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At least 469 records · Page 26

Design Optimization for EUROPA Critical Experiment

The Experiment for Unresolved Region Of Plutonium Actinides (EUROPA) is an integral critical experiment currently being designed to target the intermediate energy region of plutonium. Intermediate energies, those between 0.625 eV - 100 keV, contain the end of resolved and beginning of the unresolved resonance region, making experiments in this energy range prudent for validating the representation of cross sections in this transition region. Below is the preliminary design of the experiment to be performed at the National Criticality Experiments Research Center (NCERC). Experiment optimization required an exhaustive down selection of several moderating, absorbing, and reflecting materials using Particle Swarm Optimization (PSO) in order to achieve maximum sensitivity to the intermediate energy region.

07 ISOTOPE AND RADIATION SOURCES↗

Data Associated with "Identifying Suitable Front Contacts for High-Efficiency Cd(Se,Te) Solar Cells on Space-Qualified Cover Glass"

This is data associated with the publication " Identifying Suitable Front Contacts for High-Efficiency Cd(Se,Te) Solar Cells on Space-Qualified Cover Glass " by Aesha P. Patel, Ryan Muzzio, Matthew R. Young, Robert Morrissey, Suresh Chaulagain, B. Edward Sartor, Prabodika N. Kaluarachchi, Christian Velez, Joshua A. Brown, Joel N. Duenow, Stephen Glynn, Michael J. Heben, Zhaoning Song, Nikolas J. Podraza, Adam B. Phillips, Randy J. Ellingson, Matthew O. Reese. All data associated with each figure in the manuscript and supplementary should be available in this dataset. A readme file is also included to provide some guidance. Abstract: Deployment of photovoltaics in space requires devices that combine high-efficiency, low areal mass, and resilience to harsh environments. Historically, high-efficiency multijunction III–V materials have dominated space power systems; however, their high cost and limited manufacturing throughput motivate the exploration of scalable alternatives. While CdTe-based thin-film photovoltaics offer an attractive option, their performance on non-conventional substrates can suffer from front-contact instability under higher-temperature processing. Here, the role of front-contact chemistry in limiting cell performance is investigated using CdTe-based devices fabricated on 150 μm thick Ceria-doped space-qualified 0214 Corning glass. A matrix of four transparent conducting oxides (TCOs: CTO, AZO, ITO, IZO) combined with two n-type emitters (MZO, IGO) reveals chemical stability at the front interface—rather than absorber composition alone—governs recombination losses, voltage deficits, and device reproducibility. Chemically stable front-contact combinations suppress elemental diffusion and interfacial degradation, resulting in significantly improved carrier lifetimes and junction quality. These insights are validated through record-certified Cd(Se,Te) cell efficiencies of 18.4% under AM1.5G and 16.2% under AM0 illumination on ultra-thin glass. Beyond CdTe, this work provides a general framework for the rational selection of TCO/emitter interfaces in superstrate thin-film photovoltaics, including emerging technologies like metal halide perovskites, while enabling high-efficiency, lightweight photovoltaics for space applications.

14 SOLAR ENERGY↗

A Robust Hierarchical Dispatch Scheme for Active Distribution Networks Considering Home Thermal Flexibility

Distribution networks are changing from passive absorbers of electric energy to active distribution networks (ADNs) capable of operating and participating in electricity markets. In the context of residential microgrids, which is a type of ADNs, aggregated home heating, ventilation and air-conditioning (HVAC) loads present a key opportunity to drive operational and economic objectives, facilitate high renewable energy penetration, and enhance both system resiliency and flexibility. A robust, hierarchical dispatch scheme is developed and presented in this paper, which connects an upper level multi-phase distribution optimal power flow (DOPF) to a lower level model predictive control (MPC)-based HVAC fleet controller. The approach is tested and verified on a modified IEEE 13 bus system in an intraday market application. The results demonstrate that the proposed hierarchical dispatch scheme is able to drive both economic and operational objectives for the ADN operator.

Rooks, Cody D.↗

Modeling, Design, and Testing of a Novel Biphasic Solvent-Enabled Absorption System for Post-Combustion Carbon Capture

A novel absorption process enabled by a new class of biphasic solvents for post-combustion carbon capture (BiCAP) is presently being developed at the University of Illinois at Urbana-Champaign. The new biphasic solvents are water-lean solvent blends that develop dual liquid phases with the absorbed CO2 highly enriched in one of the phases. These solvents are superior in CO2 capacity and have high thermal and oxidative stability compared to MEA. The BiCAP technology features a unique process configuration of multi-stage CO2 absorption and liquid–liquid phase separation during CO2 absorption, allowing continual separation and removal of the CO2-enriched liquid phase for maintaining low solvent viscosity and a fast absorption rate. A 40 kWe-scale skid has recently been constructed at the Abbott Power Plant in Champaign, IL, to test the BiCAP solvent in continuous operation with a slipstream of real post-combustion flue gas. Along with improvements in the stripping configuration including cold feed bypass, the process is expected to achieve a minimum reboiler duty of 2,210 kJ/kg CO2 captured at a stripper operating pressure of 6 bar.

20 FOSSIL-FUELED POWER PLANTS↗

Shaping High Efficiency, High Temperature Cavity Tubular Solar Central Receivers

High temperature solar receivers are developed in the context of the Gen3 solar thermal power plants, in order to power high efficiency heat-to-electricity cycles. Since particle technology collects and stores high temperature solar heat, CNRS (French National Center for Scientific Research) develops an original technology using fluidized particles as HTF (heat transfer fluid). The targeted particle temperature is around 750 °C, and the walls of the receiver tubes, reach high working temperatures, which impose the design of a cavity receiver to limit the radiative losses. Therefore, the objective of this work is to explore the cavity shape effect on the absorber performances. Geometrical parameters are defined to parametrize the design. The size and shape of the cavity, the aperture-to-absorber distance and its tilt angle. A thermal model of a 50 MW hemi-cylindrical tubular receiver, closed by refractory panels, is developed, which accounts for radiation and convection losses. Parameter ranges that reach a thermal efficiency of at least 85% are explored. This sensitivity analysis allows the definition of cavity shape and dimensions to reach the targeted efficiency. For an aperture-to-absorber distance of 9 m, the 85% efficiency is obtained for aperture areas equal or less than 20 m2 and 25 m2 for high, and low convection losses, respectively.

Gueguen, Ronny (ORCID:0000000252368638)↗

TCR Central Shutdown Rod Fine Motion Control

Transformational Challenge Reactor (TCR) is a Helium cooled 3 MWt test reactor that leverages advances in materials and manufacturing, computing, and AI in its design. Classical design of a shutdown rod uses either gravity, pneumatic, or springs to quickly release the Central Shutdown Rod (CSR) containing neutron absorber into the reactor core stopping nuclear reaction. Generally, the motor/actuator resides outside the reactor, but the motion is transmitted through a penetration into the pressure vessel. There are also designs where the control rod drive incorporates magnetic latches with coil residing outside the pressure boundary for precise position control of the rod. We are proposing a magnetic coupling to position the shutdown rod without any penetration into the pressure vessel for the entire drive length of TCR shutdown rod. Electromagnets are currently used in non-power nuclear reactors for shutdown rods, but these electromagnets are resident inside the reactor pressure vessel. This paper will describe the use of an electromagnet outside the pressure vessel to position and release the shutdown rod. A prototype was developed at ORNL to demonstrate the concept, and a design optimization of the ferritic core and material was conducted to maximize the lift force of the electromagnet. An elevated temperature testing was also performed to ensure that the system will perform under the temperature conditions inside an operating reactor.

Fountain, Eliott J.↗

Design and Optimization of Structured Multi-Functional Trapping Catalysts for Conversion of Hydrocarbons and NOx from Diesel and Advanced Combustion Engines

Oxides of nitrogen in the form of nitric oxide (NO) and nitrogen dioxide (NO 2 ) commonly referred to as NOx, is one of the two chemical precursors that lead to ground-level ozone, a ubiquitous air pollutant in urban areas. A major source of NOx is generated by equipment and vehicles powered by diesel engines, which have a combustion exhaust that contains NOx in the presence of excess O 2 . Vehicular emission control catalysts are ineffective in eliminating CO, hydrocarbons, and NOx during engine cold-start when exhaust temperatures are below 200°C. The objective of the project was to develop and demonstrate a multi-functional, catalyzed trap that enables vehicles with advanced combustion strategies to meet Tier 3 emissions standards while achieving the 150 °C challenge for sustained co-oxidation of HCs and CO and ≥90% NO trapping and release during warmup. Specifically, the multi-functional Lean HC+NOx (LHCNT) was developed for application in the exhaust aftertreatment of conventional diesel engines and engines having low temperature combustion (LTC) regimes. Activities included the design and synthesis of adsorbents and catalysts, screening and evaluation. Passive NOx absorbers (PNA), hydrocarbon (HC) traps, and oxidation catalysts (OC) were evaluated for use in series or as integrated devices. Predictive tools were developed utilizing the characterization and analysis of these materials, and an emission system was designed and optimized utilizing the catalyst systems. Microkinetic models were developed for the PNA for the simple NO-only feed and complex feed containing CO, H 2 , and model hydrocarbons (ethylene and dodecane). A first-principles, mechanistic-based model of the PNA was developed which utilized molecular-scale estimates (density functional theory) of energy barriers, mechanistic-based kinetics and realistic treatments of the flow and transport processes. Two new oxidation catalysts were developed (PdCu alloy, mixed copper-ceria-cobalt oxide), both of which significantly lessened the detrimental inhibition by CO on hydrocarbon and NO oxidation. A method for lessening the detrimental impact of CO on PNA activity was developed that involves use of an oxidation catalyst upstream of the PNA. The SwRI Ectolab TM burner system was applied to evaluate the baseline PNA material and confirmed performance comparable to the benchflow PNA studies using simulated exhaust. Spatially-resolved mass spectrometry (SpaciMS) was used to measure the transient spatial profiles of reacting species spanning the length of a three-function LHCNT containing PNA, HCT, and OC. The findings from this study provide diesel vehicle and catalyst companies valuable information to develop more cost effective emission control catalysts which helps to expand the use of more fuel efficient diesel power. The fundamental modeling and experimental tools and findings from this project can be applied to catalyst technologies used in the energy and chemical industries. The project led to 14 publications in the peer-reviewed literature with 2 additional currently under review. Finally, the project also led to training of several doctoral students who were placed in research jobs in industry and academia. Specifically, Mugdha Ambast (UH) has joined Cummins, Kevin Gu (UVa) has joined GM, and Abhay Gupta (UH) is to join Caterpillar.

02 PETROLEUM↗

Design and Optimization of Structured Multi-Functional Trapping Catalysts for Conversion of Hydrocarbons and NOx from Diesel and Advanced Combustion Engines

Oxides of nitrogen in the form of nitric oxide (NO) and nitrogen dioxide (NO 2 ) commonly referred to as NOx, is one of the two chemical precursors that lead to ground-level ozone, a ubiquitous air pollutant in urban areas. A major source of NOx is generated by equipment and vehicles powered by diesel engines, which have a combustion exhaust that contains NOx in the presence of excess O 2 . Vehicular emission control catalysts are ineffective in eliminating CO, hydrocarbons, and NO x during engine cold-start when exhaust temperatures are below 200°C. The objective of the project was to develop and demonstrate a multi-functional, catalyzed trap that enables vehicles with advanced combustion strategies to meet Tier 3 emissions standards while achieving the 150 °C challenge for sustained co-oxidation of HCs and CO and ≥90% NO trapping and release during warmup. Specifically, the multi-functional Lean HC+NOx (LHCNT) was developed for application in the exhaust aftertreatment of conventional diesel engines and engines having low temperature combustion (LTC) regimes. Activities included the design and synthesis of adsorbents and catalysts, screening and evaluation. Passive NOx absorbers (PNA), hydrocarbon (HC) traps, and oxidation catalysts (OC) were evaluated for use in series or as integrated devices. Predictive tools were developed utilizing the characterization and analysis of these materials, and an emission system was designed and optimized utilizing the catalyst systems. Microkinetic models were developed for the PNA for the simple NO-only feed and complex feed containing CO, H 2 , and model hydrocarbons (ethylene and dodecane). A first-principles, mechanistic-based model of the PNA was developed which utilized molecular-scale estimates (density functional theory) of energy barriers, mechanistic-based kinetics and realistic treatments of the flow and transport processes. Two new oxidation catalysts were developed (PdCu alloy, mixed copper-ceria-cobalt oxide), both of which significantly lessened the detrimental inhibition by CO on hydrocarbon and NO oxidation. A method for lessening the detrimental impact of CO on PNA activity was developed that involves use of an oxidation catalyst upstream of the PNA. The SwRI Ectolab TM burner system was applied to evaluate the baseline PNA material and confirmed performance comparable to the benchflow PNA studies using simulated exhaust. Spatially-resolved mass spectrometry (SpaciMS) was used to measure the transient spatial profiles of reacting species spanning the length of a three-function LHCNT containing PNA, HCT, and OC. The findings from this study provide diesel vehicle and catalyst companies valuable information to develop more cost effective emission control catalysts which helps to expand the use of more fuel efficient diesel power. The fundamental modeling and experimental tools and findings from this project can be applied to catalyst technologies used in the energy and chemical industries. The project led to 14 publications in the peer-reviewed literature with 2 additional currently under review. Finally, the project also led to training of several doctoral students who were placed in research jobs in industry and academia. Specifically, Mugdha Ambast (UH) has joined Cummins, Kevin Gu (UVa) has joined GM, and Abhay Gupta (UH) is to join Caterpillar.

42 ENGINEERING↗

Design and testing of a free floating dual flap wave energy converter

With a wide variety of wave energy device archetypes currently under consideration, it is a major challenge to ensure that research findings and methods are broadly applicable. In particular, the design and testing of wave energy control systems, a process which includes experimental design, empirical modeling, control design, and performance evaluation, is of interest. This goal motivated the redesign and testing of a floating dual flap wave energy converter. As summarized in this paper, the steps taken in the design, testing, and analysis of the device mirrored those previously demonstrated on a three-degree of freedom point absorber device. The method proposed does not require locking WEC degrees of freedom to develop an excitation model, and presents a more attainable system identification procedure for at-sea deployments. The results show that the methods employed work well for this dual flap device, lending additional support for the broad applicability of the design and testing methods applied here. The aim of this paper is to demonstrate that these models are particularly useful for deducing areas of device design or controller implementation that can be reasonably improved to increase device power capture.

16 TIDAL AND WAVE POWER↗

A model for radiative heating of a high-Z pusher

Several approaches to Inertial Confinement Fusion (ICF), including double-shell, pushered-single-shell, and the Revolver designs, have fuel surrounded by pushers made from high-Z materials. An advantage of these designs is that radiation emitted by the hot fuel will be absorbed and re-radiated into the fuel to reduce cooling. This process is referred to as radiation-trapping, and it lowers the fuel temperature required for ignition. To elucidate the physics of radiation trapping, a simplified model comprising a set of coupled differential equations has been developed to model the arbitrary time-dependent wall temperature from the Hammer and Rosen solution [J. H. Hammer and M. D. Rosen, Phys. Plasmas 10, 1829 (2003)] to a Marshak wave. The derivation of the model and a set of analytical power-law solutions will be presented. A discussion on numerical implementation of the differential equations into a model for burn in ICF capsules is also included.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advancing Post-Combustion CO 2 Capture through Increased Mass Transfer and Lower Degradation

The over-arching goal of the proposed project is to develop three techniques to enable aqueous post-combustion CO 2 capture technologies to meet the DOE performance and cost targets of 90% CO 2 capture, 95% purity, at a cost of less than $30/tonne CO 2 captured. This will be accomplished by the development of materials and processes to increase mass transfer in the absorber and reduce the environmental impacts. While constantly working to reduce the cost of CO 2 capture via solvent development and process & heat integration, increasing CO 2 mass transfer through development of custom dynamic packing materials and tuning solvent physical properties may offer a route to increased solvent capacity, lower energy consumption and reduced aerosol formation. The environmental concerns that have been identified in amine-based CO 2 capture systems, nitrosamines specifically, are another critical element that will be addressed in this project. The specific objectives of the project were to: 1) conduct detailed studies to understand how solvent physical properties and aerosol formation are impacted by additives; 2) quantify the CO 2 mass transfer improvement from the dynamic polarity packing in the absorber and the additive-modified solvent using the existing UK bench-scale CO 2 capture unit; 3) quantify the energy consumption savings associated with enhanced mass transfer; 4) quantify the benefits of the UK’s electrochemical cell to decompose nitrosamines; and 5) collect the necessary information/data to conduct a high-level TEA assessment of the proposed technologies. The project involved the fabrication and installation of customized dynamic polarity packing and an investigation into the understanding of the impact of chemical additives on solvent properties to increase CO 2 mass transfer in the absorber column, and lastly the design of an electrochemical cell to decompose nitrosamines in a water wash. After both systems were fabricated, they were tested at UK facilities, including on the bench-scale CO 2 capture unit under parametric and long-term operation.

20 FOSSIL-FUELED POWER PLANTS↗

Bulk Production of Any Ratio 12 C: 13 C Turbostratic Flash Graphene and Its Unusual Spectroscopic Characteristics

As graphene enjoys worldwide research and deployment, the biological impact, geologic degradation, environmental retention, and even some physical phenomena remain less well studied. Bulk production of 13 C-graphene yields a powerful route to study all of these questions. Gram scale synthesis of high quality and high purity turbostratic flash graphene with varying amounts of 13 C-enrichment, from 5% to 99% is reported here. Here, the material is characterized by solid state nuclear magnetic resonance spectroscopy, Raman spectroscopy, infrared (IR) spectroscopy, X-ray photoelectron spectroscopy and inductively coupled plasma mass spectrometry. Notably, an unusual enhancement in the Raman spectroscopic D’ peak is observed, resulting from the modification in vibrational frequency through isotopic enrichment favoring intravalley phonon scattering modes. While the IR absorbance spectrum of graphene is for the most part silent, we prepare here 13 C-enhanced graphene samples that show a large aromatic 12 C= 13 C stretch that reveals this IR-active mode.

01 COAL, LIGNITE, AND PEAT↗

A deep, multi-epoch Chandra HETG study of the ionized outflow from NGC 4051

Actively accreting supermassive black holes significantly impact the evolution of their host galaxies, truncating further star formation by expelling large fractions of gas with wide-angle outflows. The X-ray band is key to understanding how these black hole winds affect their environment, as the outflows have high temperatures ~10 5–8 K). We have developed a Bayesian framework for characterizing active galactic nucleus outflows with an improved ability to explore parameter space and perform robust model selection. We applied this framework to a new 700 ks and an archival 315 ks Chandra High Energy Transmission Gratings observation of the Seyfert galaxy NGC 4051. We have detected six absorbers intrinsic to NGC 4051. These wind components span velocities from 400 to 30000 km s -1 . We have determined that the most statistically significant wind component is purely collisionally ionized, which is the first detection of such an absorber. This wind has T ≈ 10 7 K and v ≈ 880 km s -1 and remains remarkably stable between the two epochs. Other slow components also remain stable across time. Fast outflow components change their properties between 2008 and 2016, suggesting either physical changes or clouds moving in and out of the line of sight. For one of the fast components, we obtain one of the tightest wind density measurements to date, log n/(cm -3 ) = 13.0$^{+0.01}_{-0.02}$, and determine that it is located at ~240 gravitational radii. The estimated total outflow power surpasses 5 percent of the bolometric luminosity (albeit with large uncertainties) making it important in the context of galaxy–black hole interactions.

79 ASTRONOMY AND ASTROPHYSICS↗

Laser-damage performance of gallium-alloy liquid metal mirrors

We explore the characteristics and laser-damage behavior of gallium-based liquid metal alloy mirrors under exposure to ns laser pulses. One of the key advantages of using liquid metal mirrors is the self-healing potential following perturbations arising from exposure to high-power laser pulses. In this work, key performance metrics, such as reflectivity and the laser-damage initiation mechanism and initiation threshold, were investigated using fused-silica cells filled with three different liquid metal Ga alloys. The results suggest that irreversible modification (damage) under 355-nm, 6-ns pulses are associated with the formation of gallium oxide, taking place at a fluence significantly higher than that for damage initiation in conventional metal mirrors. This behavior is believed to arise from the different damage initiation mechanism in liquid metal mirrors requiring increased laser absorbed energy for an irreversible modification of the material surface to occur. As a result, this exploratory work is the first of its kind and highlights some favorable performance characteristics of gallium-alloy metal mirrors.

47 OTHER INSTRUMENTATION↗

Flexible Perovskite-Perovskite PV for Mobile Power Applications (Final Technical Report)

This is the final report for the referenced TCF award which ran from Oct. 2019 through Jan. 2024 in conjunction with the industry partner Swift Solar. The long duration of the program was due to several factors including the pandemic and a technical work stoppage due to changes in the scope. Additionally, Swift’s business focus shifted during the course of the program. As a result of these factors, this program underwent two distinct modifications that dramatically changed the work scope. The following report is organized into three separate sections, each of which addresses a distinct work scope. Those scope changes, what necessitated them, and any new tasks/milestones are given, briefly, at the top of each section. The work performed was research on the hybrid halide perovskites (HHP), both the absorber material itself as well as other material layers that are required in a full device stack. At the start of the period of performance, there were two distinct challenges that we sought to address: (1) a wide band gap absorber (>1.6 eV), and (2) a recombination layer for tandem devices that provided good sequestration of the individual cell absorber materials in their respective device layers. NREL had previously published, and patented, advancements in both of these areas and they were the focus of much of the work throughout the program.

14 SOLAR ENERGY↗

Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = m b /M h « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $αα^2_sL^k$ in the three-loop decay amplitude, where $L=ln(-M^2_h/m^2_b)$ and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $~αα^n_sL^{2n+1}$

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗