequency. These results are obtained using an action functional—argued to yield exact results at low frequencies—that expands in powers of a spin-glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p -rotor model at nonzero h : here, the spin-glass state has one-step replica symmetry breaking and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted. Published by the American Physical Society 2024

Tikhanovskaya, Maria↗

DOE OSTI2024

Dataset for scientific paper "Simulated plant‑mediated oxygen input has strong impacts on fine‑scale porewater biogeochemistry and weak impacts on integrated methane fluxes in coastal wetlands", a modeling study based on field observation at the tidal salt marshes of the Parker River Estuary, Massachusetts, United States

This dataset is the raw and processed data for the paper "Simulated plant ‑ mediated oxygen input has strong impacts on fine ‑ scale porewater biogeochemistry and weak impacts on integrated methane fluxes in coastal wetlands". This study investigated how plant-mediated oxygen input affects subsurface biogeochemical reactions of organic carbon degradation and the resulting methane emissions of coastal wetlands by model simulation. We used the subsurface geochemical simulator PFLOTRAN for the modeling, which produced the simulated changes in porewater chemical substances and methane emissions over 10 days under different scenarios of plant-mediated oxygen input.Specifically, this dataset contains: 1) the input files for PFLOTRAN of all simulation runs conducted in this study. Those files are with an extension of ".in", containing information of the biogeochemical reaction network (stoichiometry, reaction rate, Monod constants, etc), fluid flow rate and oxygen concentration in the fluid which together simulated the plant-mediated oxygen input, the configuration of artificial reactions that simulated the methane fluxes, etc. The PFLOTRAN input files are text files, which can be opened by NotePad, but running these input files will require proper installation of PFLOTRAN (instruction: https://documentation.pflotran.org/user_guide/how_to/installation/installation.html). 2) the raw and processed model output from PFLOTRAN of all simulation runs, and 3) the python scripts used to process the raw model output, including random allocation of root cells, converting raw data into organized formats, calculating the methane fluxes based on the model output, data visualization, etc. The raw and processed model output from PFLOTRAN are in .spydata format, which can be viewed with Python. and 3) the python scripts for data processing and analysis are programming scripts, which can be opened with Python.This modeling work, in particular the model parameterization of root density and initial conditions of porewater concentrations of biogeochemical substances, was based on field measurements at the salt marsh of the Upper Parker River Estuary, Massachusetts, United States.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression

Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. Additionally, the method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.

58 GEOSCIENCES↗

NASA NTRS1985

Forced MHD turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx' ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗

NASA NTRS1985

Forced magnetohydrodynamic turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx, ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗

NASA NTRS1990

Wave propagation through random media: A local method of small perturbations based on the Helmholtz equation

Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.

Grosse, Ralf↗

DOE OSTI2026

Molecular Diradical Spin Qubits in a Crystalline Host as a Platform for Quantum Sensing

Doping a luminescent tris(2,4,6-trichlorophenyl)methyl diradical m (TTM) 2 into a host crystal of its diamagnetic precursor m (HTTM) 2 creates a molecular color center with enhanced optical-spin interface properties important for quantum sensing. Optical polarization of the |T 0 ⟩ sublevel of the diradical triplet ground state is achieved by spin-selective intersystem crossing from the |T + ⟩ and |T – ⟩ sublevels of the triplet excited state at ambient and cryogenic temperatures. Coherent spin control of m (TTM) 2 doped into m (HTTM) 2 using pulsed optically detected magnetic resonance (ODMR) spectroscopy results in a 10-fold improvement in ODMR contrast over that observed for randomly oriented m (TTM)2 using continuous-wave ODMR. The diradical doped crystal powders achieve spin coherence times of 2.8, 3.4, and 7.4 μs at 294, 85, and 5 K, respectively. The diradical photoluminescence is sensitive to weak applied magnetic fields independent of temperature, excitation wavelength, and dopant concentration, providing a promising pathway toward robust quantum sensing of anisotropic magnetic fields under ambient conditions.

crystal structure↗

DOE OSTI2021

A data-driven global soil heterotrophic respiration dataset and the drivers of its inter-annual variability

Soil heterotrophic respiration (SHR), one of the primary carbon fluxes from terrestrial ecosystems to the atmosphere, is important for carbon-climate feedbacks because of its sensitivity to available litter and soil carbon, climatic conditions, and nutrient availability. However, until recently limited SHR data were available, and most published global SHR estimates have either a short time span, coarse spatial resolution, or reply on overly-simple model formulations. To better understand and quantify the global distribution of SHR and its sensitivity to climate variability, we produced a new global SHR dataset using Random Forest algorithms, up-scaling 455 point data from the Global Soil Respiration Database (SRDB 4.0) with gridded fields of climatic, edaphic and productivity as explanatory variables. We estimated a global total SHR of 46.8 Pg C yr-1 over 1985-2013 (95% confidence interval: 38.6-56.3 Pg C yr-1), with a significant increasing trend of 0.03 Pg C yr-2 during this period. We found that the choice of soil moisture datasets contributes more to the difference among these data-driven SHR members rather than that of productivity, temperature and precipitation data sources. We also analyzed the influence of climatic variables on the inter-annual variability (IAV) of our SHR product. Water availability was the dominant driver of IAV at global scales, although the inferred sensitivity depends on the choice of the soil moisture gridded dataset. At the ecosystem scale, temperature strongly controls the IAV of SHR in tropical forests, while water availability dominates in extra-tropical forest and semi-arid regions. Our machine-learning gridded SHR dataset and outputs from process-based land surface models (TRENDYv6) show agreement for a strong association between water variability and SHR IAV at the global scale, but the two approaches lead to different temporal trend globally and different controlling variables for IAV at the ecosystem scale. Our study provides evidence for the pervasive and important role of water availability in driving SHR, indicating both a direct effect limiting decomposition rates and an indirect effect through the amount of fresh organic matter made available to SHR from productivity. In consideration of potential limitations and uncertainties remaining in our data-driven SHR datasets, we call for a more scientifically designed observation network for SHR, more observation data compilation, and increased use of deep learning methods making maximum use of observation data in hand. This will benefit process-based models, and improve our understanding of SHR response to future anomalous environmental conditions.

Yao, Yitong↗

DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Flocking ferromagnetic colloids

Assemblages of microscopic colloidal particles exhibit fascinating collective motion when energized by electric or magnetic fields. The behaviors range from coherent vortical motion to phase separation and dynamic self-assembly. While colloidal systems are relatively simple, understanding their collective response, especially in out of equilibrium conditions, remains elusive. Here, we report on the emergence of flocking and global rotation in the system of rolling ferromagnetic microparticles energized by a vertical alternating magnetic field. By combing experiments and discrete particle simulations, we have identified primary physical mechanisms leading to the emergence of largescale collective motion: spontaneous symmetry breaking of the clock / counterclockwise particle rotation, collisional alignment of particle velocities, and random particle re-orientations due to shape imperfections. We have also shown that hydrodynamic interactions between the particles do not have a qualitative effect on the collective dynamics. Lastly, our findings shed light on the onset of spatial and temporal coherence in a large class of active systems, both synthetic (colloids, swarms of robots, biopolymers) and living (suspensions of bacteria, cell colonies, bird flocks).

36 MATERIALS SCIENCE↗

NASA NTRS1996

Numerical Analysis of the Sea State Bias for Satellite Altimetry

Theoretical understanding of the dependence of sea state bias (SSB) on wind wave conditions has been achieved only for the case of a unidirectional wind-driven sea. Recent analysis of Geosat and TOPEX altimeter data showed that additional factors, such as swell, ocean currents, and complex directional properties of realistic wave fields, may influence SSB behavior. Here we investigate effects of two-dimensional multimodal wave spectra using a numerical model of radar reflection from a random, non-Gaussian surface. A recently proposed ocean wave spectrum is employed to describe sea surface statistics. The following findings appear to be of particular interest: (1) Sea swell has an appreciable effect in reducing the SSB coefficient compared with the pure wind sea case but has less effect on the actual SSB owing to the corresponding increase in significant wave height. (2) Hidden multimodal structure (the two-dimensional wavenumber spectrum contains separate peaks, for swell and wind seas, while the frequency spectrum looks unimodal) results in an appreciable change of SSB. (3) For unimodal, purely wind-driven seas, the influence of the angular spectral width is relatively unimportant; that is, a unidirectional sea provides a good qualitative model for SSB if the swell is absent. (4) The pseudo wave age is generally much better fo parametrization the SSB coefficient than the actual wave age (which is ill-defined for a multimodal sea) or wind speed. (5) SSB can be as high as 5% of the significant wave height, which is significantly greater than predicted by present empirical model functions tuned on global data sets. (6) Parameterization of SSB in terms of wind speed is likely to lead to errors due to the dependence on the (in practice, unknown) fetch.

Glazman, R. E.↗