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At least 577 records · Page 32

Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. In this work, we derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ash Fouling Free Regenerative Air Preheater for Deep Cyclic Operation

The University of Kentucky (UKy) project titled “Ash Fouling Free Regenerative Air Preheater for Deep Cyclic Operation”, DE-FE0031757, was conducted from 8/15/2019 to 8/14/2024 in two Budget Periods. Other participants included PPL Corporation and Black Dragon Double Boiler. The overall goal was to investigate the proposed self-cleaning technology to achieve ash fouling free air preheater operation in a coal-fired power plant, especially during deep cycling. All project deliverables, milestones, and success criteria were met. UKy obtained the following scientific findings. • Temporary and periodic high temperature of heating elements (450 ~ 500 °F) can prevent ash accumulation and maintain air preheater free of clogging. • The ash samples analysis and unit operation provide solid evidence of ABS formed during low load with SCR ammonia slip being the major cause of ash accumulation, and air preheater clogging can be prevented by raising the heating element temperature up to 450 °F~ 500 °F at which ABS is decomposed. • In-situ self-cleaning can be controlled by monitoring temperature and/or presetting fixed number of cleanings per day. Both approaches in pilot testing show positive results for maintaining an ash free state for the air preheater. • Temperature criteria (cold end or gas outlet temperature) for entering self-cleaning service is critical to balance the number of cleaning cycles with maintaining the ash level. • Temperature criteria (cold end or gas outlet temperature) for exiting self-cleaning service is critical to balance the duration of the cleaning cycles with maintaining the ash level.

01 COAL, LIGNITE, AND PEAT↗

High Yield Muon Catalyzed Fusion

Fusion holds great promise as a clean and abundant energy source. However, traditional thermonuclear fusion encounters significant challenges due to the extreme temperatures required to overcome the coulomb barrier for two nuclei to fuse. In contrast, muon-catalyzed fusion presents an alternative approach that can surmount this barrier at significantly lower temperatures. Muons, with properties resembling those of electrons but 200 times heavier, can effectively reduce the atomic orbital radius, enabling central nuclei to overcome the coulomb force through the strong force. By introducing muons into a mixture of deuterium and tritium (two hydrogen isotopes), fusion is facilitated, releasing a 3.5MeV alpha particle and a 14.1MeV neutron. In the majority of cases, the muon is liberated and can initiate further fusions. However, approximately 0.8% of the time, it adheres to the alpha particle and remains bound until it either decays or undergoes reactivation through collisional ionization. To maximize the number of fusions per muon, it is crucial to enhance the cycling rate and reactivation fraction. Theoretical predictions and experimental data both suggest that the sticking rate decreases with increasing density. However, there exists a discrepancy between experimental observations and theoretical estimations regarding the extent of this decrease. To address these disparities, this experiment aims to investigate the cycling rate and sticking fraction under higher temperatures and pressures than previously explored.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Beam Design for Muon Catalyzed Fusion

Fusion holds great promise as a clean and abundant energy source. However, traditional thermonuclear fusion encounters significant challenges due to the extreme temperatures required to overcome the coulomb barrier for two nuclei to fuse. In contrast, muon-catalyzed fusion presents an alternative approach that can surmount this barrier at significantly lower temperatures. Muons, with properties resembling those of electrons but 200 times heavier, can effectively reduce the atomic orbital radius, enabling central nuclei to overcome the coulomb force through the strong force. By introducing muons into a mixture of deuterium and tritium (two hydrogen isotopes), fusion is facilitated, releasing a 3.5MeV alpha particle and a 14.1MeV neutron. In the majority of cases, the muon is liberated and can initiate further fusions. However, approximately 0.8% of the time, it adheres to the alpha particle and remains bound until it either decays or undergoes reactivation through collisio nal ionization. To maximize the number of fusions per muon, it is crucial to enhance the cycling rate and reactivation fraction. Theoretical predictions and experimental data both suggest that the sticking rate decreases with increasing density. However, there exists a discrepancy between experimental observations and theoretical estimations regarding the extent of this decrease. To address these disparities, this experiment aims to investigate the cycling rate and sticking fraction under higher temperatures and pressures than previously explored.

43 PARTICLE ACCELERATORS↗

Muon-Catalyzed Fusion

Fusion holds great promise as a clean and abundant energy source. However, traditional thermonuclear fusion encounters significant challenges due to the extreme temperatures required to overcome the coulomb barrier for two nuclei to fuse. In contrast, muon-catalyzed fusion presents an alternative approach that can surmount this barrier at significantly lower temperatures. Muons, with properties resembling those of electrons but 200 times heavier, can effectively reduce the atomic orbital radius, enabling central nuclei to overcome the coulomb force through the strong force. By introducing muons into a mixture of deuterium and tritium (two hydrogen isotopes), fusion is facilitated, releasing a 3.5MeV alpha particle and a 14.1MeV neutron. In the majority of cases, the muon is liberated and can initiate further fusions. However, approximately 0.8% of the time, it adheres to the alpha particle and remains bound until it either decays or undergoes reactivation through collisional ionization. To maximize the number of fusions per muon, it is crucial to enhance the cycling rate and reactivation fraction. Theoretical predictions and experimental data both suggest that the sticking rate decreases with increasing density. However, there exists a discrepancy between experimental observations and theoretical estimations regarding the extent of this decrease. To address these disparities, this experiment aims to investigate the cycling rate and sticking fraction under higher temperatures and pressures than previously explored.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal modeling of directed energy deposition additive manufacturing using graph theory

Purpose: The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach: Here, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings: The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications: This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermal camera data from large parts. Practical implications: The DED process is particularly valuable for near-net shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation. Originality/value: This paper presents a new mesh-free computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.

42 ENGINEERING↗

Building materials genome from ground‐state configuration to engineering advance

Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of individual phases from experimental observations is nonunique. The density functional theory (DFT), as a state-of-the-art solution of quantum mechanics, prescribes the existence of a ground-state configuration at 0 K for a given system. It is self-evident that the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above 0 K. Our multiscale entropy approach (recently terms as Zentropy theory) postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground-state and symmetry-breaking non-ground-state configurations represents the building blocks of materials and can be used to quantitatively predict free energy of individual phases with the free energy of each configuration predicted from DFT as well as all properties derived from free energy of individual phases.

CALPHAD↗

A Study of Temperature Distribution and Thermal Stresses in a Hot Rock Due to Rapid Cooling

Thermal stresses may be induced in a hot dry rock when a cold fluid is injected in the well. To study this problem, we look at the thermoelastic response of a hot rock that is suddenly cooled. The cooling is assumed to be either at a constant temperature or at a constant heat flux per unit depth. Our approach is to nondimensionalize the equations and perform a parametric study and look at the temperature distribution and the induced-thermal stresses. The results indicate that depending on the extent of cooling and the cooling time, thermal stresses can be induced. Numerical simulations on sandstone, with an initial uniform temperature of 473 K, are also carried out. The results show that if the cooling is due to the surface temperature maintained at 463 K (10 °C lower than the initial temperature of the hot rock), thermal stresses that are larger than the rock tensile strength could be induced. When the cooling is due to a constant surface heat flux, this temperature can be reached after about 777 days of cooling with a minimum value of a heat flux of -20 W/m.

Tran, Phuoc↗

Volumetrically Absorbing Thermal Insulator (VATI) for High-temperature Receivers

This project seeks to exploit volumetric absorption of concentrated solar irradiation in a thin, high-temperature, thermally conductive medium. High efficiency thermal conversion is achieved by volumetric absorption of both incoming solar irradiation (short wavelength) and emitted irradiation (long wavelength), demonstrating a volumetrically absorbing thermally insulating (VATI) effect. The thermalized energy is conducted to the back wall, enclosing the working fluid (molten salt or supercritical CO 2 ). Reliance on conductive thermal transport requires a thermally conductive medium, in the absence of which large temperature gradients drive losses due to emission. The project’s outcomes are important to realize a cost-effective approach to reduce optical and thermal losses from CSP receivers at high temperatures (720°C). High-temperature stable and commercially available porous SiC structures (open-cell foams) were explored as a volumetrically absorbing and thermally insulating layer. To the best of our knowledge, the current state-of-the-art for industrially deployed coatings is Pyromark. However, Pyromark suffers degradation at 700+°C and diurnal temperature changes. This necessitates periodic recoating, and the downtime increases the overall levelized cost of energy (LCOE) production. On the other hand, contemporary research activities have generated significant advances in the development of selective emitter coatings, which present challenges with costs, scalability, and stability. The pursued approach alleviates these concerns by developing a receiver that utilizes the inherent structure of high-temperature stable porous materials to enable robust and cost-effective receivers which require no periodic maintenance downtimes. The overall goal of the project is to experimentally demonstrate a figure of merit (FOM) of 0.92 at a temperature of 720°C and solar irradiation of 1000x concentration with porous receivers. The relevant crystallographic (phase) optical and thermal properties of porous SiC were first characterized. Second, the 3-D geometry of the porous SiC was analyzed using micro-X-ray tomography and converted to CAD data using image processing analysis. Utilizing this 3-D geometry and relevant optical/thermal properties, Monte Carlo- Ray Tracing (MCRT) analysis was performed to extract important parameters governing solar-thermal energy conversion such as extinction coefficient (β, 1/m), scattering albedo (ω) and the scattering phase function (Φ). These properties were then integrated into an in-house radiative and conduction transport model to solve for temperature and transport fluxes characterizing the solar-thermal energy conversion. This model was utilized to predict the FOM for various SiC porous geometries and to identify the highest possible FOM. Testing of the optimized porous structures will be accomplished with a custom-built high-accuracy (< ±4%) FOM measurement test-stand and a 1000x solar concentrator. When neglecting convective losses and resistance at the open boundary and the back wall, the optimized SiC foam leads to a FOM of 0.84. This FOM does not surpass the performance of Pyromark 2500. Yet, conversely to Pyromark 2500, SiC is stable at high temperatures and does not degrade over time. Also, it is possible to boost the FOM of SiC by engineering its effective thermal conductivity and its scattering albedo. A FOM of 0.92 is predicted for an optimized foam by accounting for convective losses and resistance at the open boundary and the back wall. This largely exceeds the FOM of Pyromark 2500 (~0.86) predicted by neglecting convective losses and resistance. Therefore, further engineering of the foam could lead to unprecedented FOMs.

14 SOLAR ENERGY↗

Architected mesoporous crystalline magnesium silicates with ordered pore structures

Novel approaches to harness earth abundant silicates as building blocks for carbon dioxide removal, capture, utilization, and storage are gaining increasing attention in the context of sustainable and low carbon energy and resource recovery. Advancing a calibrated understanding of these fluid-silicate interactions is essential for developing scalable processes. One of the challenges in developing predictive controls over these interactions is the compositional and morphological heterogeneity of naturally occurring, heterogeneous magnesium silicate minerals. To address this challenge, the synthesis of architected mesoporous crystalline magnesium silicate (Mg 2 SiO 4 ) is proposed. While synthesis routes for producing amorphous mesoporous magnesium silicates have been developed via sol-gel methods, approaches to synthesize crystalline magnesium silicates with well-controlled pore size distributions have not been explored. The conventional approaches of converting matter that is amorphous to crystalline states at elevated temperatures results in a heterogeneous pore size distribution. To develop controls on pore size distribution, amorphous mesoporous magnesium silicates are coated with carbon. This approach preserves the pore size distributions during the amorphous to crystalline transformations of Mg-silicates at elevated temperatures. The carbon coating is removed on heating. Magnesium silicate particles produced using this approach have highly ordered pores around 2.58 nm and a specific surface area of 124.25 m 2 /g. In this study, we report the chemical compositions, morphologies, phase transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. The transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. Furthermore, the synthesis routes discussed in this study can be applied translationally to produce metal silicates with ordered mesoporous structures.

36 MATERIALS SCIENCE↗

Development of an Improved RELAP5-3D Model for the High Temperature Test Facility

High-temperature gas-cooled reactors (HTGRs) are rapidly approaching deployment. Confidence in transient analysis of these systems for design, optimization, and licensing calculations requires modeling and simulation tools that have been validated against data relevant to HTGR conditions. The High Temperature Test Facility (HTTF) is an integral effects thermal hydraulics test facility for prismatic HTGRs. In spring and summer of 2019, HTTF was used for a series of experiments that now serve as the basis for the OECD/NEA Thermal Hydraulic Code Validation Benchmark for High Temperature Gas-Cooled Reactors using HTTF Data (HTGR T/H Benchmark). This benchmark contains problems for systems code, computational fluid dynamics (CFD), and coupled systems code/CFD modeling representing lower plenum mixing and both the depressurized and pressurized conduction cooldown (DCC and PCC respectively) transients. Benchmark problems include exercises for code-to-code and code-to-data comparisons as well as an exercise for error scaling between HTTF and the Modular High Temperature Gas-Cooled Reactor, which serves as the basis for the HTTF design. Previous analysis as part of the HTGR T/H benchmark used a RELAP5-3D model developed at Idaho National Laboratory (INL) and demonstrated an ability to reproduce trends in the measured data but difficulties reproducing experimental values within their uncertainty. These difficulties were largely attributed to assumptions made during the development of the initial RELAP5-3D model, which predated the HTTF experiments. A significant cause of difficulty reproducing the measured temperatures may be the radial nodalization of the previous RELAP5-3D model. The new model provides a finer nodalization to assess the impact of radial nodalization and allows for asymmetric heating within the core, which was a feature of multiple HTTF experiments. In this paper, we present the new RELAP5-3D model of HTTF. In addition to describing the new model, this paper compares the new and old models and provides results for a full-power steady state, a DCC, and a PCC in HTTF. These analyses are based on the code-to-code comparison exercises for the DCC and PCC problems of the HTGR T/H benchmark. We present the results of these exercises from the new model and compare them to the results of the old model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Defect graph neural networks for materials discovery in high-temperature clean-energy applications

We present a graph neural network approach that fully automates the prediction of defect formation enthalpies for any crystallographic site from the ideal crystal structure, without the need to create defected atomic structure models as input. Here we used density functional theory reference data for vacancy defects in oxides, to train a defect graph neural network (dGNN) model that replaces the density functional theory supercell relaxations otherwise required for each symmetrically unique crystal site. Interfaced with thermodynamic calculations of reduction entropies and associated free energies, the dGNN model is applied to the screening of oxides in the Materials Project database, connecting the zero-kelvin defect enthalpies to high-temperature process conditions relevant for solar thermochemical hydrogen production and other energy applications. The dGNN approach is applicable to arbitrary structures with an accuracy limited principally by the amount and diversity of the training data, and it is generalizable to other defect types and advanced graph convolution architectures. In conclusion, it will help to tackle future materials discovery problems in clean energy and beyond.

97 MATHEMATICS AND COMPUTING↗

Optimization of gold germanium (Au 0.17 Ge 0.83 ) thin films for high sensitivity resistance thermometry

Gold–germanium (Au x Ge 1–x ) solid solutions have been demonstrated as highly sensitive thin film thermometers for cryogenic applications. However, little is known regarding the performance of the films for thicknesses less than 100 nm. In response, here we report on the resistivity and temperature coefficient of resistance (TCR) for sputtered films with thicknesses ranging from 10 to 100 nm and annealed at temperatures from 22 to 200°C. The analysis is focused upon composition x=0.17, which demonstrates a strong temperature sensitivity over a broad range. The thinnest films are found to provide an enhancement in TCR, which approaches 20% K –1 at 10 K. Furthermore, reduced anneal temperatures are required to crystallize the Ge matrix and achieve a maximum TCR for films of reduced thickness. These features favor the application of ultra-thin films as high-sensitivity, on-device thermometers in micro- and nanolectromechanical systems.

59 BASIC BIOLOGICAL SCIENCES↗

Machine learning enables reconstruction of past fire regimes from charcoal-derived fire intensity and fuel composition

Background Fire is a foundational ecological process that shapes ecosystem structure, diversity, and resilience. Quantifying paleofire regime attributes such as frequency, severity, and intensity is essential for understanding the historical range of variability in fire behavior and its ecological effects. While frequency and severity are often reconstructed in paleofire studies, quantitative reconstructions of fire intensity remain limited. Recent work has shown that maximum pyrolysis temperature—a proxy for fire intensity—and plant species type can be inferred from charcoal using transmission Fourier-transform infrared (FTIR) spectroscopy. However, the sample preparation for transmission FTIR is destructive and time-consuming, limiting application and reuse of materials for other analyses. We evaluated reflectance FTIR spectroscopy as a non-destructive alternative for reconstructing combustion temperature and plant species from laboratory-generated charcoal. We also examined the influence of contrasting airflow environments (ambient air versus nitrogen-rich) on pyrolysis temperature and plant species reconstruction prediction accuracies and compared predictive performance between a novel, neural network–based deep learning model with the traditional modern analogue technique (MAT) using k-nearest neighbor functions. As proof of concept, we apply our enhanced methodology to ancient charcoal to demonstrate applicability at improving long-term fire regime reconstructions and the ability to link paleofire records with contemporary fire ecology. Results Our analysis shows that transmission and reflectance FTIR spectra yield comparable spectral profiles. However, sample preparation for reflectance FTIR is minimal and non-destructive, unlike transmission FTIR which is destructive. We demonstrate that oxygen environments improved reconstruction accuracy relative to nitrogen-rich conditions. Finally, our deep learning neural network (DL) achieved testing accuracies of 98.7% for temperature and 96.2% for species identification, outperforming MAT’s k-NN approach (89.8% and 65.9%, respectively). A Shapley importance analysis identified 5 key spectral regions that greatly influenced the model’s temperature or species categorization. When applied to ancient charcoal, our results show historic fires from the most recent past primarily burned at low intensities (400–500 °C), reflective of natural fire regimes in ponderosa pine forests. Our results corroborate charcoal morphology data that suggests all ancient charcoal originated from burned woody plant types. Conclusions By combining reflectance FTIR spectroscopy with a deep learning approach, we provide the first accuracies high enough to confidently identify both species and temperature from laboratory-produced charcoal, improving quantitative reconstructions of fire intensity and fuel composition from paleofire records. This opens a wide range of research into the link between fire and larger drivers (i.e., climate or human) and greater ecological understanding of fire regimes beyond that of burn scars or recent observations. These methodological improvements have direct relevance for fire management by improving interpretation of historical fire behavior, informing fuel–fire relationships, and providing a scalable analytical framework applicable to both long-term ecological studies and contemporary fire science.

54 ENVIRONMENTAL SCIENCES↗

Cation Short-Range Ordering of MgAl 2 O 4 and NiAl 2 O 4 Spinel Oxides at High Temperatures via In Situ Neutron Total Scattering

Complex oxides that adopt the isometric spinel structure (AB 2 O 4 ) are important for numerous technological applications and are relevant for certain geological processes, which involve exposure to extreme environments such as high pressures and temperatures. Recent studies have shown that the changes to the spinel structure caused by these environments are complex and depend on the material length scale under consideration. In this study we have expanded this approach to the behavior of spinels under high temperature. In situ neutron total scattering experiments, coupled with pair distribution function analysis, performed on two spinel compositions with various levels of pre-existing disorder (MgAl 2 O 4 and NiAl 2 O 4 ) revealed that both compositions trend to a state of maximum disorder where the A and B cations are randomly distributed amongst the two available sites. Temperature-induced cation inversion, conventionally understood as exchange of cations on the A and B sites, is locally expressed as an atomic rearrangement to a tetragonal symmetry, a correlation that is retained up to the maximum temperature studied (1000 °C). Furthermore, a complex thermal expansion behavior is revealed wherein the oxide materials expand heterogeneously at the level of coordination polyhedral with an apparent dependence on bond strength.

36 MATERIALS SCIENCE↗

Bioinspired Catalyst Design Principles: Progress in Emulating Properties of Enzymes in Synthetic Catalysts

Catalysis enables many aspects of modern life, including fuels, products, plastics, and medicines. Recent advances in catalysis have enabled us to realize higher efficiencies and new processes. Ideally, we seek to achieve high rates of selective conversions using catalysts derived from abundantly available elements and operating under mild conditions, specifically lower reaction temperatures and pressures. Such catalysts could enable decentralized, on-demand synthesis of chemicals and energy carriers. Nature has demonstrated the feasibility of this approach with enzymes, which showcase catalytic processes at low temperatures and pressures with nonprecious metals. Current thinking holds that in addition to the active site, the complexity of the enzyme structure, specifically the protein scaffold, is also critical to achieving this performance. Recreating this environment has been a long-standing scientific goal. However, we still understand the functions of enzymes better than we understand the de novo design of catalysts that mimic enzymes features, while also retaining their activity and selectivity under more demanding conditions. Here, in this Perspective, we will critically examine four key areas of catalyst design that incorporate the chemical and structural properties of enzymes into synthetic catalysts: (i) the use of confinement to enhance catalytic activity, (ii) tailoring the environment around the active site, (iii) proton transport, and (iv) bifunctionality and cooperativity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗