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At least 973 records · Page 54

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗

Understanding polaronic transport in complex oxides by combining precise synthesis and first-principles many-body theory

In complex oxides, charge carriers often couple strongly with lattice vibrations to form polarons–entangled electron–phonon quasiparticles whose transport properties remain difficult to characterize. Experimental access to intrinsic polaronic transport requires ultraclean samples, while theoretical description demands methods beyond low-order perturbation theory. Here, we show a predictive theory–experiment workflow to study polaron transport in complex oxides. Focusing on a prototypical polaronic oxide, anatase TiO 2 , we combine growth of high-quality oxygen-vacancy-doped films using hybrid molecular beam epitaxy with a first-principles electron–phonon diagrammatic Monte-Carlo (FEP-DMC) framework recently developed for accurate polaron predictions. Our films exhibit record-high electron mobility for anatase TiO 2 , in excellent agreement with FEP-DMC calculations conducted prior to experiment, which predict a room-temperature mobility of 45 ± 15 cm −2 V −1 s −1 and a mobility-temperature scaling of μ ∝ T −1.9 ± 0.077 . Microscopic analysis using scanning transmission electron microscopy and x-ray photoelectron spectroscopy reveals the role of oxygen vacancies in modulating transport at lower temperatures. FEP-DMC further provides quantitative insight into polaron formation energy, phonon cloud distribution, lattice distortion around the polaron, and the polaronic contribution to mobility. Together, these results provide a deeper microscopic understanding of large-polaron transport in a complex oxide and provide the blueprint to characterize other polaronic materials.

anatase TiO2↗

Large-Angle Rocking Beam Electron Diffraction of Large Unit Cell Crystals Using Direct Electron Detector

We report a large-angle rocking beam electron diffraction (LARBED) technique for electron diffraction analysis. Diffraction patterns are recorded in a scanning transmission electron microscope (STEM) using a direct electron detector with large dynamical range and fast readout. We use a nanobeam for diffraction and perform the beam double rocking by synchronizing the detector with the STEM scan coils for the recording. Using this approach, large-angle convergent beam electron diffraction (LACBED) patterns of different reflections are obtained simultaneously. By using a nanobeam, instead of a focused beam, the LARBED technique can be applied to beam-sensitive crystals as well as crystals with large unit cells. Here, this paper describes the implementation of LARBED and evaluates the performance using silicon and gadolinium gallium garnet crystals as test samples. We demonstrate that our method provides an effective and robust way for recording LARBED patterns and paves the way for quantitative electron diffraction of large unit cell and beam-sensitive crystals.

4DSTEM↗

Experimental decoy-state Bennett-Brassard 1984 quantum key distribution through a turbulent channel

In free-space quantum key distribution (QKD) in turbulent conditions, scattering and beam wandering cause intensity fluctuations which decrease the detected signal-to-noise ratio. This effect can be mitigated by rejecting received bits when the channel's transmittance is below a threshold. Thus, the overall error rate is reduced and the secure key rate increases despite the deletion of bits. In this work, we implement recently proposed selection methods focusing on the prefixed-threshold real-time selection (P-RTS) where a cutoff can be chosen prior to data collection and independently of the transmittance distribution. We perform finite-size decoy-state Bennett-Brassard 1984 QKD in a laboratory setting where we simulate the atmospheric turbulence using an acousto-optical modulator. We show that P-RTS can yield considerably higher secure key rates for a wide range of the atmospheric channel parameters. In addition, we evaluate the performance of the P-RTS method for a realistically finite sample size. We demonstrate that a near-optimal selection threshold can be predetermined even with imperfect knowledge of the channel transmittance distribution parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

SARS-CoV-2 wastewater variant surveillance: pandemic response leveraging FDA’s GenomeTrakr network

ABSTRACT Wastewater surveillance has emerged as a crucial public health tool for population-level pathogen surveillance. Supported by funding from the American Rescue Plan Act of 2021, the FDA‘s genomic epidemiology program, GenomeTrakr, was leveraged to sequence SARS-CoV-2 from wastewater sites across the United States. This initiative required the evaluation, optimization, development, and publication of new methods and analytical tools spanning sample collection through variant analyses. Version-controlled protocols for each step of the process were developed and published on protocols.io. A custom data analysis tool and a publicly accessible dashboard were built to facilitate real-time visualization of the collected data, focusing on the relative abundance of SARS-CoV-2 variants and sub-lineages across different samples and sites throughout the project. From September 2021 through June 2023, a total of 3,389 wastewater samples were collected, with 2,517 undergoing sequencing and submission to NCBI under the umbrella BioProject,PRJNA757291. Sequence data were released with explicit quality control (QC) tags on all sequence records, communicating our confidence in the quality of data. Variant analysis revealed wide circulation of Delta in the fall of 2021 and captured the sweep of Omicron and subsequent diversification of this lineage through the end of the sampling period. This project successfully achieved two important goals for the FDA’s GenomeTrakr program: first, contributing timely genomic data for the SARS-CoV-2 pandemic response, and second, establishing both capacity and best practices for culture-independent, population-level environmental surveillance for other pathogens of interest to the FDA. IMPORTANCE This paper serves two primary objectives. First, it summarizes the genomic and contextual data collected during a Covid-19 pandemic response project, which utilized the FDA’s laboratory network, traditionally employed for sequencing foodborne pathogens, for sequencing SARS-CoV-2 from wastewater samples. Second, it outlines best practices for gathering and organizing population-level next generation sequencing (NGS) data collected for culture-free, surveillance of pathogens sourced from environmental samples.

Microbiology↗

Galvanostatic Intermittent Titration Technique Reinvented: Part II. Experiments

Following a critical review of the galvanostatic intermittent titration technique in Part I, here we experimentally demonstrate how to extract chemical diffusivity with a modified method. We prepare dense bulk samples that ensure diffusion-limitation. We utilize the scaling with $\sqrt{{t}_{\mathrm{relax}}+\tau }-\sqrt{{t}_{\mathrm{relax}}}$ (trelax: relaxation time; τ: pulse duration), avoiding problems with composition-dependent overpotentials. The equilibrium Nernst voltage is measured separately using small porous particles. This separation between the diffusion measurement and the titration procedure is critical for performing each measurement in a reliable setting. We report the chemical diffusion coefficients of LixNi1/3Mn1/3Co1/3O2 and their activation energy. We extract ionic conductivity and compare it with total conductivity to confirm ion-limitation in chemical diffusion. The measurements suggest that the time scale for diffusion in typical Li-ion battery particles could be much shorter than that of the intercalation/deintercalation processes at the particle surface (Biot number less than 0.1).

25 ENERGY STORAGE↗

UQ Toolkit v 2.0

The Uncertainty Quantification (UQ) Toolkit is a software library for the characterizaton and propagation of uncertainties in computational models. For the characterization of uncertainties, Bayesian inference tools are provided to infer uncertain model parameters, as well as Bayesian compressive sensing methods for discovering sparse representations of high-dimensional input-output response surfaces, and also Karhunen-Loève expansions for representing stochastic processes. Uncertain parameters are treated as random variables and represented with Polynomial Chaos expansions (PCEs). The library implements several spectral basis function types (e.g. Hermite basis functions in terms of Gaussian random variables or Legendre basis functions in terms of uniform random variables) that can be used to represent random variables with PCEs. For propagation of uncertainty, tools are provided to propagate PCEs that describe the input uncertainty through the computational model using either intrusive methods (Galerkin projection of equations onto basis functions) or non-intrusive methods (perform deterministic operation at sampled values of the random values and project the obtained results onto basis functions).

Safta, Cosmin↗

TTW (Transition to Wire Device) [SWR-25-02]

The Transition to Wire (TTW) hardware project is a method for connecting solar research samples with fragile interconnects to robust, weatherproof and consistent commercial connectors. The Transition to Wire device is a printed circuit board designed to facilitate the transition from tab ribbon or other unsecured electrical contacts on research samples to either wires or a connector. The four pin connector provides a kelvin (4 wire) connection at the solder pad where the sample connects.

McDanold, Byron↗

Combining biomarker and virus phylogenetic models improves HIV-1 epidemiological source identification

To identify and stop active HIV transmission chains new epidemiological techniques are needed. Here, we describe the development of a multi-biomarker augmentation to phylogenetic inference of the underlying transmission history in a local population. HIV biomarkers are measurable biological quantities that have some relationship to the amount of time someone has been infected with HIV. To train our model, we used five biomarkers based on real data from serological assays, HIV sequence data, and target cell counts in longitudinally followed, untreated patients with known infection times. The biomarkers were modeled with a mixed effects framework to allow for patient specific variation and general trends, and fit to patient data using Markov Chain Monte Carlo (MCMC) methods. Subsequently, the density of the unobserved infection time conditional on observed biomarkers were obtained by integrating out the random effects from the model fit. This probabilistic information about infection times was incorporated into the likelihood function for the transmission history and phylogenetic tree reconstruction, informed by the HIV sequence data. To critically test our methodology, we developed a coalescent-based simulation framework that generates phylogenies and biomarkers given a specific or general transmission history. Testing on many epidemiological scenarios showed that biomarker augmented phylogenetics can reach 90% accuracy under idealized situations. Under realistic within-host HIV-1 evolution, involving substantial within-host diversification and frequent transmission of multiple lineages, the average accuracy was at about 50% in transmission clusters involving 5–50 hosts. Realistic biomarker data added on average 16 percentage points over using the phylogeny alone. Using more biomarkers improved the performance. Shorter temporal spacing between transmission events and increased transmission heterogeneity reduced reconstruction accuracy, but larger clusters were not harder to get right. More sequence data per infected host also improved accuracy. We show that the method is robust to incomplete sampling and that adding biomarkers improves reconstructions of real HIV-1 transmission histories. The technology presented here could allow for better prevention programs by providing data for locally informed and tailored strategies.

60 APPLIED LIFE SCIENCES↗

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

97 MATHEMATICS AND COMPUTING↗

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon ( e e -ph) interactions, including non-linear e e -ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Codebase release r0.3 for SmoQyDQMC.jl

We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon ( e e -ph) interactions, including non-linear e e -ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

Cohen-Stead, Benjamin (ORCID:0000000279156280)↗

Synthesis and Flash Sintering of (Hf1-xZrx)B2 Solid Solution Fine Powders

Fine powders of (Hf1-xZrx)B2 solid solution were synthesized by two methods. In the first one, solution-based processing of HfCl4, ZrCl4, sucrose and H3BO3 was carried out followed by heat treatment (e.g., at 1500 °C for 1 h) in Argon to achieve the carbothermal reduction (CTR) reaction to form the boride solid solution. In the second one, called boron hydride reduction (BHR) method, HfCl4, ZrCl4 and NaBH4 were directly mixed in a glove box followed by heat treatment in Argon at elevated temperatures from 700 to 1500 °C. In addition, the powders synthesized via both methods were flash sintered without sample preheating in a homemade setup. The synthesized powders as well as the flash sintered bulk ceramics were characterized using different techniques including XRD, SEM, EDS, TEM, TGA-DSC, and Vickers hardness test to reveal the inter-relationships between starting materials composition, processing conditions, and the resulting materials microstructure and physical/chemical properties.

Belisario, Jose↗

Atomic-Scale Surface Studies of Bulk Metallic Glasses. Final Report

Bulk metallic glasses (BMGs) are of both scientific and technological interest because the absence of periodic atomic arrangements provides them with unique physical, chemical, and mechanical properties. Their high strength, superior elasticity, and an ability to be easily formed into virtually unlimited shapes with feature sizes from centimeters to Angstroms by blow molding and thermoplastic forming makes them an attractive choice for more and more practical applications and products. Due to their complex internal structure, however, experiments that yield insight into their exact atomic arrangements have been scarce. As a result, glass physics is one of the last remaining unexplored fields of materials science despite the scientific and technological importance of glasses in our daily lives, and the question how to characterize and control matter away from equilibrium, as glasses are, was listed as one of five Grand Challenges in a recent DoE report. The main reason for the slow progress in glass physics is the lack of experimental tools that enable access to atomic-scale structural and behavioral information for disordered materials. Such atomic-scale knowledge is mandatory to establish structure-property relationships that ultimately could allow to custom-design alloys featuring specific desired characteristics. With no such relationships available, theory development in glass remains basic and the few that exist are often untested. The aim of this research was to enable progress in our understanding of BMGs by developing a new approach that will allow a meaningful application of local surface science methods to specially prepared BMG samples to obtain a wealth of quantitative information on their atomic arrangements. Key was the availability of specially prepared samples whose surfaces feature large atomically flat terraces despite being entirely amorphous, which we have produced from a Pt 57.5 Cu 14.7 Ni 5.3 P 22.5 alloy (‘Pt-BMG’) both under ambient conditions as well as in ultrahigh vacuum using a unique setup that has been specially developed within this grant. Our approach starts with the in-situ preparation of oxide crystals that are terminated by large terraces, from which exact mirror images out of BMG will be produced using thermoplastic forming (TPF); for the research within this grant, we have successfully used (001)-oriented SrTiO 3 single crystal surfaces as well as (100)-, (110)-, and (111)-oriented single crystals made from LaAlO 3 . Since the resulting BMG replicas display all features of the original crystal with sub-Angstrom fidelity, thereby mimicking the original crystal’s termination by atomically flat terraces without being crystalline themselves, they are ideally suited for further investigation. The following atomic-scale local studies were then carried within this proposal: (i) high-resolution surface imaging and local spectroscopy using scanning probe microscopy, which showed disordered atom-like features and revealed changes in the gradient of the local surface potential on a 1-2 nm length scale; (ii) characterization of atomic-scale plastic flow with affected volumes as low as 1000 atoms, which showed local hardness near or above the theoretically predicted maximum and, once plastic deformation was initiated, homogeneous flow of the atoms involved; (iii) characterization of surface relaxation processes and the onset of crystallization induced by annealing, which showed that upon heating over the material’s glass transition temperature, the surface rearranges and relaxes towards a more stable, denser packed glass, which increases on-terrace surface roughness, while surface tension smoothens step edges; and (iv) studies that investigate the dependence of the material’s mechanical properties and structure on processing parameters, revealing that relaxed glasses get denser, harder, and more elastic. In combination, this information allows to combine structural models with mechanical properties and preparation history, thereby facilitating the development of preparation-structure-property relationships for metallic glasses. With the availability of such information, bulk metallic glasses can be further optimized to be used in more and more applications in industry.

36 MATERIALS SCIENCE↗

Examining United States Nuclear Weapon Educational Initiatives_A Quantitative Research Study on the Satisfaction of Participants Within the Nuclear Weapons Community

This study focused on a few United States nuclear weapons educational initiatives exploring six classroom environment factors that may or may not influence Satisfaction in a virtual or live classroom environment within the nuclear weapons community. The research explored Personalization, Involvement, Student Cohesiveness, Task Orientation, Innovation, and Individualization. The United States nuclear weapons community needed to attract new and talented individuals to the nuclear weapons profession. This study added to the nuclear weapons community by researching factors that may aid academic instructors, and curriculum developers create new and inventive ways of incorporating these factors into existing or new nuclear weapons educational courses. Convenience sampling was the data collection method used to gather quantitative research data. One hundred and seven voluntary participants utilized the College and University Classroom Environment Inventory with the Los Alamos National Laboratory's consent. There is not much concurrent research on Satisfaction within the live and virtual classroom environment. This research was vital for future research into how to increase participant satisfaction. The study provided the nuclear weapons community with grounded analysis to help create and guide new classes and course creation, possibly increasing Satisfaction in a live and virtual classroom environment. According to binary logistic regression, there was a statistically significant relationship among the dependent variable, Satisfaction, and two independent variables, Involvement, and Task Orientation in the classroom environment within the nuclear weapons community. Future nuclear educational programs may increase Satisfaction in the classroom environment by increasing participant Involvement and Task Orientation within a class using the CUCEI as a reference.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Multiplexing and Demultiplexing Signals for Radiography Application Using the Discrete Fourier Transform

Our goal is to develop an X-ray phase-contrast imaging system that can provide excellent soft tissue contrast of phase, attenuation, and small-angle scatter. We propose to replace the common system of G0, G1, and G2 gradings with a biprism array to replace the G1 grading and introduce a novel X-ray tube designed to replace the motion of the phase stepping grading G2. The proposed X-ray tube uses temporal multiplexing to provide simultaneous virtual “electronic phase stepping.” In this work the discrete Fourier transform is used to separate from the composite measurement individual X-ray phase contrast measurements sampled at different frequencies. The method performs a discrete Fourier transform of a composite refence sequence to obtain using the frequency amplitudes calibration factors needed to extract the X-ray phase contrast measurement amplitudes from the composite image. The composite reference sequence is the sum of the individual sequences, at different frequencies, with amplitudes of one. The method takes the discrete Fourier transform of this composite reference sequence; whereby, the amplitude of each frequency component is compared with the total sum of its stand-alone sequence amplitude. A calibration factor is determined so that the amplitude of this composite reference frequency times the calibration factor must equal the total sum of the sequence amplitude—the zero-frequency amplitude of the discrete Fourier transform of its stand-alone sequence. To demultiplex the composite measured signal these calibration factors are multiplied by the amplitudes of the frequency components of the discrete Fourier transform of the composite X-phase-contrast measurement to obtain the amplitude of each frequency encoded measurement. Using these calibration factors, we demonstrate with the discrete Fourier transform in Mathematica the extraction of individual images from a composite image that one would expect obtaining from our proposed new X-ray phase contrast imaging system. We then demonstrate as an example how using images from X-ray phase contrast data one can calculate phase, attenuation and the dark field images using grading phase step data supplied to use from Microworks, GmbH in Karlsruhe, Germany.

42 ENGINEERING↗

Thermal Compton Scattering of Electron Beams on Blackbody Photons: A Monte Carlo Event Generator for Multi-Turn Tracking at the Electron-Ion Collider

Compton scattering of ultra-relativistic electrons on thermal (blackbody) photons is typically a subdominant process in electron storage rings, but at sufficiently high electron energy and low residual gas pressure it can become competitive with beam-gas scattering and contribute to dis tributed losses and backgrounds. We present a self-contained Monte Carlo event generator for thermal Compton scattering designed for integration into multi-turn tracking workflows. The im plementation follows H. Burkhardt’s proposal method: trial scattering angles are sampled from the Thomson differential cross section and accepted/rejected using the Klein-Nishina to Thomson ratio, yielding the correct Compton spectrum while retaining simple absolute-rate normalization. Ther mal photon energies are sampled from the blackbody photon-number spectrum via an exact mixture representation.

43 PARTICLE ACCELERATORS↗