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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Radiative Heat Transfer and 2D Transition Metal Dichalcogenide Materials

Here we study the radiative heat transfer power in the family of transition metal dichalcogenide monolayers in their H- and T-symmetries. For this purpose, the electronic and optical properties computed from first-principles are used in effective models to understand the emerging scaling laws for metals and semiconductors as well as specific material signatures as control knobs for radiative heat transfer. Our combined approach of analytical modeling with properties from ab initio simulations can be used for other materials families to build a materials database for radiative heat transfer.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tensorized Interior Radiative Heat Transfer for a Scalable and Calibrated Building Energy Simulator

Building energy simulation is a critical tool for developing and testing advanced control strategies, such as Reinforcement Learning (RL), to provide demand flexibility and affordable energy costs. The recently introduced Smart Buildings Control Suite (sbsim) provides a lightweight, scalable, and data-calibrated simulation environment based on a 2D finite-difference model. However, the initial model primarily focused on conductive and convective heat transfer, neglecting the significant impact of long-wave radiative heat exchange between interior surfaces. This paper presents a significant extension to the sbsim framework by incorporating a physically-grounded model for interior radiative heat transfer. Our primary contribution is the development and integration of a fully tensorized radiative heat transfer module, which preserves the computational efficiency and scalability of the original simulator. This was achieved by developing a pipeline for view factor calculation, including an algorithm to identify directly seeing surfaces within complex floor plans, and formulating the net radiation equations for efficient execution on modern hardware accelerators. We validate the numerical accuracy of our tensorized implementation by comparing its results against a traditional iterative approach, demonstrating identical outcomes. This enhancement increases the physical fidelity of sbsim, enabling more accurate training of RL agents for building energy optimization.

Ham, Sang woo↗
DOE OSTI2026

Data for Clumping Index Estimation With 30°-tilted Cameras in Row Crops: Evaluation of Methods and Segment Size Effects

The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.

Modeling↗
DOE OSTI2026

A Comparison of Three Neodymium Atomic Data Sets for Kilonova Modeling

We examine the impact of input neodymium (Nd) atomic data on the light curves and spectra of kilonovae (KNe), probing the sensitivity of kilonova observables to the atomic physics of this important lanthanide element. We use the SuperNu Monte Carlo radiative transfer code, simulating a simple semianalytic 1D kilonova (KN) with a pure Nd atmosphere, fixing the radiative transfer method while using input atomic data generated by three different codes: the LANL suite of atomic physics codes, HULLAC, and Autostructure. We see that the choice of atomic data significantly shapes the resulting light curves and spectra. Peak bolometric luminosities differ by a ratio of nearly 1.5 between HULLAC/Autostructure and LANL data sets. Moreover, we observe significant near- to mid-IR differences in the structure of the spectra. We specifically attribute these differences to the choice of atomic data for neutral Nd I. Many of the results here have been adapted from a presentation at “Radiative Transfer and Atomic Physics of Kilonovae” in Stockholm, 2023. We additionally present a LANL data set with energies calibrated to available values in the NIST Atomic Spectra Database, and demonstrate that this calibration also significantly affects IR spectral structure at late time. The substantial differences in KN observables that arise from tuning the atomic data of just one lanthanide element highlight the special attention that must be paid to atomic physics uncertainties when modeling KNe, from AT2017gfo to beyond.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Multi-physics Modeling of Radiative Heat Transfer and Fluid Flow for the Reactor Cavity Cooling System

High-temperature gas-cooled reactors (HTGRs) are notable for their high thermal efficiency and potential for combined heat and power applications. These reactors are particularly appealing due to their advanced passive safety features. HTGRs utilize passive safety systems that function without requiring active components like pumps or compressors during emergencies. These reactor designs depend on a Reactor Cavity Cooling System (RCCS) to manage decay heat removal from the reactor pressure vessel (RPV) during accident conditions. The RCCS consists of vertical rectangular channels known as "risers" or riser ducts positioned around the RPV. These risers receive heat from the RPV through both convective and radiative heat transfer mechanisms. Understanding the interplay of multiple physical phenomena, such as fluid dynamics, heat transfer, and neutron interactions, is essential for the effective design and operation of nuclear reactors, particularly for systems like the RCCS. Multi-physics simulations provide a comprehensive approach to studying these interactions, offering detailed insights and enhancing accuracy. They are especially important in RCCS designs, where the interaction between radiative and convective heat transfer can significantly impact system performance. By leveraging multi-physics simulations, complex reactor behaviors can be modeled without compromising the fidelity of the underlying physical processes. This work aims to establish a robust methodology for coupling multiple physical processes in an air-cooled RCCS. By focusing on validating this multi-physics approach, the study involves designing test cases that simulate various conditions to verify the numerical models employed. The outcomes of this research will provide critical insights for accurately modeling and optimizing complex nuclear systems like the RCCS.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Characterizing leaf-scale fluorescence with spectral invariants

Sun-induced chlorophyll fluorescence (SIF) is increasingly recognized as a non-destructive probe for tracking terrestrial photosynthesis. Emerging developments in spectral invariants theory provide an innovative and efficient approach for representing SIF radiative transfer processes at the canopy scale. However, modeling leaf-scale fluorescence based on the spectral invariants properties (SIP) remains underexplored. In this study, the spectral invariants theory is employed for the first time to model the leaf-scale total, backward and forward fluorescence (leaf-SIP SIF). The leaf-SIP SIF model separates the leaf-scale radiative transfer process into two distinct components: the wavelength-dependent one associated with leaf biochemical properties, and the wavelength-independent component linked to leaf structural characteristics. The leaf structure-related effects are characterized by two spectrally invariant parameters: the photon recollision probability (p) and the scattering asymmetry parameter (q), which are parameterized using the directly measurable leaf dry matter. Evaluation against field measurements shows that the proposed leaf-SIP SIF model has a good performance, with coefficient of determination (R 2 ) of 0.89, 0.89, 0.90 and root mean squared errors (RMSE) of 1.28, 0.69, 0.74 Wm -2 µm -1 sr -1 , respectively for the total, backward, and forward fluorescence (660–800 nm). The leaf-SIP SIF model with a more concise formulation demonstrates comparable performance with the widely used Fluspect model. Further, the leaf-SIP SIF model provides a simple and efficient approach for simulating leaf-scale fluorescence, with the potential to be integrated into a unified SIP-based model framework for simulating the radiative transfer processes across the soil-leaf-canopy-atmosphere continuum.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Temperature Field Reconstruction of Surfaces Heated Through Radiative Heat Transfer Using Convolutional Neural Networks

Microreactors could play a crucial role in decarbonizing our energy portfolio. However, their development and implementation come with specific challenges, particularly regarding cost. Due to their compact size and the harsh operational environment, collecting real-time data on reactor operation can be challenging. Many probe designs are unable to withstand extreme conditions (e.g., temperature, radiation) in the reactor. In this context, using convolutional neural networks (CNNs) can pave the way for developing a nonintrusive approach that relies solely on ex-core sensors. A well-trained physics-informed CNN can reconstruct the distribution of a given physical quantity over a domain using only a few sensors, allowing us to reconstruct the desired field distribution even in a limited space or complex geometries where a large array of sensors is impractical. In this work, we present the initial steps toward developing a real-time tool for monitoring the thermal behavior of nuclear reactor pressure vessels. Based on an experimental setup, a computational model using the Multiphysics Object-Oriented Simulation Environment (moose) framework was built, where the Ray Tracing and Heat Conduction modules were used to evaluate the temperature distribution over a convex metal surface heated through radiative heat transfer. This metal surface represents a section of a heated nuclear reactor vessel wall. The model also accounts for solid mechanics physics through the moose Solid Mechanics module. In situ experimental data, acquired from a Texas A&M facility, were used to validate the computational model. Part of the data generated by the moose model was used to train the convolutional neural network to reconstruct the vessel wall's outer surface temperature. The CNN generalization was then compared against the experimental and computational data.

Aldeia Machado, Luiz Carlos↗
DOE OSTI2025

Molecular theory capability: LANL-PEM-Atomic implements universal descriptions of molecular photoionization

Photoionization of atomic ions, the process through which atoms in bound states absorb radiation by losing electrons, is a vital part of describing radiative transfer in mission-relevant dynamics. The photoionization of molecules dominates radiative transfer of ultraviolet (UV) and extreme UV (EUV) radiation in colder atmospheres (temperature < 30,000 degrees Kelvin). Consequently, air, which is quite transparent to our eyes (i.e., in the visible frequency regime) is remarkably opaque to radiation in much of the UV and EUV frequency regimes. This opacity makes air and other gas systems quite efficient at absorbing UV and EUV radiation, which heats the gas until ionization makes it transparent. This effect is important in describing a host of relevant phenomena, ranging from charge separation in high-altitude nuclear events and the dynamics of a nuclear fireball to the electrostatic discharges (sparks) that complicate weapons disassembly at Pantex.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Sensitivity of Simulated Polar Climate to Improved Partitioning of Spectral Solar Irradiance Between Visible and Near‐Infrared Bands

The solar radiative processes that contribute to Earth's surface and atmospheric energy budgets are strongly dependent on wavelength. For example, snow and water vapor become more absorptive as incident radiation shifts from visible (VIS) to near-infrared (NIR) wavelengths. Some earth system models (ESMs) aggregate solar radiation into just two bands (VIS and NIR) partitioned at 0.7 μm for transmission between the atmospheric and surface components. In the widely used radiative transfer model RRTMG_SW this partition is near the center of the overlap spectral band spanning 0.625–0.778 μm, whose flux is often approximated as being evenly divided between the VIS and NIR surface bands. Using a hyperspectral radiative transfer model, we show that the fractional downwelling surface flux within the overlap band is usually distributed about 55.5%:44.5% VIS:NIR. This improved approximation shifts as much as 4.27 W m −2 from the NIR to the VIS band, leading to an instantaneous decrease in surface absorption of up to 0.91 W m −2 over snow-covered surfaces. Century-long fully coupled ESM simulations show surface absorption over snow decreases by over 1.6 W m −2 . The coupled response in sea ice regions amplifies the initial forcing ten-fold, and increases seasonal sea ice area by up to 4.9%. These results highlight the importance of accurately representing the spectral distribution of solar radiation in the cryosphere.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Leveraging transfer learning and leaf spectroscopy for leaf trait prediction with broad spatial, species, and temporal applicability

Accurate and reliable prediction of leaf traits is crucial for understanding plant adaptations to environmental variation, monitoring terrestrial ecosystems, and enhancing comprehension of functional diversity and ecosystem functioning. Currently, various approaches (e.g., statistical, physical models) have been developed to estimate leaf traits through hyperspectral remote sensing and leaf spectroscopy. However, the absence of high-performing, transferable, and stable models across various domains of space, plant functional types (PFTs) and seasons hinder our ability to quantify and comprehend spatiotemporal variations in leaf traits. This study proposes robust and highly transferable models for better predicting leaf traits with hyperspectral reflectance. Initially, three datasets were assembled, pairing common leaf traits — chlorophyll (Chla+b), carotenoids (Ccar), leaf mass per area (LAM), equivalent water thickness (EWT) — with leaf spectra measurements collected across diverse geographic locations in the U.S. and Europe, PFTs, and seasons. Measurements were acquired using spectroradiometers (e.g., ASD FieldSpec 3/4/Pro and SVC HR-1024i) with integrating spheres, leaf clips, and contact probes. Here, we then developed transfer learning-based hybrid models that incorporated the domain knowledge of radiative transfer models (RTMs) through pretraining processes and were well-constrained by fine-tuning with field measurements. Through comparison with other state-of-the-art statistical models, including partial-least squares regression (PLSR) and Gaussian Process Regression (GPR), as well as pure physical models, we found that the proposed transfer learning models achieved better predictive performance and higher transferability. Specifically, compared to other statistical models and pure RTMs, the transfer learning model exhibited higher coefficient of determination (R 2 ) values with range of 0.01 to 0.79, lower normalized root mean square error (NRMSE) with range of 0.06 % to 33.25 % in model performance. Additionally, the models exhibited improved transferability, with higher R 2 values range from 0.04 to 0.32, lower NRMSE range from 0.08 % to 30.81 %. The findings underscore that transfer learning models through integrating domain knowledge from RTMs and limited observations, can harness the advantages of both RTMs and statistical models and serve as a promising approach for effectively predicting leaf traits.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

LANL T1 t25_mlgpu

The CPU allocation was primarily used for nucleosyn thesis calculations using LANL’s PRISM code, radiative transfer simulations using LANL’s SuperNu code, and parameter inference of the radiative transfer simulations. Below, I document all relevant publications where Inti tutional Computing (IC) resources were used in relation to this allocation and their scientific impacts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Inferring Neutron Star Merger Ejecta Morphology with Kilonovae

In this study we incorporate a new grid of kilonova simulations produced by the Monte Carlo radiative transfer code SuperNu in an inference pipeline for astrophysical transients and evaluate their performance. These simulations contain four different two-component ejecta morphology classes. We analyze follow-up observational strategies by Vera Rubin Observatory in optical and James Webb Space Telescope (JWST) in mid-infrared (MIR). Our analysis suggests that, within these strategies, it is possible to discriminate between the four different morphologies only when late-time JWST observations in MIR are available. We conclude that follow-ups by the new Vera Rubin Observatory alone are not sufficient to determine ejecta morphology. Additionally, we make comparisons between surrogate models based on radiative transfer simulation grids by SuperNu and POSSIS, by analyzing the historic kilonova AT2017gfo that accompanied the gravitational wave event GW170817. We show that both SuperNu and POSSIS models provide similar fits to photometric observations but their qualitative interpretations differ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

RSPECT: A PROSPECT-based model incorporating the real structure of rice leaves

Radiative transfer models (RTMs) describe how light is absorbed, scattered, and transmitted within leaves by simulating mechanistic light propagation processes. The PROSPECT model is based on measurable parameters (the leaf biochemical content) and a non-measurable parameter (the leaf anatomical structure represented by the leaf structure parameter (N)). The effect of N on the optical properties of leaves has been investigated through a number of local and global sensitivity analyses. Other studies have directly evaluated the effect of the leaf anatomical structure on spectral reflectance, particularly in the near infrared region. However, the relationship between N and the anatomical structure is unclear. Here, in this study, we leveraged eLeaf, a ray tracing-based 3D rice leaf simulator, to establish relationships between leaf anatomical features and spectral properties, enabling us to replace N in the PROSPECT-4 model with measurable leaf anatomical parameters and develop the RSPECT model. The leaf thickness at minor vein, leaf thickness at bulliform cells, mesophyll thickness at minor vein, and distance between two minor veins could be used to predict N effectively. The RSPECT model achieved spectral simulation accuracy comparable to PROSPECT-4 and was more suitable for parameter inversion of the physical and chemical properties of rice leaves, with relative root mean square errors of 7.4% for chlorophyll content, 5.6% for equivalent water thickness, and 7.5% for dry matter content. In conclusion, RSPECT improves radiative transfer modeling by integrating measurable anatomical features and provides a framework for extending this approach to other vegetation types.

hyperspectral↗
DOE OSTI2026

Photon (Non)Conservation in the Reduced Speed of Light Approximation and How to (Almost) Fix It

The "Reduced Speed of Light" (RSL) approximation is commonly used to speed up radiative transfer calculations in cosmological simulations. However, it has been shown previously that the RSL approximation leads to photon non-conservation when the radiation field is rapidly evolving in time. I show that these missing photons can be counted exactly for some numerical schemes. Adding them back into a simulation, however, is a much harder task. I show one example of such a scheme, which achieves sub-percent accuracy on simple tests. Unfortunately, the scheme performs much worse on semi-realistic simulations of cosmic reionization, leading to a faster overlap and significant errors in the point-wise comparison of the RSL radiation field with the reference simulation that maintains the full speed of light for the radiative transfer.

Gnedin, Nickolay Y. [Fermilab; Chicago U., KICP; C↗
DOE OSTI2025

A Unified Interpretation of Variability in Precipitation Isotope Ratios

Abstract Several mechanisms have been proposed to explain why the isotope ratios of precipitation vary in space and time and why they correlate with other climate variables like temperature and precipitation. Here, we argue that this behavior is best understood through the lens of radiative transfer, which treats the depletion of atmospheric vapor transport by precipitation as analogous to the attenuation of light by absorption or scattering. Building on earlier work by Siler et al., we introduce a simple model that uses the equations of radiative transfer to approximate the two-dimensional pattern of the oxygen isotope composition of precipitation ( δ p ) from monthly mean hydrologic variables. The model accurately simulates the spatial and seasonal variability in δ p within a state-of-the-art climate model and permits a simple decomposition of δ p variability into contributions from gradients in evaporation and the length scale of vapor transport. Outside the tropics, δ p is mostly controlled by gradients in evaporation, whose dependence on temperature explains the positive correlation between δ p and temperature (i.e., the temperature effect). At low latitudes, δ p is mostly controlled by gradients in the transport length scale, whose inverse relationship with precipitation explains the negative correlation between δ p and precipitation (i.e., the amount effect). This suggests that the temperature and amount effects are both mostly explained by the variability in upstream rainout, but they reflect distinct mechanisms governing rainout at different latitudes. Significance Statement The isotopic composition of precipitation has long been used to make inferences about past climates based on its observed relationship with precipitation in the tropics and with temperature at higher latitudes. These relationships—known as the “amount effect” and “temperature effect,” respectively—have been attributed to many different mechanisms, most of which are thought to operate at either high or low latitudes but not both. Here, we present a unified framework for interpreting the isotope variability that can explain the latitude dependence of the temperature and amount effects despite making no distinction between high and low latitudes. Although our results are generally consistent with certain interpretations of the amount effect, they suggest that the temperature effect is widely misunderstood.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

University of Miami G-band Vapor Radiometer Calibration (UMGVR_CAL) Field Campaign Report

Cold-air outbreak (CAO) clouds in the Arctic are commonly mixed-phase (MP); however, the partitioning of the amount of ice and water in CAO clouds and precipitation is not always well observed. Understanding how cloud phases partition as a function of cloud life cycle is important for predicting snowfall rates, convective life cycle, and intensity at weather timescales. The partitioning into liquid versus ice also has radiative impacts that are consequential for climate. These concerns motivated the incorporation of an airborne G-band vapor radiometer (GVR) into an National Science Foundation-supported aircraft campaign named the Cold Air outbreak Experiment in the Sub-Arctic Region (CAESAR). The GVR is an upward-pointing passive microwave radiometer using four frequencies centered around the 183.31 GHz water vapor absorption line, displaced by +- 1, 3, 7, and 14 GHz. For context, The U.S. Department of Energy (DOE)’s Atmospheric Radiation Measurement (ARM) user facility operates a surface-based GVR at its North Slope of Alaska (NSA) site. The same GVR has been used previously for a field campaign in the southeast Pacific, where an offset was noticed between brightness temperatures (Tbs) measured under clear skies compared to those calculated from a radiative transfer model. To account for any calibration offsets to the Tbs, a request was made to DOE to allow the GVR to operate at ARM’s Southern Great Plains (SGP) observatory and enable comparisons between its measurements and those available at SGP. This request was granted, titled ‘UMGVR_CAL’, short for ‘UMGVR_Calibration’. From October 30 to November 10, 2023, the GVR was deployed to the ARM SGP site to take advantage of their regular, nearby radiosonde launches under clear-sky conditions. The latter were determined using the SGP total sky imagery data. The GVR brightness temperatures in these clear-sky conditions were compared to those calculated by a radiative transfer code (PAMTRA) based on the SGP radiosondes. During the campaign, four suitable clear-sky episodes could be used for the GVR calibration. While few in number, these proved to be enough to satisfy our goal.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Clumping index estimation with 30°-tilted cameras in row crops: Evaluation of methods and segment size effects

The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Furthermore, applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.

30°-tilted camera↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗