A General Conditional Large Deviation Principle
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Sensible-Enthalpy-Based Conditional Moment Closure Model for Homogeneous Charge Compression Ignition with Temperature Inhomogeneity
Abstract This paper presents a sensible-enthalpy-based conditional moment closure (CMC) model for homogeneous charge compression ignition (HCCI) with temperature inhomogeneity. The focus of study is placed on the effects of a conditioning variable on the prediction of heat release rates and developing the mixing models for sensible enthalpy, a reacting scalar. The sensible-enthalpy-based CMC model is validated a priori with 2-D direct numerical simulation (DNS) data for HCCI, and compared with the total-enthalpy-based formulation. Sensible enthalpy is shown to be strongly correlated with temperature, which makes sensible enthalpy well suited for a conditioning variable in CMC for HCCI. Results show that sensible-enthalpy-based CMC performs well for the prediction of heat release rates for all temperature stratification levels investigated in this study, while total-enthalpy-based CMC leads to the overprediction of heat release rates when the temperature stratification level is high. While conditional fluctuations of species mass fractions are substantial, sensible-enthalpy-based CMC is found to accurately estimate heat release rates during ignition, as well as reaction rates of key species, due to substantially suppressed conditional temperature fluctuations. The mapping closure models for the probability density function (PDF) and conditional dissipation rates of sensible enthalpy are proposed. The proposed models are found to capture the characteristics of reactive scalar mixing.
42 ENGINEERING↗
Validation of RELAP-7 for Forced Convective and Natural Circulation Reactor Flows
New reactor designs such as small modular reactors and newly proposed passive safety systems rely on natural circulation two-phase flow cooling of the reactor core under accident conditions. Without a pump to drive the flow, the circulation rate is a strong function of void fraction. Under these conditions where the flow rate, pressure drop, and heat transfer are all closely coupled through the mixture density, the accurate prediction of void fraction is pivotal. Furthermore, while these passive systems boast a more reliable cooling option, the sensitivity of the system to two-phase flow instabilities is more likely than in forced convective cooling and can result in dangerous density wave or flow excursion conditions. Improvement of one-dimensional system codes and further development of three-dimensional code capability are all important efforts in addressing these issues. The proposed work is a critical step towards providing confidence through validation of the capability of thermal-hydraulic tools to meet the emerging challenges in reactor simulation. Historically, system analysis codes develop a stiffness over time due to fine-tuning of adjustable code parameters that result in a reluctance or inability to adopt improved models. Therefore, a rigorous effort should be invested in preparation for RELAP-7 to identify required modeling improvements of constitutive relations and validation of the code applicability to the wide range of possible reactor flow conditions. Part of this validation involves the uncertainty quantification which is a critical step in the Code Scaling, Applicability, and Uncertainty (CSAU) methodology and Best-Estimate Plus Uncertainty (BEPU) licensing method. BEPU allows recovery of safety margins and potentially optimizing plant performance, resulting in economic benefit for the reactor operators. Beginning with the collection of past experimental data covering prototypic LWR conditions, this document reviews three critical datasets available for the validation of system codes. The experimental methods, procedures, facilities, instrumentation, and supplementary information are consolidated to aid the validation efforts of this work and future projects. These three datasets (824 conditions) are chosen due to their wide acceptance and demonstrated application for code validation. Two experimental datasets from the Nuclear Power Engineering Corporation (NUPEC) span prototypic conditions of Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). These datasets are labeled as the BFBT (BWR Full-size Fine-mesh Bundle Test) and the PSBT (PWR Subchannel and Bundle Test) datasets respectively. The third dataset is taken in an internally heated annulus that is scaled based on a BWR subassembly and includes two-phase flows important to post-blowdown analysis. Together, the datasets consider the full range of pressure and mass flux expected in LWR forced convective flows from steady-state to long term cooling conditions. Recognizing the deficiency of available data under low-pressure, low-flow, a new natural circulation dataset consisting of 107 conditions is obtained. With system pressures ranging between 145 and 950 kPa, natural circulation is driven by a heat flux up to 275 kW/m2 in a 3 m long heated region of the annulus test section which is followed by a 2 m long unheated region before entering a condenser. Stable natural circulation flow rates in this facility were measured to be between 182 and 590 kg/m2-s. Pressure and temperature are measured at ten locations in the facility. In addition, measurements of void fraction, interfacial area concentration, and gas velocity are obtained at five axial locations in the annulus test section. The RELAP5-3D code demonstrates good accuracy for void fraction predictions in BFBT and PSBT benchmarks, but shows relatively large discrepancy in the annulus experiments at lower pressures. In two-phase natural circulation, large oscillations are observed in many system parameters during the simulation of 19 experiment cases which were conducted at low pressures, and the model shows good predictive performance with the remaining 88 experiment cases. However, some discrepancies in void fraction and temperature predictions are found which may require improved constitutive modeling under these low-pressure, low-flow condition. The quantified uncertainty in void fraction predictions in three forced convection benchmarks due to uncertainties in boundary conditions and geometries are relatively small, except for a few cases in the annulus experiment. The output uncertainty of the natural circulation model is quantified by considering the measurement error in boundary conditions, and it is shown that the output uncertainty ranges are relatively small for the range of conditions considered. Through this work, a clear pathway is provided for validation of RELAP7 once the code is available.
42 ENGINEERING↗
Scale dependence in functional equivalence and difference in the soil microbiome
Climatic history can shape the functioning of soil microbial communities and thus rates of ecosystem processes such as organic matter decomposition. For example, broad spatial scale differences in climatic history, such as contrasting precipitation regimes, have been shown to generate unique microbial functional responses to contemporary moisture conditions. Yet it is an open question as to whether local differences in soil microclimate similarly influence the functional potential of decomposer communities. Here, we use a multi-scale approach within and among two temperate forest field sites to investigate this question. Soils from fifty-four microsites, that vary in their soil moisture climate-regimes, were used as inocula for a common leaf litter (Quercus rubra L.) in a controlled, laboratory microcosm study. Microcosms were placed under dry, mesic and wet lab-moisture conditions and the rate of carbon (C) mineralization of the litter was measured over 202 days. Our results reveal differences in decomposition rates under controlled conditions that highlight broad-scale functional differences between the soil communities at each site. Specifically, we found that C mineralization differed by as much as two-fold for soil communities when compared between the sites. Our results also show that functional differences of soil communities are observable within one site but not the other. In the site where local-scale functional legacies were apparent, the historical soil moisture microclimate-regimes generated as much as an 89% change in C mineralization rates of the leaf litter under the same contemporary, lab-imposed moisture conditions. Here, a similar pattern was not observable in the other site; instead, laboratory moisture conditions explained almost all variation in C mineralization. Notably, for the site with pronounced local-scale functional legacies, there was much greater within-site variation in field-soil microsite moisture than at the site which did not exhibit functional legacies, suggesting that the extent of local-scale variation in microclimate may act as control on whether local-scale functional legacies are observed. Regardless of whether this mechanism does explain our findings, our observations do confirm those from prior studies where regional-scale moisture-regime differences shape microbial function, and extend this prior work by providing evidence that pronounced local-scale differences in soil moisture microclimate-regimes are associated with microbial functional legacies.
54 ENVIRONMENTAL SCIENCES↗
Markov and semi-Markov processes as a failure rate
In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.
97 MATHEMATICS AND COMPUTING↗
Autotuning of Double-Dot Devices In Situ with Machine Learning
The current practice of manually tuning quantum dots (QDs) for qubit operation is a relatively time-consuming procedure that is inherently impractical for scaling up and applications. In this work, we report on the in situ implementation of a recently proposed autotuning protocol that combines machine learning (ML) with an optimization routine to navigate the parameter space. In particular, we show that a ML algorithm trained using exclusively simulated data to quantitatively classify the state of a double-QD device can be used to replace human heuristics in the tuning of gate voltages in real devices. Here, we demonstrate active feedback of a functional double-dot device operated at millikelvin temperatures and discuss success rates as a function of the initial conditions and the device performance. Modifications to the training network, fitness function, and optimizer are discussed as a path toward further improvement in the success rate when starting both near and far detuned from the target double-dot range.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dynamic properties of FeCrMnNi, a high entropy alloy
The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode was brittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys.
36 MATERIALS SCIENCE↗
Dynamic properties of FeCrMnNi, a High Entropy Alloy
The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode wasbrittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys. DOE/NV/03624--1298
36 MATERIALS SCIENCE↗
Effect of wind pressure and modulation schemes on rain interrupted optical wireless links under tropical climates
Tropical and subtropical regions experience heavy rain intensities often accompanied with medium to strong winds. In this work, the effect of perpendicular wind flow and various modulation formats on a rain interrupted optical wireless link is investigated experimentally under controlled laboratory conditions. Attenuation as a function of rain rate is observed at different wind pressure. It is found that rain induced scattering dominates the rain specific attenuation however significant attenuation is expected at much higher wind pressure which normally increases with altitudes. A comparative performance of modulation formats like direct intensity modulation (D-IM), pulse width modulation (PWM) and various subcarrier intensity modulated (SIM) signals under heavy rain conditions is reported. It is found that SIM-FSK and SIM-AM offer better signal to noise performance (approximately two times) followed by subcarrier phase (SIM-PM) and frequency (SIM-FM) respectively. Also, SIM-FSK and PWM are least attenuated in heavy precipitation.
42 ENGINEERING↗
Temporal dynamics of CO 2 and CH 4 loss potentials in response to rapid hydrological shifts in tidal freshwater wetland soils
Earth System Models predict climate extremes that will impact regional and global hydrology. Aquatic-terrestrial transition zones like wetlands are subjected to the immediate consequence of climate change with shifts in the magnitude and dynamics of hydrologic flow. Such fluctuating hydrology can alter the nature and rate of biogeochemical transformations and significantly impact the carbon balance of the ecosystem. We tested the impacts of fluctuating hydrology and, specifically, the role of antecedent moisture conditions in determining the dominant carbon loss mechanisms in soils sampled from a tidal freshwater wetland system in the lower Columbia River, WA, USA. Our objective was to understand shifts in biogeochemical processes in response to changing soil moisture, based on soil respiration and methane production rates, and to elucidate such responses based on the observed electron acceptor and metabolite profiles under laboratory conditions. Metabolomics and biogeochemical process rates provided evidence that soil redox was the principal factor driving metabolic function. Fluctuating redox conditions altered terminal electron acceptor and donor availability and recovery strengths of their concentrations in soil such that a disproportionate release of carbon dioxide stemmed from alternative anaerobic degradation processes like sulfate and iron reduction compared to carbon loss due to methano genesis. Our results show that extended and short-term saturation created conditions conducive to increasing metabolite availability for anaerobic decomposition processes, with a significant lag in methanogenesis. In contrast,extended drying caused a cellular-level stress response and rapid recycling of alternate electron acceptors.
anaerobic respiration, tidal wetlands, methane pro↗
Entangled chain polymer liquids under continuous shear deformation: consequences of a microscopically anharmonic confining tube
Here, we generalize our non-classical theory for the shear rheology of entangled flexible polymer liquids to address the consequences of a deformation-modified anharmonic tube confinement field. Numerical results for stress–strain curves, orientational relaxation time, primitive path (PP) step orientational order parameter, dynamic tube diameter and transverse entropic barrier under nonequilibrium conditions are presented as a function of dimensionless shear rate, strain and degree of entanglement. Deformation-induced changes of the tube field have essentially no effect on rheology under fast deformations conditions corresponding to Rouse Weissenberg numbers Wi R > 1 because of the dominance of PP chain stretch. However, the scaling behavior of the effective orientational relaxation time and rheological response at low deformation rates Wi R < 1 are significantly modified, with the stress overshoot coordinates predicted to become shear rate and degree of entanglement dependent. Stress-assisted transverse activated barrier hopping as a new channel of orientational relaxation is found to be potentially important when Wi R < 1. The dynamic tube diameter and transverse entropic barrier that confines chains in a tube are rich functions of strain, shear rate and degree of entanglement. Deformation can increase or decrease the tube diameter, and non-monotonic changes with strain are possible due to competing consequences of PP orientation, chain stretch and stress. The transverse barrier is relatively high for all strains below the stress overshoot, for weaker entanglement, and for Wi R > 1, corresponding to a dynamically stable tube. But for high enough degrees of entanglement and Wi R < 1, although the barrier still exists it can become very low.
36 MATERIALS SCIENCE↗
Electrocatalytic Hydrogenation of Oxygenated Compounds in Aqueous Phase
Electrocatalytic hydrogenation is a fascinating strategy to hydrogenate biogenic compounds at ambient conditions by replacing the thermal and H2 inputs by cathodic potential. This work compares the performance of this approach (in aqueous phase at room temperature) for a variety of model oxygenated compounds reacted over a series of metals. The target functionalities were carbonyl groups, aromatic rings, and ether bonds. All metals explored (Pt, Rh, Pd, Cu) are active for the reduction of carbonyl compounds to alcohols. For instance, conversion rates of benzaldehyde increased as a function of metal as: Pt < Rh < Pd (Cu was tested at different conditions). In contrast, only Rh and Pt were found active for hydrogenation of aromatic rings (Rh was more active than Pt). Comparing among the target functionalities, carbonyl groups are more reactive than aromatic rings and ether bonds in phenolic compounds and di-aryl ethers on all explore metals. This carbonyl reactivity, however, is enabled by the aromaticity of the molecule. Hence, the reactivity trend of the examined molecules is: butyraldehyde < furfural < acetophenone < benzaldehyde. For phenolic compounds, phenol is more reactive than cresol and methoxy phenol. Thus, the presence of substituting groups at the functionality being converted (either carbonyl or aromatic ring) decreases conversion rates. Ether bonds are cleaved under electrocatalytic conditions, which opens two main pathways for the conversion of aryl ethers: hydrogenation of the aromatic ring and hydrogenolysis of the ether bonds, whereas hydrolysis occurs as a minor pathway. Electrocatalytic hydrogenation competes with the H2 evolution reaction at the conditions of the tests, therefore Faradaic efficiency (fraction of current utilized in hydrogenation) and hydrogenation rates are correlated. That is, within the potential range explored, increasing hydrogenation rates lead to higher Faradaic efficiencies. The slope of this correlation, however, depends on the potential and on the functionality being hydrogenated. Keywords: Hydrogenation, electrocatalysis, metal catalysis, aqueous phase hydrogenation, biomass conversion. Acknowledgements The authors would like to thank Yang Song, Prof. Johannes Lercher, and the group of Prof. Hubert A. Gasteiger at the Technische Universität München for advice and support. The authors are grateful to Donald M. Camaioni, Nirala Singh, and Juan Herranz for fruitful discussions. The research described in this paper is part of the Chemical Transformation Initiative at Pacific Northwest National Laboratory (PNNL), conducted under the Laboratory Directed Research and Development Program at PNNL, a multi-program national laboratory operated by Battelle for the U.S. Department of Energy.
Hydrogenation, electrocatalysis, metal catalysis, ↗
Assessment of Enthalpy-Based Conditional Moment Closure Models in Predicting Ignition of Lean and Stoichiometric PRF-Air Mixtures with Temperature Inhomogeneity
Accurate prediction of the ignition delay in turbulent flows is important in developing advanced combustion technology for internal combustion engines. Enthalpy-based conditional moment closure (CMC) models are assessed with 2-D direct numerical simulation (DNS) data for ignition of homogeneous PRF-air mixtures with temperature inhomogeneity in homogeneous isotropic turbulence. The sensible-enthalpy-based CMC model is compared with the total-enthalpy-based formulation, with the focus being placed on assessing the capability of the CMC models in predicting ignition processes under different engine conditions. A priori analysis shows that the total-enthalpy-based CMC gives good predictions of the heat release rates in the lean mixtures when the temperature inhomogeneity level is low, but leads to significant overprediction under the stoichiometric condition regardless of the thermal stratification levels. On the other hand, the sensible enthalpy formulation performs well for all conditions considered in this study due to the suppressed conditional temperature fluctuations. A mapping method to model conditional scalar dissipation rates and probability density function of sensible enthalpy is also assessed.
Wang, Wei↗
Modeling and Validation of Irradiation Damage in Ni-based Alloys for Long-Term LWR Applications (Final Report)
As light water reactor (LWR) plant lives are extended, the need for predictive modeling tools for materials degradation increase in order to ensure safe operation and plan for component replacements. The Grizzly code, which is built on the MOOSE multi-physics simulation environment, is being developed for exactly this purpose. To extend Grizzly to include capabilities for modeling Ni-based alloys, we propose a US/UK integrated program to address thermal and irradiation-induced transformations mechanisms of Alloys 690 and 625. Alloy 690 is widely used in existing LWR plants due to its superior stress corrosion cracking (SCC) resistance compared to Alloy 600. Alloy 625 is used in more limited applications but offers the benefits of both high strength (in the aged condition) and corrosion/SCC resistance. Research has shown that both alloys can undergo phase changes due to thermal or irradiation exposure. In the precipitation-hardened condition, Alloy 625 “softens” during neutron irradiation as the strengthening precipitates decompose and metastable precipitates form. However, the nature and rates of these transformations as a function of exposure conditions are not well understood. Similarly, the effects of these thermal and irradiation-induced microstructural changes on mechanical properties require evaluation. The proposed program combines thermal and irradiation experiments, mechanical testing, microstructural characterization using state-of-the art analytical techniques, atomistic modeling, micro-and macro-scale modeling via Grizzly. This multi-pronged approach yields several benefits: 1) atomistic scale models capture the physics of the mechanisms of phase transformations, which can be generalized to other systems, 2) the modeling results (from atomistic to continuum) will be validated experimentally to ensure the predictive aspect, 3) the microstructure/property relationships captured with mechanical testing provides information at the engineering scale that is needed to validate the integration of the proposed new capability into Grizzly
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms
Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, the rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.
97 MATHEMATICS AND COMPUTING↗
Decoding Zeolite Crystallization and Stage III in Nuclear Waste Glasses by Coupled Modeling and Experiments
Under specific conditions of pH and temperature, nuclear waste immobilization borosilicate glasses may exhibit a sudden acceleration in their corrosion kinetics (stage III)—a behavior that has been associated with the formation of zeolite crystals. Such accelerated dissolution may compromise the integrity of nuclear wasteforms placed in geological depositories. However, thus far, none of the available models is able to predict the thermodynamic propensity and kinetics of zeolite precipitation as a function of the solution conditions due to (i) a lack of fundamental knowledge regarding the nucleation & growth mechanisms of zeolitic phases, (ii) uncertainty regarding the compositions (types) of zeolites that may form and the rate-limiting step in their precipitation as a function of the solution conditions, and (iii) the complexities that arise due to the vast parametric space (i.e., solution chemistry, temperature, number of secondary phases, etc.) that encompass these systems under conditions of environmental exposure. To resolve these challenges, this project aimed to unambiguously identify the thermodynamic propensity for zeolite precipitation and the kinetics thereof as a function of the solution conditions (composition, pH, and temperature). To achieve this goal: 1) We identified the solution conditions and zeolite phases relevant to nuclear glass dissolution. 2) We performed a series of ab initio molecular dynamics (AIMD) simulations to compute the thermodynamic properties of a group of characteristic zeolites that features a large range of compositions, various hydration levels, a wide range of framework structures, and partial atomic site occupancies. 3) We released a first-of-a-kind self-consistent thermodynamic database that can be used to assess the kinetics and the stability fields of zeolitic phases within a Gibbs energy minimization (GEM) framework. 4) We developed a robust geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. 5) We introduced a model that predicts the dissolution kinetics of a series of borosilicate nuclear waste immobilization glasses in terms of the topology of their atomic network. 6) We investigated the roles of the solution composition on the crystallization kinetics of phillipsite zeolites and tobermorite silicate hydrates. Via PNNL’s collaboration and engagement, this project directly supports DOE’s nuclear waste immobilization activities by offering a technical, science-based foundation that will (i) facilitate predictions of the long-term corrosion rates and extents of existing nuclear waste immobilization glasses to help ensure safe and successful vitrification operations, (ii) inform the development of advanced glass formulations with enhanced durability, and, (iii) enable cost-savings that result from making more decisive and hence less conservative predictions while offering higher levels of nuclear waste embedment in smaller, more compact glass volumes.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Role of Low Molecular Weight Polymers on the Dynamics of Silicon Anodes During Casting
This work probes the slurry architecture of a high silicon content electrode slurry with and without low molecular weight polymeric dispersants as a function of shear rate to mimic electrode casting conditions for poly(acrylic acid) (PAA) and lithium neutralized poly(acrylic acid) (LiPAA) based electrodes. Rheology coupled ultra-small angle neutron scattering (rheo-USANS) was used to examine the aggregation and agglomeration behavior of each slurry as well as the overall shape of the aggregates. The addition of dispersant has opposing effects on slurries made with PAA or LiPAA binder. With a dispersant, there are fewer aggregates and agglomerates in the PAA based silicon slurries, while LiPAA based silicon slurries become orders of magnitude more aggregated and agglomerated at all shear rates. The reorganization of the PAA and LiPAA binder in the presence of dispersant leads to a more homogeneous slurry and a more heterogeneous slurry, respectively. This reorganization ripples through to the cast electrode architecture and is reflected in the electrochemical cycling of these electrodes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Degrees of Rate Control at Non(pseudo)steady-State Conditions
The degrees of rate control enable identification of rate-controlling transition states and species during (pseudo-)steady-state reaction. We demonstrate a method for identifying rate-controlling transition states and species at non-(pseudo-)steady-state conditions through modification of the definitions for degrees of rate control and sensitivities by superimposing the condition that time constants of the analytical rate function are kept constant when taking the partial derivatives of rate with respect to the rate constants/free energies. In conclusion, the utility of transient degrees of rate control is demonstrated for catalytic reaction networks to rationalize features of the transient rate including extrema and discontinuities.
42 ENGINEERING↗