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DOE OSTI2023

The winter central Arctic surface energy budget: A model evaluation using observations from the MOSAiC campaign

This study evaluates the simulation of wintertime (15 October, 2019, to 15 March, 2020) statistics of the central Arctic near-surface atmosphere and surface energy budget observed during the MOSAiC campaign with short-term forecasts from 7 state-of-the-art operational and experimental forecast systems. Five of these systems are fully coupled ocean-sea ice-atmosphere models. Forecast systems need to simultaneously simulate the impact of radiative effects, turbulence, and precipitation processes on the surface energy budget and near-surface atmospheric conditions in order to produce useful forecasts of the Arctic system. This study focuses on processes unique to the Arctic, such as, the representation of liquid-bearing clouds at cold temperatures and the representation of a persistent stable boundary layer. It is found that contemporary models still struggle to maintain liquid water in clouds at cold temperatures. Given the simple balance between net longwave radiation, sensible heat flux, and conductive ground flux in the wintertime Arctic surface energy balance, a bias in one of these components manifests as a compensating bias in other terms. This study highlights the different manifestations of model bias and the potential implications on other terms. Three general types of challenges are found within the models evaluated: representing the radiative impact of clouds, representing the interaction of atmospheric heat fluxes with sub-surface fluxes (i.e., snow and ice properties), and representing the relationship between stability and turbulent heat fluxes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Evaluation of idealized large-eddy simulations performed with the Weather Research and Forecasting model using turbulence measurements from a 250 m meteorological mast

Abstract. We investigate the ability of the Weather Research and Forecasting model to perform large-eddy simulation of canonical flows. This is achieved through comparison of the simulation outputs with measurements from sonic anemometers on a 250 m meteorological mast located at Østerild, in northern Denmark. Østerild is on a flat and rough area, and for the predominant wind directions, the atmospheric flow can be considered to be close to homogeneous. The idealized simulated flows aim at representing atmospheric boundary layer turbulence under unstable, neutral, and stable stability conditions at the surface, which are statistically significant conditions observed at Østerild. We found that the resolved fields from the simulations appear to have the characteristics of the three stability regimes. Vertical profiles of observed mean wind speeds and direction are well reproduced by the simulations, with the largest differences under near-neutral conditions, where the effect of the subgrid-scale model is evident on the vertical wind shear close to the surface. Vertical profiles of observed eddy fluxes are also well reproduced by the simulations, with the largest differences for the three velocity component variances under stable stability conditions, although nearly always within the observed variability. With regards to turbulent kinetic energy, we find good agreement between observations and simulations at all vertical levels. Simulated and observed velocity spectra match very well and show very similar behavior with height and with atmospheric stability within the low-frequency interval; at the effective resolution, the simulated spectra show the typical drop-off of finite differences. Our findings demonstrate that these idealized simulations reproduce the characteristics of atmospheric stability regimes often observed at a high turbulent and flat site within a direction sector, where the air flows over nearly homogeneous land.

17 WIND ENERGY↗

NASA NTRS1973

System statistical reliability model and analysis

A digital computer code was developed to simulate the time-dependent behavior of the 5-kwe reactor thermoelectric system. The code was used to determine lifetime sensitivity coefficients for a number of system design parameters, such as thermoelectric module efficiency and degradation rate, radiator absorptivity and emissivity, fuel element barrier defect constant, beginning-of-life reactivity, etc. A probability distribution (mean and standard deviation) was estimated for each of these design parameters. Then, error analysis was used to obtain a probability distribution for the system lifetime (mean = 7.7 years, standard deviation = 1.1 years). From this, the probability that the system will achieve the design goal of 5 years lifetime is 0.993. This value represents an estimate of the degradation reliability of the system.

Lekach, V. S.↗

DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A thermal-driven graupel generation process to explain dry-season convective vigor over the Amazon

Large-eddy simulations (LESs) are conducted for each day of the intensive observation periods (IOPs) of the Green Ocean Amazon (GoAmazon) field campaign to characterize the updrafts and microphysics within deep convective cores while contrasting those properties between Amazon wet and dry seasons. Mean Doppler velocity (V dop ) values simulated using LESs are compared with 2-year measurements from a radar wind profiler (RWP) as viewed by statistical composites separated according to wet- and dry-season conditions. In the observed RWP and simulated LES V dop composites, we find more intense low-level updraft velocity, vigorous graupel generation, and intense surface rain during the dry periods compared with the wet periods. To investigate coupled updraft–microphysical processes further, single-day golden cases are selected from the wet and dry periods to conduct detailed cumulus thermal tracking analysis. Tracking analysis reveals that simulated dry-season environments generate more droplet-loaded low-level thermals than wet-season environments. This tendency correlates with seasonal contrasts in buoyancy and vertical moisture advection profiles in large-scale forcing. Employing a normalized time series of mean thermal microphysics, the simulated cumulus thermals appear to be the primary generator of cloud droplets. When subsequent thermals penetrate the ice crystal layer, droplets within the thermals interact with entrained ice crystals, which enhances riming in the thermals. This appears to be a production pathway of graupel/hail particles within simulated deep convective cores. In addition, less-diluted dry-case thermals tend to be elevated higher, and graupel grows further during sedimentation after spilling out from thermals. Therefore, greater concentrations of low-level moist thermals likely result in more graupel/hail production and associated dry-season convective vigor.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗

DOE OSTI2022

Direct Numerical Simulations of Turbulent Flow over Misaligned Traveling Waves

Direct numerical simulations of turbulent flow over prescribed traveling waves in a half-channel flow setup subject to a combined streamwise and spanwise pressure gradient are performed at a friction Reynolds number of 180. The simulations undertaken in this study consider both flow-aligned (including opposing and following) and misaligned waves as we attempt to quantify the effect of wave misalignment on turbulence statistics, the pressure drag force, and the wave attenuation rate. For the simulations, we consider three characteristic wave age values corresponding to slow-, intermediate-, and fast-moving waves. Wave misalignment is taken into account by applying a spanwise pressure gradient vertical to the traveling waves, which results in a three-dimensional turbulent flow field above the moving waves. Key flow quantities such as the mean velocity, velocity variances, and momentum fluxes are found to vary with the wave parameters, confirming the findings of previous studies.

direct numerical simulation↗

DOE OSTI2020

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗

NASA NTRS1999

On-Line Analysis of Physiologic and Neurobehavioral Variables During Long-Duration Space Missions

The goal of this project is to develop reliable statistical algorithms for on-line analysis of physiologic and neurobehavioral variables monitored during long-duration space missions. Maintenance of physiologic and neurobehavioral homeostasis during long-duration space missions is crucial for ensuring optimal crew performance. If countermeasures are not applied, alterations in homeostasis will occur in nearly all-physiologic systems. During such missions data from most of these systems will be either continually and/or continuously monitored. Therefore, if these data can be analyzed as they are acquired and the status of these systems can be continually assessed, then once alterations are detected, appropriate countermeasures can be applied to correct them. One of the most important physiologic systems in which to maintain homeostasis during long-duration missions is the circadian system. To detect and treat alterations in circadian physiology during long duration space missions requires development of: 1) a ground-based protocol to assess the status of the circadian system under the light-dark environment in which crews in space will typically work; and 2) appropriate statistical methods to make this assessment. The protocol in Project 1, Circadian Entrainment, Sleep-Wake Regulation and Neurobehavioral will study human volunteers under the simulated light-dark environment of long-duration space missions. Therefore, we propose to develop statistical models to characterize in near real time circadian and neurobehavioral physiology under these conditions. The specific aims of this project are to test the hypotheses that: 1) Dynamic statistical methods based on the Kronauer model of the human circadian system can be developed to estimate circadian phase, period, amplitude from core-temperature data collected under simulated light- dark conditions of long-duration space missions. 2) Analytic formulae and numerical algorithms can be developed to compute the error in the estimates of circadian phase, period and amplitude determined from the data in Specific Aim 1. 3) Statistical models can detect reliably in near real- time (daily) significant alternations in the circadian physiology of individual subjects by analyzing the circadian and neurobehavioral data collected in Project 1. 4) Criteria can be developed using the Kronauer model and the recently developed Jewett model of cognitive -performance and subjective alertness to define altered circadian and neurobehavioral physiology and to set conditions for immediate administration of countermeasures.

Brown, Emery N.↗

DOE OSTI2020

Global Simulation of Electron Cyclotron Harmonic Wave Instability in a Storm-Time Magnetosphere

Electron cyclotron harmonic (ECH) waves are electrostatic emissions between the ECHs and play a dominant role for precipitating energetic electrons in the magnetotail. Statistically, the ECH wave intensity is stronger at nightside and dawnside than at dayside and duskside. In this study, we, for the first time, simulate the global ECH wave evolution during a geomagnetic storm event using Ring current Atmosphere interactions Model with Self-Consistent Magnetic field (RAM-SCB) combined with a linear growth rate solver.We find that the simulation results are generally consistent with the statistical and real-time observations. The ECH wave instability is much stronger at nightside and dawnside, compared to the instability at dayside and duskside. Before a geomagnetic storm (quiet time), the unstable regions of the ECH waves lie beyond $5R_E$ with a weak instability level. During the main phase of a geomagnetic storm, the unstable regions can extend to a lower altitude $(3R_E)$ with a strong instability level. Finally, during the recovery phase, the unstable regions return to $5$ ~ $6R_E$. We also find that the inner boundary of unstable ECH wave regions is coincident with the plasmapause location during the whole geomagnetic storm event.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

Bayesian Statistical Models for Community Annoyance Survey Data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study.Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models’ summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Musical instruments↗

DOE OSTI2023

Modeling the Photoelectrochemical Evolution of Lead-Based, Mixed-Halide Perovskites Due to Photosegregation

Lead-based, mixed-halide perovskites such as methylammonium lead iodide-bromide [MAPb(I 1-x Br x ) 3 ] undergo anion photosegregation under illumination. This is observed as low band gap photoluminescence from photogenerated iodine-rich domains due to favorable band offsets that induce carrier funneling into them. Unfortunately, theoretical rationalizations of mixed-halide photosegregation are complicated by biases inherent to photoluminescence-based observations. Recent compositionally-weighted X-ray diffraction (XRD) measurements now reveal broad distributions of photosegregated stoichiometries not captured by existing photosegregation models. To better bridge experiment and theory, we perform kinetic Monte Carlo (KMC) simulations of photosegregation within the context of a band gap-based thermodynamic model, which has previously accounted for numerous experimental observations. Our KMC simulations are modified to consider high carrier density Fermi-Dirac statistics that result from carrier funneling and accumulation within photosegregated I-rich domains. Obtained KMC results reproduce broad x terminal distributions seen experimentally and illustrate how they are characterized by a central, heavily I-enriched stoichiometry. I-rich domain “drifting” during photosegregation rationalizes the long photosegregation timescales seen experimentally with drifting simultaneously producing a wake of variable stoichiometry I-rich inclusions that form the lion’s share of stoichiometric heterogeneities seen in compositionally-weighted XRD measurements. These simulations and accompanying rationalizations further reveal a general criterion for realizing favorable free energies to induce demixing. Central to the criterion is the statistical occupation of low gap inclusions in the parent alloy by excitations. Furthermore, the resulting model thus provides a general framework for conceptualizing mixed-halide perovskite light and temperature sensitivities, mediated by photocarriers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Isolating the effect of biomass burning aerosol emissions on 20th century hydroclimate in South America and Southeast Asia

Abstract Biomass burning is a significant source of aerosol emissions in some regions and has a considerable impact on regional climate. Earth system model simulations indicate that increased biomass burning aerosol emissions contributed to statistically significant decreases in tropical precipitation over the 20th century. In this study, we use the Community Earth System Model version 1 Large Ensemble (CESM1-LENS) experiment to evaluate the mechanisms by which biomass burning aerosol contributed to decreased tropical precipitation, with a focus on South America and Southeast Asia. We analyze the all-but-one forcing simulations in which biomass burning aerosol emissions are held constant while other forcings (e.g., greenhouse gas concentrations) vary throughout the 20th century. This allows us to isolate the influence of biomass burning aerosol on processes that contribute to decreasing precipitation, including cloud microphysics, the radiative effects of absorbing aerosol particles, and alterations in regional circulation. We also show that the 20th century reduction in precipitation identified in the CESM1-LENS historical and biomass burning experiments is consistent across Coupled Model Intercomparison Project Phase 5 models with interactive aerosol schemes and the CESM2 single-forcing experiment. Our results demonstrate that higher concentrations of biomass burning aerosol increases the quantity of cloud condensation nuclei and cloud droplets, limiting cloud droplet size and precipitation formation. Additionally, absorbing aerosols (e.g., black carbon) contribute to a warmer cloud layer, which promotes cloud evaporation, increases atmospheric stability, and alters regional circulation patterns. Corresponding convectively coupled circulation responses, particularly over the tropical Andes, contribute to further reducing the flow of moisture and moisture convergence over tropical land. These results elucidate the processes that affect the water cycle in regions prone to biomass burning and inform our understanding of how future changes in aerosol emissions may impact tropical precipitation over the 21st century.

Environmental Sciences & Ecology↗

DOE OSTI2021

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey quasar sample: testing observational systematics on the Baryon Acoustic Oscillation measurement

ABSTRACT Baryon Acoustic Oscillations (BAO) are considered to be a very robust standard ruler against various systematics. This premise has been tested against observational systematics, but not to the level required for the next generation of galaxy surveys such as the Dark Energy Spectroscopic Instrument (DESI) and Euclid. In this paper, we investigate the effect of observational systematics on the BAO measurement of the final sample of quasars from the extended Baryon Oscillation Spectroscopic Survey Data Release 16 in order to prepare and hone a similar analysis for upcoming surveys. We employ catalogues with various treatments of imaging systematic effects using linear and neural network-based non-linear approaches and consider how the BAO measurement changes. We also test how the variations to the BAO fitting model respond to the observational systematics. As expected, we confirm that the BAO measurements obtained from the DR16 quasar sample are robust against imaging systematics well within the statistical error, while reporting slightly modified constraints that shift the line-of-sight BAO signal by less than 1.1 per cent. We use realistic simulations with similar redshift and angular distributions as the DR16 sample to conduct statistical tests for validating the pipeline, quantifying the significance of differences, and estimating the expected bias on the BAO scale in future high-precision data sets. Although we find a marginal impact for the eBOSS QSO data, the work presented here is of vital importance for constraining the nature of dark energy with the BAO feature in the new era of big data cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Cluster-Graph Fingerprinting: A Framework for Quantitative Analysis of Machine-Learned Interatomic Model Training and Simulation Data

Machine-learned interatomic models represent a significant advancement in simulation methods, extending the predictive ability of first-principles methods to previously inaccessible length and time scales. However, the data-driven nature of these models can lead to difficult-to-detect errors that can compromise prediction accuracy. To address this challenge, we introduce a novel fingerprinting approach based on the Chebyshev Interaction Model for Efficient Simulation (ChIMES) ML-IAM graph-based descriptor. Our strategy enables efficient and statistically rigorous analysis of system configurations used in ML-IAM training and those generated by their application, e.g., in molecular dynamics simulations. We demonstrate that these fingerprints can effectively assess novelty of a configuration relative to an existing data set and determine dissimilarity among individual configurations, which are two key tasks in workflows for active learning-based ML-IAM training, data set curation, and on-the-fly uncertainty quantification.

36 MATERIALS SCIENCE↗

NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗

NASA NTRS2003

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Howell, L. W., Jr.↗

DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗