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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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At least 595 records · Page 33

Quantification of Hydrogen Isotopes Utilizing Raman Spectroscopy Paired with Chemometric Analysis for Application across Multiple Systems

On-line and real-time analysis of a chemical process is a major analytical challenge that can drastically change the way the chemical industry or chemical research operates. With in situ analyses, new and powerful understanding of chemistry can be gained; however, building robust tools for long-term monitoring faces many challenges that include compensating for instrument drift, instrument replacement, and sensor or probe replacement. Accounting for these changes by recollecting calibration data and rebuilding quantification models can be costly and time consuming. Here, in this study, methods to overcome these challenges are demonstrated with an application of Raman spectroscopy to monitoring hydrogen isotopes with varied speciation within dynamic gas streams. Specifically, chemical data science tools such as chemometric modeling are leveraged along with several examples of calibration transfer approaches. Furthermore, the optimization of instrument and sensors cell parameters for targeted gas phase analyses is discussed. While the particular focus on hydrogen is highly beneficial within the nuclear energy sector, mechanisms built and demonstrated here are widely applicable to optical spectroscopy monitoring in numerous other chemical systems that can be leveraged in other hazardous processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kelvin probe force microscopy under ambient conditions

Kelvin probe force microscopy (KPFM) is a technique derived from atomic force microscopy that provides maps of surface potential or work function differences across material systems, with nanometre-scale resolution. KPFM is a useful tool for investigating electrical phenomena such as dipole orientation, interfacial charge transfer, charge accumulation, band bending and doping levels. This Primer aims to provide an overview of typical ambient-condition KPFM measurements, covering their underlying principles, experimental implementations and wide-ranging applications. Key KPFM variants, including amplitude and frequency modulation, heterodyne detection schemes and innovative open loop and pulsed force techniques, are discussed, with practical guidance on optimizing signal acquisition and reducing errors. Specialized approaches, such as time-resolved KPFM and multimodal KPFM, are discussed for their ability to capture dynamic charge processes and chemical information, respectively. Here, we highlight recent advances in KPFM applications, spanning metal alloys, soft matter, ferroelectrics, photovoltaics and 2D materials, showcasing its versatility across research domains. By addressing current limitations and identifying future opportunities, this Primer underscores the transformative potential of KPFM in advancing the understanding of nanoscale electrical phenomena.

Zahmatkeshsaredorahi, Amirhossein [Lehigh Univ., B↗

Integrated Routing and Traffic Signal Control for CAVs via Reinforcement Learning Approach

Incorporating Connected and Automated Vehicles (CAVs) into urban traffic networks presents opportunities and challenges for traffic management systems. This paper aims to develop an integrated routing and traffic signal control system designed explicitly for CAVs, utilizing a Reinforcement Learning (RL) approach. The objective is to enhance traffic flow and improve overall transportation efficiency in the controlled areas. We propose an innovative framework that employs the Deep Reinforcement Learning (DRL) algorithm, especially the Deep Q-network (DQN), to dynamically adjust the number of vehicles in the routes and the duration of traffic signals. Our simulation results demonstrate that a DQN agent successfully optimizes the number of vehicles in the routes and traffic signal timings of traffic signal controllers, eventually reducing total travel time. The study illustrates the potential usage of RL-based systems in managing routing and traffic signals for CAVs, offering a promising opportunity for future urban traffic management strategies.

Park, Jiho [New York University]↗

Signal Whisperers: Enhancing Wireless Reception Using DRL-Guided Reflector Arrays

This paper presents a multi-agent reinforcement learning (MARL) approach for controlling adjustable metallic reflector arrays to enhance wireless signal reception in non-line-of-sight (NLOS) scenarios. Unlike conventional reconfigurable intelligent surfaces (RIS) that require complex channel estimation, our system employs a centralized training with decentralized execution (CTDE) paradigm where individual agents corresponding to reflector segments autonomously optimize reflector element orientation in three-dimensional space using spatial intelligence based on user location information. Through extensive ray-tracing simulations with dynamic user mobility, the proposed multi-agent beam-focusing framework demonstrates substantial performance improvements over single-agent reinforcement learning baselines, while maintaining rapid adaptation to user movement within one simulation step. Comprehensive evaluation across varying user densities and reflector configurations validates system scalability and robustness. The results demonstrate the potential of learning-based approaches for adaptive wireless propagation control.

deep reinforcement learning↗

Interleaved dual-species arrays of single atoms using a passive optical element and one trapping laser

We demonstrate trapping of individual rubidium (Rb) and cesium (Cs) atoms in an interleaved array of bright tweezers and dark bottle-beam traps, using a microfabricated optical element illuminated by a single-laser beam and a 4f system with spatial filtering. Our approach exploits the opposite-sign dynamic polarizabilities of Rb and Cs, ensuring that each species is exclusively trapped in either bright or dark sites. The passive optical mask creates optimal trap depths for both species using three transmittance levels while minimizing the optical phase difference, implemented using a variable-thickness absorbing layer of amorphous germanium. This trapping architecture achieves atom loading rates close to 50% while reducing system complexity compared to conventional methods using active optoelectronic components and/or multiple-laser wavelengths.

Fang, Chengyu [Univ. of Wisconsin, Madison, WI (Un↗

Non-Destructive, Three-Dimensional Imaging of Processes in the Rhizosphere Utilizing High Energy Photons

Soil structure, which can be described as the aggregation and distribution of pore spaces, regulates carbon, nutrient, and water cycling across the Earth system. Yet the inability to make quantitative, dynamic, in situ measurements of soil structure and rhizosphere carbon flow has prevented meaningful incorporation of soil structural processes into Earth System Models (ESMs). The key limitations are: (i) Lack of scale integration between micron-scale soil structure and ecosystem-scale models, (ii) Poor functional linkage between soil structural properties and biogeochemical processes, and (iii) Absence of dynamic 3D measurements of rhizosphere structural changes and carbon transformations. To address these challenges, we developed a new integrated positron emission tomography (PET) - microcomputed tomography (CT) imaging platform that enables the first 4D (spatial 3D and time), non-invasive, quantitative imaging of carbon allocation and rhizosphere structural dynamics in living plants and intact soils. The system combines: • Rhizo-PET (R-PET): a high-resolution positron emission tomography scanner optimized for 11 CO 2 tracing in plant roots. • a-Se micro-CT: a high-contrast, high-spatial resolution CT system based on amorphous selenium (a-Se) direct conversion technology, enabling micron-scale visualization of soil structure and root–soil interfaces. Together, these advances allow us to quantify how carbon exudates move, transform, and stabilize within the rhizosphere, directly informing missing processes in BER-relevant carbon cycle models.

42 ENGINEERING↗

Self-consistent modeling of tokamak edge plasma transport with lithium sources

Magnetic confinement fusion devices require effective heat and particle exhaust solutions on the divertor plates to operate sustainably, especially under reactor-relevant conditions. Liquid lithium divertors have been proposed to address two major challenges: control of excessive heat flux to plasma-facing components through vapor shielding and minimization of core plasma contamination from impurities. The National Spherical Torus Experiment-Upgrade (NSTX-U) will explore lithium as a divertor material due to its potential to meet both objectives. We present a self-consistent coupling framework between the plasma boundary transport code UEDGE and the lithium wall transport code Wall–Li to evaluate the feasibility and operational limits of lithium-based divertors. The model aims to optimize lithium sourcing levels to prevent core plasma contamination via fuel dilution while ensuring divertor protection through vapor shielding. This integrated framework, applicable to any tokamak with lithium sources, dynamically adjusts lithium sourcing based on local plasma conditions and surface temperature. The coupled model is tested using NSTX-like geometry and plasma conditions to assess its performance and reliability. Wall–Li calculates lithium fluxes from plasma-facing components, incorporating physical sputtering, thermally enhanced sputtering, and evaporation driven by surface temperature and ion flux. These fluxes are reintroduced into UEDGE as neutral lithium atoms, enabling simulation of their transport and distribution within the plasma. UEDGE computes plasma and neutral transport, surface heat flux, and iteratively feeds this information back to Wall–Li. A small time step is employed to ensure numerical stability and convergence, enabling accurate simulations over typical tokamak discharge durations. This integrated modeling approach provides a robust tool for identifying operational regimes that balance effective lithium sourcing with minimal core plasma contamination, offering critical insights for optimizing lithium-based divertor systems in current and future fusion devices.

Magnetic confinement fusion↗

Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques in terms of computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU–GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation are used on well-conditioned numerics. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is observed on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8 node baseline and stretching to the full system.

Wilfong, Benjamin [Georgia Institute of Technology↗

Optimizing spectral phase transfer in four-wave mixing with gas-filled capillaries

Four-wave mixing (FWM) in gas-filled hollow-core capillaries, a nonlinear optical process that mixes signal and pump photon frequencies to generate idler frequency photons, offers a method for precise spectral phase transfer from signal to idler at ultrashort timescales and extreme powers. However, this regime is challenged by competing linear and nonlinear dynamics, leading to significant trade-offs between spectral phase transfer and conversion efficiency. Our computational investigation focuses on the upconversion of femtosecond pulses from the infrared (IR) to the ultraviolet (UV), a range notoriously difficult to manipulate. We explore an intermediate energy regime that strikes an optimal balance between FWM-mediated phase-transfer fidelity and nonlinear conversion efficiency. By adjusting the energy ratios and spectral phase profiles of the input signal, we achieve conversion efficiencies of approximately 5-15% while maintaining an effective quasi-linear spectral phase transfer. These findings will contribute to establishing first-principles and scaling laws essential for applications such as high-precision imaging, spectroscopy, quantum transduction, and distributed entangled interconnects, facilitating advanced control of ultrafast photonic and electronic wavepackets in quantum materials with unprecedented spatial and temporal precision.

Zhang, Hao↗

Iodine recombination in xenon solvent: Clusters in the gas to liquid-like state transition

Supercritical fluids (SCFs) have attracted significant attention as solvents for chemical reactions due to their unique properties, such as high diffusivity, low viscosity, and tunable solvation properties. These properties profoundly influence reaction kinetics and are often attributed to the formation of molecular clusters within SCFs. To study the effect of supercritical solvent on chemical reactivity and dynamics of reactions, one needs to understand the dynamics of clusters in supercritical fluid. Extensive experiments on the photodissociation and recombination of iodine in supercritical fluids served as a model system for understanding these effects. Experimental studies have been complemented by theoretical and computational investigations, which mostly employ Monte Carlo or empirical molecular dynamics simulations. However, computational studies using non-reactive force fields and ab initio approaches present challenges in capturing reactive processes at larger scales within supercritical fluids. Here, in this work, we developed the ReaxFF parameters by training against quantum mechanics data. ReaxFF reactive force field based molecular dynamics simulations were performed, studying the dynamics of a xenon solvent and cage effect at different thermodynamic conditions for the iodine recombination reaction. We show that the conditions near the critical point are the optimal conditions to study the cage effect. We show that the average lifetime of xenon clusters ranging between 5 and 11 ps is comparable to iodine geminate recombination. Our simulation results of iodine recombination in xenon solvent demonstrate the higher probability of iodine molecule formation in the presence of xenon clusters. Finally, we show that the supercritical condition exhibits the highest recombination rate for iodine atoms.

Cage effect↗

How Does Escherichia coli Allocate Proteome?

Microorganisms are shown to actively partition their intracellular resources, such as pro- teins, for growth optimization. Recent experiments have begun to reveal molecular com- ponents unpinning the partition; however, it remains unclear quantitatively how individual parts orchestrate to yield precise resource allocation that is both robust and dynamic. Here we developed a coarse-grained mathematical framework that centers on guanosine pentaphosphate (ppGpp)-mediated regulation, and used it to systematically uncover the design principles of proteome allocation in Escherichia coli. Our results showed that cellular ability of resource partition lies in an ultrasensitive, negative feedback control- ling topology with the ultrasensitivity arising from zero-order amino acid kinetics and the negative feedback from ppGpp-controlled ribosome synthesis. In addition, together with the time-scale separation between slow ribosome kinetics and fast turnovers of ppGpp and amino acids, the network topology confers the organism an optimization mechanism which mimics sliding mode control, a nonlinear optimization strategy that is widely used in man-made systems. We further showed that such a controlling mechanism is robust against parameter variations and molecular fluctuations, and is also efficient for biomass production over time. Furthermore, this work elucidates the fundamental controlling mechanism of E. coli proteome allocation, thereby providing insights into quantitative microbial physiology as well as the design of synthetic gene networks.

59 BASIC BIOLOGICAL SCIENCES↗

An Evaluation of The Dynamic Physical Security Risk Assessment Methodology for Fleet-Wide Applications

The requirements for U.S. nuclear power plants to maintain a large onsite physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This integrated process for physical security analysis is named Modeling and Analysis for Safety Security using Dynamic EMRALD Framework (MASS-DEF). This document provides an update on the progress in applying the MASS-DEF process to an operating commercial nuclear power plant as well as additional industry feedback regarding use of the tool for other physical security risk-informed topics. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, and integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5 or MAAP. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report is an update the progress of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report also provides an update to the procedural guidance for the MASS-DEF process and an overview of the generic models available for use by utilities. This report does not contain any plant’s sensitive information and/or safeguards information. This study’s purpose was to verify that the results achieved using generic models are similar to actual plant results and refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimization of distributed compute resources utilization in the CMS Global Pool

The CMS Submission Infrastructure is the primary system for managing computing resources for CMS workflows, including data processing, simulation, and analysis. It integrates geographically distributed resources from Grid, HPC, and cloud providers into federated pools managed by HTCondor and Glidein- WMS, for a total of around 500k CPU cores. This system dynamically manages workloads based on priorities defined by the collaboration. Additionally, CMS scheduling strategies must be flexible to handle multiple concurrent workloads while considering changing processing demands and resource availability from various providers.Efficient utilization of vast amounts of distributed compute resources is a key element for the success of the scientific programs of the LHC experiments. Optimizing the system is essential to maximize resource efficiency and fully utilize the distributed computing power. The CMS Submission Infrastructure team thus systematically investigates sources of inefficiency in workload scheduling to reduce their impact. In addition, a strategy of pilot overloading has been introduced to compensate for other inefficiency sources, thereby optimizing resource utilization and enhancing computational throughput.

Mascheroni, Marco [UC, San Diego (main)]↗

Multiphysics Design Optimization and Additive Manufacturing of Nuclear Components (Final CRADA Report - Executive Summary)

Westinghouse Electric Company (WEC) actively participated in the advancement of the nuclear fuel and reactor design space and requested the help of Oak Ridge National Laboratory (ORNL) in the creation of a new design tool set. This report details the creation of a collection of software tool sets that are linked together to collectively assist WEC design engineers in developing novel ideas outside the normal scope of traditional nuclear fuel and reactor design formulas. Specifically, Siemens HEEDS, a design space exploration and parametric optimization software, monitored and changed parameters in a collection of softwares to meet the team’s objective. The HEEDS parametric optimization method, SHERPA, was developed to control the Siemens NX CAD platform to adjust the native CAD of a hexahedral spacer grid. This new geometry can be used to execute a topological design optimization by the NX Topology software add-in. The resulting geometry is additively manufacturable. This topological optimization occurred twice—once on the spacer grid’s spring, and once on the dimple geometry. These new geometries were imported by Siemens’ STAR-CCM+, a multiphysics structural and fluid dynamic computational solver in which the spring geometry is deflected to match the rod insertion configuration. Along with the dimple geometry, this new deflected spring was used to complete a hydraulic assessment of a single-unit cell comprising one rod, one spring, and two dimples. The HEEDS SHERPA algorithm ranks the design based on the final mass of the unit cell and the hydraulic pressure drop performance. The ORNL team demonstrated the ability to use this software and provided engineering judgement to apply modern aerospace aerodynamic design. The effort has been focused on thinking outside the conventional design space and redesigning a spacer grid to perform beyond the WEC set objectives. Furthermore, the ORNL team also demonstrated that the HEEDS optimization routine can independently develop a design that meets the WEC design goals. Although these designs were at a low technology readiness level, their demonstration confirmed the team’s capability to create novel advanced nuclear concepts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Connected Traffic Signal Coordination Optimization Framework through Network-Wide Adaptive Linear Quadratic Regulator–Based Control Strategy

Traffic congestion in metropolitan areas causes several significant challenges, such as longer travel times, decreased productivity, increased fuel consumption and vehicle emissions, and even severe injuries during crashes. Traffic signal control is a management approach to reduce traffic congestion and allocate the appropriate right of way for safety and mobility efficiency, both in temporal and spatial domains. Here, this study proposes a network-wide adaptive signal control coordination optimization framework based on the linear quadratic regulator algorithm. The traffic flow conditions driven by signal control inputs are formulated based on their network-wide state-space representation. After modeling traffic control regulation constraints, an adaptive linear quadratic regulator algorithm is designed to maximize the network-wide total throughput under the current conditions. Optimal signal control split time durations for multiple intersections in the network are derived by solving the algebraic Riccati equation. Furthermore, the recursive least square parameter estimation method is employed to quantify dynamic traffic condition changes. To verify the effectiveness of this proposed signal control framework, both simulation and real-world experimental tests are conducted for multiple intersections in downtown Chattanooga, Tennessee, United States. In preparation for real-world experimental tests, pipelines for real-time data processing implementation and historical traffic flow data analysis are conducted. The test results demonstrate that the proposed control framework achieves a decrease in travel time by up to 19.4%, total time spent (TTS) by up to 11.9%, and relative queue balance (RQB) by up to 15.6%. The research findings indicate that the proposed signal control framework can be generalized to handle large scale signal control optimization network-wide.

97 MATHEMATICS AND COMPUTING↗

A Difluoro‐Methoxylated Ending‐Group Asymmetric Small Molecule Acceptor Lead Efficient Binary Organic Photovoltaic Blend

Abstract Developing a new end group for synthesizing asymmetric small molecule acceptors (SMAs) is crucial for achieving high‐performance organic photovoltaics (OPVs). Herein, an asymmetric small molecule acceptor, BTP‐BO‐4FO, featuring a new difluoro‐methoxylated end‐group is reported. Compared to its symmetric counterpart L8‐BO, BTP‐BO‐4FO exhibits an upshifted energy level, larger dipole moment, and more sequential crystallinity. By adopting two representative and widely available solvent additives (1‐chloronaphthalene (CN) and 1,8‐diiodooctane (DIO)), the device based on PM6:BTP‐BO‐4FO (CN) photovoltaic blend demonstrates a power conversion efficiency (PCE) of 18.62% with an excellent open‐circuit voltage (V OC ) of 0.933 V, which surpasses the optimal result of L8‐BO. The PCE of 18.62% realizes the best efficiencies for binary OPVs based on SMAs with asymmetric end groups. A series of investigations reveal that optimized PM6:BTP‐BO‐4FO film demonstrates similar molecular packing motif and fibrillar phase distribution as PM6:L8‐BO (DIO) does, resulting in comparable recombination dynamics, thus, similar fill factor. Besides, it is found PM6:BTP‐BO‐4FO possesses more efficient charge generation, which yields betterV OC –J SC balance. This study provides a new ending group that enables a cutting‐edge efficiency in asymmetric SMA‐based OPVs, enriching the material library and shed light on further design ideas.

Chemistry↗

Nature-inspired lotus-shaped fins combined with hybrid nanoparticles and metal foam for high-performance latent heat thermal energy storage

Latent heat thermal energy storage (LHTES) systems play a critical role in renewable energy integration by providing high energy density and nearly isothermal operation during phase transitions. However, their performance is often limited by slow melting/charging rates, which motivates the search for enhanced heat transfer designs. This study investigates the melting behavior of RT-82 phase change material (PCM) using novel lotus-shaped fins combined with copper metal foam and conductive graphene nanoparticles and carbon nanotubes. A two-dimensional enthalpy-porosity model in ANSYS Fluent was developed to simulate the charging/melting process, capturing non-thermal equilibrium between the foam and PCM/nano-PCM. In this study, effects of fin geometry, nanoparticle concentration, and foam porosity on melting dynamics and cost-performance trade-offs were investigated. Results showed that natural convection accelerated melting by ~12% compared to conduction-only scenarios. Optimized lotus-shaped fins with higher fin density (T3F4 and T3F10) achieved up to 63% faster melting relative to sparse configurations. Graphene nanoparticles improved thermal conductivity, with a 6% volume fraction, by reducing melting time by ~6.9%, while their combination with 75% porosity foam achieved a maximum reduction in the melting time of ~51% compared to pure PCM. Cost-performance analysis identified T3F4 as the most balanced design, offering rapid thermal response without excessive material costs, while moderate-density designs like T3S6 provided economical alternatives with acceptable performance. These results highlight the performance enhancement that can be achieved by integrating bio-inspired fins, nanoparticles, and foams, into compact and efficient LHTES for solar heating, building thermal management, and industrial waste-heat recovery applications.

25 ENERGY STORAGE↗

Discovery of Multiple Light-Harvesting States of the Photosynthetic Protein PE545

Cryptophytes are photosynthetic microalga that flourish in a remarkable diversity of natural environments by using pigment-containing proteins with absorption maxima tuned to each ecological niche. While this diversity in the absorption has been well established, the subsequent photophysics is highly sensitive to the local protein environment and so may exhibit similar variation. Thermal fluctuations of the protein conformation are expected to introduce photophysical heterogeneity of the pigments that may have evolved important functional properties in a manner similar to that of the absorption. However, such heterogeneity is averaged out in ensemble measurements and, therefore, has not yet been probed. Here, we report single-molecule measurements of phycoerythrin 545 (PE545), the prototypical cryptophyte antenna protein, in its native dimeric form. A conformational ensemble was resolved consisting of distinct photophysical states with different light-harvesting properties. Proteins that did not quench, partially quenched, or fully quenched absorbed light were observed. Light intensity increased the quenched-state population of the dimer, potentially as a mechanism to deal with the extreme light intensities found in aqueous environments. Cross-linking, which mimics local interactions, introduces this light-dependent functionality while also suppressing other conformational dynamics. The cellular organization can, therefore, actively modulate the protein conformation and dynamics, selecting for distinct levels of light harvesting. Furthermore, the complex conformational equilibrium provides an additional mechanism for cryptophytes and likely other photosynthetic organisms to optimize solar energy capture and conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗