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NASA NTRS2003

Polarization Evolution of the Afterglow of GRB 030329

The association of a supernova with GRB 030329l strongly supports the collapsar model of gamma-ray bursts (GRBs), where a relativistic jet forms after the progenitor star collapses. Such jets cannot be spatially resolved because of their cosmological distances. Their existence is conjectured based on breaks in GRB afterglow light curves and the theoretical desire to reduce the GRB energy requirements. Temporal evolution of polarization may provide independent evidence for the jet structure of the relativistic outflow. Small-level polarization (approx. 1-3%) has been reported for a few bursts, but the temporal evolution of polarization properties could not be established. Here, we report polarimetric observations of the afterglow of GRB 030329 with high signal-to-noise and high sampling frequency. We establish the polarization light curve, detect sustained polarization at the percent level, and find significant variability. The data imply that the afterglow magnetic field has small coherence length and is mostly random, probably generated by turbulence, in contrast with the high polarization detected in the prompt gamma-rays from GRB 02120618. Our results suggest a different structure and origin of the magnetic field in the prompt vs. afterglow emission regions.

Greiner, Jochen↗

NASA NTRS2004

Synthesis, Characterization, and Modeling of Nanotube Materials with Variable Stiffness Tethers

Synthesis, mechanical testing, and modeling have been performed for carbon nanotube based materials. Tests using nanoindentation indicated a six-fold enhancement in the storage modulus when comparing the base material (no nanotubes) to the composite that contained 5.3 wt% of nanotubes. To understand how crosslinking the nanotubes may further alter the stiffness, a model of the system was constructed using nanotubes crosslinked with a variable stiffness tether (VST). The model predicted that for a composite with 5 wt% nanotubes at random orientations, crosslinked with the VST, the bulk Young's modulus was reduced by 30% compared to the noncrosslinked equivalent.

Frankland, S. J. V.↗

NASA NTRSDate not supplied

Artificial Neural Networks to Predict Cognitive Impairment of Rodents Subjected to Space Radiation

INTRODUCTION We use artificial neural networks (ANNs) as an example machine learning (ML) tool to predict the cognitive performance impairment of rats induced by irradiation. The experimental data in the analyses is attentional set-shifting (ATSET) test scores from a rodent model exposed to ≤15 cGy of individual galactic cosmic radiation (GCR) ions: 4He, 28Si, or 56Fe, expected for a Lunar or Mars mission [1]. This work investigates rats at a subject-based level and uses applied dose and performance scores taken before irradiation to predict whether a rat will be impaired when irradiated. The results of this study are significant to crewed space missions as they support the potential of predicting an astronaut’s impairment in a specific task before spaceflight through the implementation of appropriately trained ML tools. METHODS Data used in this work are scores from the ATSET, a multi-stage constrained cognitive flexibility test [2]. Our computational model utilizes the number of attempts to reach the criterion to pass a stage as a behavioral performance measure for rats. We use the post-irradiation scores, generate thresholds from cumulative distribution plots of non-irradiated rats, and calculate the percent of irradiated rats whose scores fall below the threshold to infer how each radiation type/dose affects a population. Rats scoring above the threshold are labeled impaired while the others are non-impaired. We then employ ANNs as a typical ML technique, and use each subject’s individual scores taken before radiation along with the applied dose, to predict their personal susceptibility to cognitive impairment due to space radiation exposure. RESULTS AND CONCLUSION A significant finding is the exhibition of a dose-dependent increasing probability of impairment for 1 to 10 cGy of 28Si or 56Fe in the simple discrimination (SD) stage of the ATSET, and for 1 to 10 cGy of 56Fe in the compound discrimination (CD) stage. On a subject-based level, implementing ML classifiers such as ANNs identifies rats that have a higher tendency for impairment after GCR exposure [1]. The receiver operating characteristic (ROC) and the precision-recall (PR) curves of the ML models show a better prediction of impairment when 56Fe is the ion in question in both SD (Figure 1) and CD stages. They, however, do not depict impairment due to 4He in SD (Figure 1) and 28Si in CD, suggesting no dose-dependent impairment response in these cases. In this work, “good” prediction pertains to “better-than-random-chance”, due to the limited sample size and the high inter- and intra-individual variabilities in response to brain stimulation paradigms, as applicable to both animals and humans. More behavioral tests and biomarkers should be investigated on the same subjects, to be fed to the ML models to capture the agents responsible for performance alterations of some individuals versus others.

machine learning↗

NASA NTRSDate not supplied

Machine Learning Models to Predict Cognitive Impairment of Rodents Subjected to Space Radiation

machine learning↗

DOE OSTI2013

A Method for Optimizing Waste Management and Disposal Practices Using a Group-Based Uncertainty Model for the Analysis of Characterization Data - 13191

It is a universal requirement for characterization of radioactive waste, that the consignor shall calculate and report a Total Measurement Uncertainty (TMU) value associated with each of the measured quantities such as nuclide activity. For Non-destructive Assay systems, the TMU analysis is typically performed on an individual container basis. However, in many cases, the waste consignor treats, transports, stores and disposes of containers in groups for example by over-packing smaller containers into a larger container or emplacing containers into groups for final disposal. The current standard practice for container-group data analysis is usually to treat each container as independent and uncorrelated and use a simple summation / averaging method (or in some cases summation of TMU in quadrature) to define the overall characteristics and associated uncertainty in the container group. In reality, many groups of containers are assayed on the same system, so there will be a large degree of co-dependence in the individual uncertainty elements. Many uncertainty terms may be significantly reduced when addressing issues such as the source position and variability in matrix contents over large populations. The systematic terms encompass both inherently 'two-directional' random effects (e.g. variation of source position) and other terms that are 'one-directional' i.e. designed to account for potential sources of bias. An analysis has been performed with population groups of a variety of non-destructive assay platforms in order to define a quantitative mechanism for waste consignors to determine overall TMU for batches of containers that have been assayed on the same system. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2014

Differential Motion Between Mediastinal Lymph Nodes and Primary Tumor in Radically Irradiated Lung Cancer Patients

Purpose/Objective: In patients with locally advanced lung cancer, planning target volume margins for mediastinal lymph nodes and tumor after a correction protocol based on bony anatomy registration typically range from 1 to 1.5 cm. Detailed information about lymph node motion variability and differential motion with the primary tumor, however, is lacking from large series. In this study, lymph node and tumor position variability were analyzed in detail and correlated to the main carina to evaluate possible margin reduction. Methods and Materials: Small gold fiducial markers (0.35 × 5 mm) were placed in the mediastinal lymph nodes of 51 patients with non-small cell lung cancer during routine diagnostic esophageal or bronchial endoscopic ultrasonography. Four-dimensional (4D) planning computed tomographic (CT) and daily 4D cone beam (CB) CT scans were acquired before and during radical radiation therapy (66 Gy in 24 fractions). Each CBCT was registered in 3-dimensions (bony anatomy) and 4D (tumor, marker, and carina) to the planning CT scan. Subsequently, systematic and random residual misalignments of the time-averaged lymph node and tumor position relative to the bony anatomy and carina were determined. Additionally, tumor and lymph node respiratory amplitude variability was quantified. Finally, required margins were quantified by use of a recipe for dual targets. Results: Relative to the bony anatomy, systematic and random errors ranged from 0.16 to 0.32 cm for the markers and from 0.15 to 0.33 cm for the tumor, but despite similar ranges there was limited correlation (0.17-0.71) owing to differential motion. A large variability in lymph node amplitude between patients was observed, with an average motion of 0.56 cm in the cranial-caudal direction. Margins could be reduced by 10% (left-right), 27% (cranial-caudal), and 10% (anteroposterior) for the lymph nodes and −2%, 15%, and 7% for the tumor if an online carina registration protocol replaced a protocol based on bony anatomy registration. Conclusions: Detailed analysis revealed considerable lymph node position variability, differential motion, and respiratory motion. Planning target volume margins can be reduced up to 27% in lung cancer patients when the carina registration replaces bony anatomy registration.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Topology optimization under uncertainty via non-intrusive polynomial chaos expansion

This paper presents a systematic approach for topology optimization under uncertainty that integrates non-intrusive polynomial chaos expansion with design sensitivity analysis for reliability-based and robust topology optimization. Uncertainty is introduced in loading and in geometry to address the manufacturing variability. The manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field. Response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments, failure probabilities and their sensitivities. The number of simulations is reduced for linear structures under loading uncertainty by means of superposition. Efficiency of the non-intrusive polynomial chaos approach is highlighted by comparison with the Monte Carlo method in terms of the number of simulations. To demonstrate the effect of uncertainty, optimized designs that consider uncertainty are compared to those that do not. Finally, comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability-based and worst case designs.

42 ENGINEERING↗

DOE OSTI2018

Efficient and Collision-Free Anticipative Cruise Control in Randomly Mixed Strings

Connected intelligent vehicle following can improve safety and efficiency compared to today's road transport, but real traffic in the near future will not provide an ideal setting for its deployment. Unconnected human-driven vehicles will follow variable behavior patterns that combine with differences in dynamic capability to create heterogeneous scenarios. In this paper, connected automated vehicles employ model predictive control for following in traffic that may include both heavy and passenger vehicles at quasi-random positions. Adding further realism, some quasi-randomly mixed vehicles are completely unconnected and equipped with the reactive intelligent driver model using pseudorandom parameters. A mixed-integer quadratic programming formulation adapts the predictive algorithm to diverse powertrain operating point constraints. The preceding vehicle's control input is estimated from velocity and brake light observations and used to probabilistically generate a preview for the ego vehicle. Here, a terminal constraint designed using particle kinematics prevents collisions due to shortsightedness. Results are simulated at various heavy and predictive vehicle concentrations in the presence of packet loss. Linear fuel economy improvements between 1.4% and 1.9% per 10% increase in predictive vehicle penetration rate are shown.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS2002

Configuration and Intraseasonal Duration of Interannual Anomalies of the Great Plains Low-Level Jet

Despite the fact that the low-level jet of the southern Great Plains (the GPLLJ) of the U.S. is primarily a nocturnal phenomenon that virtually vanishes during the daylight hours, it is one of the most persistent and stable climatological features of the low-level continental flow during the warm-season months, May through August. We have used significant-level data to validate the skill of the GEOS-1 Data Assimilation System (DAS) in realistically detecting this jet and inferring its structure and evolution. We have then carried out a 15-year reanalysis with the GEOS-1 DAS to determine its climatology and mean diurnal cycle and to study its interannual variability. Interannual anomalies of the meridional flow associated with the GPLLJ are much smaller than the mean diurnal fluctuations, than random intraseasonal anomalies, and than the mean wind itself. There are three maxima of low-level meridional flow variance over the Great Plains and the Gulf of Mexico: a 1.2 m2 s-2 peak over the southeast Texas, to the east and south of the mean velocity peak, a 1.0 m2 s-2 peak over the western Gulf of Mexico, and a .8 m2 s-2 peak over the upper Great Plains (UGP), near the Nebraska/South Dakota border. Each of the three variance maxima corresponds to a spatially coherent, jet-like pattern of low-level flow interannual variability. There are also three dominant modes of interannual variability corresponding to the three variance maxima, but not in a simple one-to-one relationship. Cross-sectional profiles of mean southerly wind over Texas remain relatively stable and recognizable from year to year with only its eastward flank showing significant variability. This variability, however, exhibits a distinct, biennial oscillation during the first six to seven years of the reanalysis period and only then. This intermittent biennial oscillation (IBO, one of the three modes discussed in the previous paragraph) in the lowlevel flow is restricted to the region surrounding eastern Texas and is also evident in the NCEP/NCAR reanalysis data set from about 1978 to 1985 or 1986 and again from 1995 to 2000. It is evident as well in surface pressure in both the GEOS-1 and NCEP/NCAR sets. The interannual anomalies do not necessarily persist uniformly throughout an entire season, but can fluctuate from one part of the season to the next. To estimate the characteristic sub-seasonal time scales for coherence of these fluctuations, we have taken the weekly anomaly of low-level wind at each point of the domain from the climatological average for that given point and that given week of the season and computed the covariance of its fluctuations over all weeks and over all years with the weekly climatological anomaly of the meridional wind at each of the three reference points discussed above. The typical duration of a coherent interannual anomaly within a given warm season increases with decreasing latitude from 2 to 3 weeks over the UGP, to 6 to 7 weeks over eastern Texas. Coherence over the western Gulf of Mexico is intermediate between the two with a typical duration of 4 to 5 weeks. There appears to be evidence that the interannual anomalies over Texas the Gulf propagate to the UGP after a week and those over the Gulf propagate there after 2 to 3 weeks. There also appears to be some reverse propagation of interannual anomalies over the UGP to Texas and to the Gulf after a period of about one week. The interannual anomalies in southerly flow over eastern Texas seem to correlate well with interannual anomalies of surface temperature and (negative) ground wetness and over western Texas.

Helfand, H. M.↗

DOE OSTI2015

Phase diagram of hopping conduction mechanisms in polymer nanofiber network

Network formation by nanofiber crosslinking is usually in polymer materials as application in organic semiconductor devices. Electron hopping transport mechanisms depend on polymer morphology in network. Conducting polymers morphology in a random network structure is modeled by a quasi-one-dimensional system coupled of chains or fibers. We observe the varying hopping conduction mechanisms in the polyaniline nanofibers of the random network structure. The average diameter d of the nanofibers is varied from approximately 10 to 100 nm. The different dominant hopping mechanisms including Efros-Shklovskii variable-range hopping (VRH), Mott VRH, and nearest-neighbor hopping are dependent on temperature range and d in crossover changes. The result of this study is first presented in a phase diagram of hopping conduction mechanisms based on the theories of the random network model. The hopping conduction mechanism is unlike in normal semiconductor materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Disturbance differentially affects alpha and beta diversity of ants in tallgrass prairies

Abstract Biodiversity conservation requires understanding how disturbance influences biodiversity patterns at multiple spatial scales. Because the total diversity of species within a given region (γ diversity) is influenced by both local diversity (α diversity) and dissimilarity in community composition (β diversity), understanding disturbance effects on both components of diversity is essential, especially if disturbance impacts α and β diversities differently. In this three‐year study, we examined how a disturbance (annual harvesting of grasslands) and environmental gradients in the proportion of sand locally, habitat size, and landscape diversity influenced the abundance and α and β diversities of ants within tallgrass prairie habitat in Wisconsin. We used a null‐model approach to examine how harvest and environmental factors influence β diversity. Following three years of treatments, we found that ant abundance was greater in harvested sites compared to control sites and ant abundance was positively correlated with soil sandiness. We also found that α diversity was lower in harvested sites compared to control sites and none of the measured environmental gradients influenced α diversity. The effects of harvest on α‐diversity patterns may have been mediated through the competitive interactions of the two dominant ant species ( Formica montana and Lasius neoniger ). In contrast, β diversity (after adjusting for random effects and changes to α diversity) was higher in harvest sites compared to control sites, and variability in community composition was largely driven by the occurrence of rare species. The proportion of sand in the local habitat and habitat size positively influenced β diversity suggesting that community dissimilarity was due in part to environmental filtering and the size of species pools. Because biomass harvest had contrasting effects on ant α and β diversities, trade‐offs in maintaining α vs. β diversity might need to be considered in land management and conservation efforts.

Kim, Tania N.↗

DOE OSTI2023

Multi-site evaluation of stratified and balanced sampling of soil organic carbon stocks in agricultural fields

Estimating soil organic carbon (SOC) stocks in agricultural fields is essential for environmental and agronomic research, management, and policy. Stratified sampling is a classic strategy for estimating mean soil properties, and has recently been codified in SOC monitoring protocols. However, for the specific task of estimating the SOC stock of an agricultural field, concrete guidance is needed for which covariates to stratify on and how much stratification can improve estimation efficiency. It is also unknown how stratified sampling of SOC stocks compares to modern alternatives, notably doubly balanced sampling. To address these gaps, we collected high-density (average of 7 samples ha -1 ) and deep (average of 75 cm) measurements of SOC stocks at eight commercial fields under maize-soybean production in two US Midwestern states. We combined these measurements with a Bayesian geostatistical model to evaluate stratified and balanced sampling strategies that use a set of readily-available geographic, topographic, spectroscopic, and soil survey data. We examined the number of samples needed to achieve a given level of SOC stock estimation accuracy. While stratified sampling using these variables enables an average sample size reduction of 17% (95% CI, 11% to 23%) compared to simple random sampling, doubly balanced sampling is consistently more efficient, reducing sample sizes by 32% (95% CI, 25% to 37%). The data most important to these efficiency gains are a remotely-sensed SOC index, SSURGO estimates of SOC stocks, and the topographic wetness index. We conclude that in order to meet the urgent challenge of climate change, SOC stocks in agricultural fields could be more efficiently estimated by taking advantage of this readily-available data, especially with doubly balanced sampling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

Here, we use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile. On top of this mean shrinkage, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening. Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events. In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2016

WE-H-BRC-06: A Unified Machine-Learning Based Probabilistic Model for Automated Anomaly Detection in the Treatment Plan Data

Purpose: The purpose of this work was to investigate the ability of a machine-learning based probabilistic approach to detect radiotherapy treatment plan anomalies given initial disease classes information. Methods In total we obtained 1112 unique treatment plans with five plan parameters and disease information from a Mosaiq treatment management system database for use in the study. The plan parameters include prescription dose, fractions, fields, modality and techniques. The disease information includes disease site, and T, M and N disease stages. A Bayesian network method was employed to model the probabilistic relationships between tumor disease information, plan parameters and an anomaly flag. A Bayesian learning method with Dirichlet prior was useed to learn the joint probabilities between dependent variables in error-free plan data and data with artificially induced anomalies. In the study, we randomly sampled data with anomaly in a specified anomaly space.We tested the approach with three groups of plan anomalies – improper concurrence of values of all five plan parameters and values of any two out of five parameters, and all single plan parameter value anomalies. Totally, 16 types of plan anomalies were covered by the study. For each type, we trained an individual Bayesian network. Results: We found that the true positive rate (recall) and positive predictive value (precision) to detect concurrence anomalies of five plan parameters in new patient cases were 94.45±0.26% and 93.76±0.39% respectively. To detect other 15 types of plan anomalies, the average recall and precision were 93.61±2.57% and 93.78±3.54% respectively. The computation time to detect the plan anomaly of each type in a new plan is ∼0.08 seconds. Conclusion: The proposed method for treatment plan anomaly detection was found effective in the initial tests. The results suggest that this type of models could be applied to develop plan anomaly detection tools to assist manual and automated plan checks. The senior author received research grants from ViewRay Inc. and Varian Medical System.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1977

Control logic to track the outputs of a command generator or randomly forced target

A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).

Trankle, T. L.↗

NASA NTRS2002

Causes of Long-Term Drought in the United States Great Plains

The United States Great Plains (USGP) experienced a number of multi-year droughts during the last century, most notably the droughts of the 1930s and 1950s. This study examines the causes of such droughts using ensembles of long term (1930-1999) simulations carried out with the NASA Seasonal-to-Interannual Prediction Project (NSIPP-1) atmospheric general circulation model (AGCM) forced with observed sea surface temperatures (SSTs). The results show that the model produces long-term (multi-year) variations in the USGP precipitation that are similar to those observed. A correlative analysis suggests that the ensemble mean low frequency (time scales longer than about 6 years) rainfall variations in the USGP are linked to a pan-Pacific pattern of SST variability that is the leading empirical orthogonal function (EOF) in the low frequency SST data. The link between the SST and the Great Plains precipitation is confirmed in idealized AGCM simulations, in which the model is forced by the 2 polarities of the pan-Pacific SST pattern. The idealized simulations further show that it is primarily the tropical part of the SST anomalies that influence the USGP. As such, the USGP tend to have above normal precipitation when the tropical Pacific SSTs are above normal, while there is a tendency for drought when the tropical SSTs are cold. The upper tropospheric response to the pan-Pacific SST EOF shows a global-scale pattern with a strong wave response in the Pacific and a substantial zonally-symmetric component in which USGP pluvial (drought) conditions are associated with reduced (enhanced) heights throughout the extra-tropics. The potential predictability of rainfall in the USGP associated with SSTs is rather modest, with on average about 1/3 of the total low frequency rainfall variance forced by SST anomalies. Further idealized experiments with climatological SST, suggest that the remaining low frequency variance in the USGP precipitation is the result of interactions with soil moisture. In particular, simulations with soil moisture feedback show a six-fold increase in the variance in annual USGP precipitation compared with simulations in which the soil feedback is excluded. In addition to increasing variance, the interactions with the soil introduce year-to-year memory in the hydrological cycle that is consistent with a red noise process, in which the low frequencies in the deep soil are the result of integrating a net forcing (precipitation-evaporation-runoff) that is white noise on interannual time scales. As such, the role of low frequency SST variability is to introduce a bias to the net forcing on the soil moisture that drives the random process preferentially to either wet or dry conditions.

Schubert, Siegfried D.↗

NASA NTRS2003

Causes of Long-Term Drought in the United States Great Plains

This study examines the causes of long term droughts in the United States Great Plains (USGP). The focus is on the relative roles of slowly varying SSTs and interactions with soil moisture. The results from ensembles of long term (1930-1999) simulations carried out with the NASA Seasonal-to- Interannual Prediction Project (NSIPP-1) atmospheric general circulation model (AGCM) show that the SSTs account for about 1/3 of the total low frequency rainfall variance in the USGP. Results from idealized experiments with climatological SST suggest that the remaining low frequency variance in the USGP precipitation is the result of interactions with soil moisture. In particular, simulations with soil moisture feedback show a five-fold increase in the variance in annual USGP precipitation compared with simulations in which the soil feedback is excluded. In addition to increasing variance, the interactions with the soil introduce year-to-year memory in the hydrological cycle that is consistent with a red noise process, in which the deep soil is forced by white noise and damped with a time scale of about 2 years. As such, the role of low frequency SST variability is to introduce a bias to the net forcing on the soil moisture that drives the random process preferentially to either wet or dry conditions.

Schubert, Siegfried D.↗

NASA NTRS2020

Electromagnetic Scattering by Discrete Random Media Illuminated by a Gaussian Beam II: Solution of the Radiative Transfer Equation

In this paper, we present numerical methods for solving the phenomenological scalar radiative transfer equation for a discrete random medium illuminated by a Gaussian beam. These rely on the Fourier transform method for the horizontal variables and the discrete ordinate method with matrix exponential for solving the underlying one-dimensional radiative transfer equation in the wavenumber domain. The problem of a Gaussian beam at oblique and normal incidence, as well as, the searchlight problem are treated. A complete description of the methods and the numerical algorithms is provided.

Gaussian beam↗