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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Advancing \textit{otsdaq}: Enhancements for Usability, Accuracy, and Robustness

High-energy physics (HEP) experiments require data acquisition (DAQ) systems that can orchestrate complex detector operations, high data throughput, and responsive, real-time feedback to operators. Traditional DAQ stacks, which are often bespoke, command-line driven and highly specific, impose large learning curves on users. The Off-The-Shelf Data Acquisition (\textit{otsdaq}) framework was created to address these issues by offering a highly customizable and scalable browser-based ’desktop’ environment, in which experiment-specific control and monitoring applications can be easily deployed and integrated. Although the initial development of the \textit{otsdaq} software was aimed at the Fermilab Test Beam Facility, \textit{otsdaq} is now being leveraged for broader deployment, including the upcoming Mu2e experiment, where real-time monitoring of field-programmable gate array (FPGA)-based Data Transfer Controllers (DTCs), Clock and Fanout (CFO) boards, and several other subsystems are critical. We contribute a set of targeted improvements to \textit{otsdaq}: bitmap visualization functionality for configured data, improved and corrected delta-based DTC throughput metrics, version control (VC)-backed source navigation for console messages, custom navigation hooks to eliminate disruptive user interface glitches, and copy-to-clipboard support for macro execution history. These changes improve usability, reduce debugging time, and increase accuracy in performance data as Mu2e moves toward commissioning.

Mohammed, A. [Unlisted, US]↗
DOE OSTI2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗
DOE OSTI2024

SIVB's 2024 In Vitro Biology Meeting Proceedings

SIVB's 2024 World Congress on In Vitro Biology took place in Saint Louis, Missouri, from June 8th to 12th, 2024. The conference featured renowned speakers from academic and non-academic institutions who will present recent advancements in critical areas like plant transformation, genome editing, synthetic biology, advanced breeding technologies, cellular agriculture, future food sources, chromosome engineering, epigenetics, artificial intelligence, and machine learning. The Society for In Vitro Biology (SIVB) has always considered the education and professional development of young researchers as an integral component of its mission. The 2024 World Congress program, along with SIVB’s student initiatives, was customized to foster scientific growth and professional development among students and young scientists empowering them in their professional journeys. The recording of the DOE supported "Single Cell RNA Sequencing" workshop was made publicly available at https://youtu.be/A0UnuYwefwg for easy retrieval and reference of all information shared during the live event, thereby increasing accessibility and knowledge transfer. Their are 14 articles in the proceedings and the full list of files is located at https://link.springer.com/journal/11626/volumes-and-issues/60-1/supplement.

10 SYNTHETIC FUELS↗
DOE OSTI2025

X‐Ray Absorption Studies of Local Structure of Dilute Ionic Species in Molten Salts

Molten salts are crucial materials with exceptional properties that make them suitable for applications such as heat transfer media, coolants, and liquid fuels in molten salt nuclear reactors and the concentrated solar power industry. Understanding their properties requires unraveling the intricate mysteries of their structure. To achieve this, advanced characterization tools are essential. Among various techniques, X‐ray absorption fine structure (XAFS) stands out as a versatile method capable of studying the structure of molten salts under in situ conditions. This review highlights recent advancements in the application of XAFS for investigating the local structure of molten salts, discusses its limitations and potential improvements, and explores complementary approaches such as simulations, machine learning, and correlative experimental methods.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Ice Phase Classification Made Easy with Score-Based Denoising

Accurate identification of ice phases is essential for understanding various physicochemical phenomena. However, such classification for structures simulated with molecular dynamics is complicated by the complex symmetries of ice polymorphs and thermal fluctuations. For this purpose, both traditional order parameters and data-driven machine learning approaches have been employed, but they often rely on expert intuition, specific geometric information, or large training data sets. In this work, we present an unsupervised phase classification framework that combines a score-based denoiser model with a subsequent model-free classification method to accurately identify ice phases. Further, the denoiser model is trained on perturbed synthetic data of ideal reference structures, eliminating the need for large data sets and labeling efforts. The classification step utilizes the smooth overlap of atomic position (SOAP) descriptors as the atomic fingerprint, ensuring Euclidean symmetries and transferability to various structural systems. Our approach achieves a remarkable 100% accuracy in distinguishing ice phases of test trajectories using only seven ideal reference structures of ice phases as model inputs. This demonstrates the generalizability of the score-based denoiser model in facilitating phase identification for complex molecular systems. The proposed classification strategy can be broadly applied to investigate structural evolution and phase identification for a wide range of materials, offering new insights into the fundamental understanding of water and other complex systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

NLML: A Deep Neural Network Emulator for the Exact Nonlinear Interactions in a Wind Wave Model

Nonlinear wave interactions describe the resonant energy transfer between wave components, playing a fundamental role in the evolution of ocean wave spectra. Nonlinear wave interactions significantly influence wave growth and development, making them essential for accurate wave modeling. However, resolving the full six-dimensional Boltzmann integral of the exact nonlinear wave interactions (Webb-Resio-Tracy method, WRT) is computationally expensive, limiting its application in real-time operational wave forecasting and for research purposes. Current approximations, such as the Discrete Interaction Approximation (DIA), prioritize computational speed over accuracy, resulting in significant errors in wave mean parameters. Here, we introduce NLML, a machine learning (ML) emulator designed to approximate the exact nonlinear wave interactions within WAVEWATCH III (WW3), with the goal of achieving the accuracy of WRT while maintaining the stability and computational speed of DIA. By leveraging GPU capabilities such as half precision inference, we achieved substantial speedups, up to 136x mathematical equation faster than the WRT and only a modest 1.04x mathematical equation slowdown relative to DIA, while achieving 2x mathematical equation the accuracy of DIA in global wave spectral energy and mean wave parameters, with up to 7x mathematical equation higher accuracy in some regions. Unlike previous ML approaches, NLML maintained inherent stability throughout model integration in a standalone, year-long WW3 simulation, without requiring additional constraints. Our new ML parameterization bridges the gap between accuracy and efficiency, offering a promising alternative for improving wave modeling in operational settings and research purposes.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Towards automated and real-time multi-object detection of anguilliform fishes from sonar data using YOLOv8 deep learning algorithm

Eels (Anguilla spp.), including American eels (Anguilla rostrata), European eels (Anguilla anguilla), and Japanese eels (Anguilla japonica), are species of critical management and regulatory concern due to their vulnerability to various stressors during downstream migrations. Accurate and efficient detection of migrating eels can improve our understanding of fish behaviors and fish-hydraulic structure interactions, thereby facilitating the design, operation, and optimization of more effective downstream passage facilities from both biological and economic perspectives. However, a real-time, automated framework for detecting migrating eels in real-world applications is currently lacking. Leveraging imaging sonar as a reliable technology for fish passage monitoring, field data are acquired using imaging sonar and then converted to single sonar frames/images for subsequent analysis. In this study, a framework based on the You Only Look Once Version 8 (YOLOv8)-based convolutional neural network is proposed for multi-object detection of eels and non-eel fish using the sonar images after image subtraction and additional wavelet denoising. The results from both training and testing phases demonstrate that the framework's ability can successfully detect both eels and non-eel fish in preprocessed sonar images, achieving F1-scores and mAP@0.50 exceeding 0.84. Additionally, the incorporation of wavelet denoising during preprocessing slightly improve detection performance. Furthermore, the transferability of this framework from eel to lamprey detection is demonstrated to be feasible given the similar morphological characteristics of these two species. Overall, the proposed framework achieves accurate and efficient detection of migrating eels, providing reliable and real-time information that can help conserve vulnerable eel and eel-like populations.

Deep learning↗
DOE OSTI2025

Deep-learning-based canopy height model generation from sub-meter resolution panchromatic satellite imagery

Canopy height models (CHMs) with sufficient resolution to distinguish individual trees are useful for a variety of applications. However, standard techniques to acquire such data, such as airborne lidar surveying, are often prohibitively expensive. Deep learning techniques for generating CHMs from high-resolution imagery are an attractive option to reduce costs. To date, success with these methods has been demonstrated using multichannel aerial photography and specialized satellite data products derived from multiple sensors, neither of which is commonly available at temporal resolutions finer than one year. Here we demonstrate a method to generate sub-meter resolution CHMs in three forests in California using a more abundant data source: sub-meter resolution, panchromatic satellite imagery from a single sensor. We show that phenology and species composition play important roles in model transferability; when trained using imagery from a single conifer forest in autumn, the model performs well on autumn imagery from a second conifer forest several hundred kilometers distant with no re-training. With modest additions to the training dataset, the same model generates minimally biased estimates of canopy height in both conifer and deciduous forests during multiple seasons. Because the model operates on satellite data with global coverage and a relatively short return interval, we propose its suitability to extrapolate tree-level canopy height data to remote regions and conduct high-temporal resolution monitoring of forest structure. We furthermore demonstrate the workflow’s applicability to fire modeling by conducting simulations in forests populated by trees measured using both this approach and airborne lidar surveying. We find minimal differences in fire behavior relative to a baseline case in which only statistical distributions of tree height and crown area are known. This result underscores the value of forest structural information derived from our workflow for improving the fidelity of wildland fire simulations, among other ecological applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Energy Technology Commercialization and Entrepreneurship: Insights From the U.S. Department of Energy's Office of Technology Transitions 2024 Energy Technology University Prize Faculty Track

The Energy Technology University Prize (EnergyTech UP) was established in 2022 with the goal of challenging student teams to develop impactful business plans for energy technologies of their choosing. EnergyTech UP is part of the The American Made Challenges program portfolio, funded by the U.S. Department of Energy. EnergyTech UP is specifically funded by the Department of Energy's Office of Technology Transfer (OTT) and is administrated by staff at the National Renewable Energy Laboratory (NREL). Since its inception, the annual prize has attracted applications from approximately 1,948 students across nearly every U.S. state and territory, awarding over $1 million in funds to student teams. In 2024, the prize expanded to include a Faculty Track, which invited faculty members from degree-granting institutions across the U.S. to design entrepreneurship-based curricula or educational activities. This new track aims to foster innovation in energy entrepreneurship education by leveraging the expertise of faculty to create robust, practical, and inclusive learning experiences. This report summarizes the themes, strategies and impacts identified in proposals from EnergyTech UP's inaugural Faculty Track. Our primary data for organizing insights are the Faculty Track applications themselves. This evaluation of 2024 EnergyTech UP Faculty Track applications aims to support future EnergyTech UP Faculty Track applicants as well as others who are interested in promoting, developing, and/or implementing educational activities that focus on energy commercialization and entrepreneurship at their institutions. By presenting insights from 2024 entries to the Faculty Track, we hope to contribute to a growing inventory of open-source curriculum development resources and provide materials to facilitate the growth of similar programs at a variety of collegiate institutions.

adoption readiness level↗
DOE OSTI2024

Fermilab s Transition to Token Authentication

Fermilab is the first High Energy Physics institution to transition from X.509 user certificates to authentication tokens in production systems. All of the experiments that Fermilab hosts are now using JSON Web Token (JWT) access tokens in their grid jobs. Many software components have been either updated or created for this transition, and most of the software is available to others as open source. The tokens are defined using the WLCG Common JWT Profile. Token attributes for all the tokens are stored in the Fermilab FERRY system which generates the configuration for the CILogon token issuer. High security-value refresh tokens are stored in Hashicorp Vault configured by htvault-config, and JWT access tokens are requested by the htgettoken client through its integration with HTCondor. The Fermilab job submission system jobsub was redesigned to be a lightweight wrapper around HTCondor. For automated job submissions a managed tokens service was created to reduce duplication of effort and knowledge of how to securely keep tokens active. The existing Fermilab file transfer tool ifdh was updated to work seamlessly with tokens, as well as the Fermilab POMS (Production Operations Management System) which is used to manage automatic job submission and the RCDS (Rapid Code Distribution System) which is used to distribute analysis code via the CernVM FileSystem. The dCache storage system was reconfigured to accept tokens for authentication in place of X.509 proxy certificates. As some services and sites have not yet implemented token support, proxy certificates are still sent with jobs for backwards compatibility but some experiments are beginning to transition to stop using them. There have been some glitches and learning curve issues but in general the system has been performing well and is being improved as operational problems are addressed.

Dykstra, David↗
DOE OSTI2025

Remote Sensing and Fluxes Upscaling for Real-world Impact (Workshop Report)

The "Remote Sensing and Fluxes Upscaling for Real-world Impact" workshop, held on July 9-10, 2024, at Lawrence Berkeley National Lab, was a collaborative effort led by the AmeriFlux Management Project, NEON, and the Carbon Dew Community of Practice. The event brought together over 200 registrants and approximately 100 attendees each day, including leading experts, researchers, and practitioners. The primary focus was on bridging the gap between cutting-edge research and practical applications in environmental monitoring by integrating remote sensing and flux data. Key themes included the importance of site-level measurements for validating remote sensing products, providing nature-based climate solutions, and addressing challenges such as instrument costs and the need for standardized methods. At the regional scale, discussions centered on addressing spatial heterogeneity and using high-resolution remote sensing and machine learning methods to enhance data interpretation. Global scale challenges included data consistency, gap filling, and accurate emission source identification, with opportunities for international collaboration and standardized practices to improve global carbon budget assessments. The workshop emphasized the critical need for integrating data across local, regional, and global scales through explicit scale-matching and developed a workflow for scaling flux data using "straight shot" and "explicit nesting" approaches. The event highlighted the importance of connecting scientific research with real-world applications in carbon, energy, and water management, ensuring that advancements translate into tangible societal benefits. These insights will guide future research, technology transfer, and collaboration, maximizing the potential of environmental fluxes to address real-world challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Understanding Adsorption and Reactions at Aqueous Oxide Interfaces with Neural Network Potential Molecular Dynamics

Chemical processes at metal oxide−water interfaces are of central importance in geochemistry, biology, and energy technologies. A better understanding of these processes would allow us to make a significant step toward optimizing and controlling them, which could in turn lead to broader impacts. Computational modeling is indispensable to accomplishing this task because complexity and disorder often make it difficult to extract atomistic information from experiments. Balancing computational cost and accuracy, simulation schemes based on efficient machine learning representations of the potential energy surface (PES) predicted by ab initio calculations have become increasingly popular over the past decade. In particular, several studies have demonstrated the ability of machine learning models to accurately reproduce the complex ab initio PESs of aqueous oxide interfaces, allowing simulations of systems and processes that are not accessible with ab initio methods. In this Account, we review our recent efforts to understand adsorption processes and reactions at aqueous oxide interfaces using deep potential molecular dynamics (DPMD), a simulation scheme employing deep neural networks (DNNs), which has proven to be quite successful in accurately describing many different systems in the condensed phase. After summarizing the DPMD methodology, we first review our work on the acid−base chemistry of oxide surfaces in contact with water, a fundamental characteristic that controls proton transfer and surface charge at the interface. We focus on the aqueous interface of rutile IrO 2 , an oxide material thus far considered the best catalyst for the oxygen evolution reaction (OER). We show that this interface is characterized by a large fraction of dissociated water and a strong Brønsted acidity of the surface sites, in good agreement with the experimentally measured value of the point of zero proton charge. In our second example, we investigate how the adsorption of organic species from ambient air or water affects the structure and wettability of the aqueous interfaces of TiO 2 , a prototypical photocatalytic material. This is a question that is relevant to understanding the UV-induced hydrophilicity of TiO 2 surfaces, a property at the basis of self-cleaning windows and related applications. Specifically focusing on formic and acetic acids, the two most common atmospheric organic acids, our simulations reveal that these acids control the wettability of TiO 2 largely through acid−base chemistry at the interface rather than chemisorption on the oxide surface, a finding that could help improve the design of self-cleaning surfaces and photocatalytic devices. Finally, we review our recent study of methanol at TiO 2 −water interfaces, a system whose interest is largely motivated by the role of methanol in enhancing photocatalytic hydrogen evolution on TiO 2 . Our simulations provide mechanistic insights into the coupled roles of the organic adsorbate and water at the TiO 2 interface, with implications for how methanol enhances the activity of H 2 evolution.

adsorption↗
DOE OSTI2024

Harnessing Machine Learning and Data Fusion for Accurate Undocumented Well Identification in Satellite Images

This study utilizes satellite data to detect undocumented oil and gas wells, which pose significant environmental concerns, including greenhouse gas emissions. Three key findings emerge from the study. Firstly, the problem of imbalanced data is addressed by recommending oversampling techniques like Rotation–GaussianBlur–Solarization data augmentation (RGS), the Synthetic Minority Over-Sampling Technique (SMOTE), or ADASYN (an extension of SMOTE) over undersampling techniques. The performance of borderline SMOTE is less effective than that of the rest of the oversampling techniques, as its performance relies heavily on the quality and distribution of data near the decision boundary. Secondly, incorporating pre-trained models trained on large-scale datasets enhances the models’ generalization ability, with models trained on one county’s dataset demonstrating high overall accuracy, recall, and F1 scores that can be extended to other areas. This transferability of models allows for wider application. Lastly, including persistent homology (PH) as an additional input improves performance for in-distribution testing but may affect the model’s generalization for out-of-distribution testing. A careful consideration of PH’s impact on overall performance and generalizability is recommended. Overall, this study provides a robust approach to identifying undocumented oil and gas wells, contributing to the acceleration of a net-zero economy and supporting environmental sustainability efforts.

SMOTE↗
DOE OSTI2025

High fidelity multiphysics tightly coupled model for a lead cooled fast reactor concept and application to statistical calculation of hot channel factors

A tightly coupled multiphysics code system is established using the MOOSE framework for hot channel factor (HCF) evaluation on a Lead Fast Reactor (LFR) concept. The coupled system is driven by the Griffin multiphysics coupling capability under which the MOOSE Heat Transfer module and NekRS computational fluid dynamics solver are coupled for conjugate heat transfer using the Cardinal application. The coupled capability is demonstrated on an LFR assembly model based on materials and geometry of a prototypical lead-cooled fast reactor design by Westinghouse Electric Company, LLC. Moreover, the work integrates the Multiphysics Object Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM) to perform calculations for statistical analysis of HCF. Furthermore, the coupling strategy and workflow demonstrated in this paper is not only useful for predicting accurate hot channel factors for different kinds of advanced reactors but also for other engineering applications such as control rod worth assessment, generation of high-fidelity database for Artificial intelligence (AI)/machine learning (ML) training, design optimization and multi-resolution modeling.

Cardinal↗
DOE OSTI2025

Uncertainty-Based Design: Finite Element and Explainable Machine Learning Modeling of Carbon–Carbon Composites for Ultra-High Temperature Solar Receivers

Design under uncertainty has significantly grown in research developments during the past decade. Additionally, machine learning (ML) and explainable ML (XML) have offered various opportunities to provide reliable predictable models. The current article investigates the use of finite element modeling (FEM), ML and XML predictions, and uncertain-based design of carbon-carbon (C-C) composites for use in ultra-high temperatures. A C-C composite concentrating solar power (CSP) as a microvascular receiver is considered as a case study. These C-C composites are fiber composites with directly integrated carbonized microchannels to form a lightweight, high-absorptivity material that includes an embedded microvascular network of channels. The topology of these microchannels is engineered to optimize heat transfer to a supercritical carbon dioxide (sCO2) heat transfer fluid. The mechanical characterization of C-C composites is highly challenging. Thus, designing every component made of C-C composites for ultra-high temperature applications needs an uncertainty-based analysis. As a part of a comprehensive project on the development of a novel carbonized microvascular C-C composite, this paper explores C-C composite sensitivity analysis, FEM, ML prediction, and XML analysis. The resulting composite can then be carbonized and coated with an oxidation-resistant coating to form a thermally efficient and mechanically robust C-C composite. An ANSYS 3-D-FE model was used to analyze the CSP’s stress/strain. To consider the variability in the mechanical and thermal properties of C-C composites, various mechanical properties are considered as the ANSYS FEM’s input. A synthetic dataset from 730 ANSYS runs was produced to feed into the ML and XML algorithms for uncertainty analysis and prediction. The ML and XML algorithms could accurately predict the CSP stresses/strains.

Daghigh, Vahid (ORCID:0000000298941620)↗
DOE OSTI2026

From diamond to BC8 to simple cubic and back: Kinetic pathways to post-diamond carbon phases from metadynamics

Understanding the kinetic pathways connecting carbon polymorphs at multimegabar pressures remains a major unsolved problem in high-pressure physics. Here, we provide insights into the long-standing question of BC8 formation and stability by combining a state-of-the-art SNAP machine-learning interatomic potential with enhanced sampling via metadynamics, enabling direct access to transition mechanisms far beyond the reach of standard molecular dynamics. Our simulations show that carbon phase transformations are intrinsically complex, proceeding through multiple intermediate disordered and crystalline states governed by nontrivial kinetic ordering. We determine the upper pressure limit for BC8 formation and reveal that hexagonal diamond transforms to BC8 faster than cubic diamond—an unexpected and experimentally testable prediction. We also identify a 𝑃⁢222 carbon phase that becomes competitive with diamond and simple cubic above 1.8 TPa, and we demonstrate that BC8 may be quenched to ambient conditions at moderate temperatures. Altogether, these results establish a general and transferable framework for resolving kinetic pathways in solid-solid phase transitions and provide physical insights into carbon's complex high-pressure landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Invertible Design Manifolds for Heat Transfer Surfaces (INVERT) (Final Technical Report)

This final report briefly reviews the main technical accomplishments of the INVERT award, summarizes existing or planned publications or transitions from the effort, and lastly reviews T2M strategies resulting from the program. Specifically, under the award, our team studied three main technical areas and performed one preliminary T2M study on the cost-benefit analysis of Inverse Design Methods and one major software release (the Maryland Inverse Design Benchmark Suite).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Minimization of Disorder as a Key Design Principle for Natural Sizes of Light Harvesting 2 Complexes

The light harvesting 2 (LH2) complex of purple bacteria has excellent energy conversion efficiency. Clarifying the design principle behind such efficiency at the atomistic level is crucial for understanding its structure–function relationship and can be utilized for the design of artificial light harvesting systems. To this end, we conducted comprehensive computational investigation of the dynamical and statistical nature of electronic excited states of pigment molecules in a natural LH2 complex with 9-fold symmetry and its two non-natural in silico analogues with 6- and 12-fold symmetries. To ensure reliable and efficient all-atomistic molecular dynamics simulations, we combined a well established interpolation approach for the construction of the potential energy surface with a neural network machine learning approach. Outcomes of these calculations clarify that non-natural forms of LH2-type complexes have significantly larger quasistatic disorder than those for the natural one. In addition, non-natural systems have more disruptions of the hydrogen bonding, underscoring its crucial role for reducing the disorder. On the other hand, local environmental dynamics are relatively insensitive to the structural changes although there is moderate enhancement in the anharmonic or interatomic components for the synthetic ones. These findings based on all-atomistic simulations provide direct computational evidence that the structure and sizes of natural LH2 complexes are designed to minimize the energetic disorder. We analyze quantitative implications of these for the energy transferring capability of the LH2 complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗