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At least 1,243 records · Page 69

L-shell spectroscopic diagnostics of radiation from krypton HED plasma sources

X-ray spectroscopy is a useful tool for diagnosing plasma sources due to its non-invasive nature. One such source is the dense plasma focus (DPF). Recent interest has developed to demonstrate its potential application as a soft x-ray source. We present the first spectroscopic studies of krypton high energy density plasmas produced on a 3 kJ DPF device in Singapore. In order to diagnose spectral features, and to obtain a more comprehensive understanding of plasma parameters, a new non-local thermodynamic equilibrium L-shell kinetic model for krypton was developed. It has the capability of incorporating hot electrons, with different electron distribution functions, in order to examine the effects that they have on emission spectra. To further substantiate the validity of this model, it is also benchmarked with data gathered from experiments on the electron beam ion trap (EBIT) at Lawrence Livermore National Laboratory, where data were collected using the high resolution EBIT calorimeter spectrometer.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Pyridine Catalysis of Anhydride Hydrolysis within Carbodiimide‐Driven Reaction Networks

Carbodiimide-fueled reaction networks offer a versatile platform for nonequilibrium chemical systems. Typically, the carbodiimide converts a carboxylic acid to its anhydride, called “activation,” which subsequently undergoes hydrolysis, called “deactivation.” Here, we investigate pyridines with variable nucleophilicity as catalysts to control deactivation (pyridine, 4-methylpyridine, 4-methoxypyridine, and 4-dimethylaminopyridine). Reactions have been monitored by NMR spectroscopy. Although this reaction network is simple, determination of well-defined rate constants from kinetic modeling is challenging because of correlation between the parameters. This issue can be addressed by analyzing the anhydride hydrolysis independently. The rate of attack of the pyridines on the anhydride follows expected nucleophilicity trends, although this is offset by increased protonation of more-nucleophilic pyridines at typical pH's. The optimized parameters can be used to model the full carbodiimide-driven process, although the presence of the common carbodiimide EDC has unanticipated effects on the anhydride hydrolysis rate. The results offer context for controlling carbodiimide-fueled reaction networks through the choice of suitable catalysts and pH.

Anhydrides↗

Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors

We propose a new form of orbital-free (OF) kinetic energy density functional (KEDF) for semiconductors that is based on the Wang-Govind-Carter (WGC99) nonlocal KEDF. We enhance within the latter the semi-local von Weizsäcker KEDF term, which is exact for a single orbital. The enhancement factor we introduce is related to the extent to which the electron density is localized. The accuracy of the new KEDF is benchmarked against Kohn-Sham density functional theory (KSDFT) by comparing predicted energy differences between phases, equilibrium volumes, and bulk moduli for various semiconductors, along with metal-insulator phase transition pressures. We also compare point defect and (100) surface energies in silicon for a broad test of its applicability. This new KEDF accurately reproduces the exact non-interacting kinetic energy of KSDFT with only one additional adjustable parameter beyond the three parameters in the WGC99 KEDF; it exhibits good transferability between semiconducting to metallic silicon phases and between various III-V semiconductors without parameter adjustment. Overall, this KEDF is more accurate than previously proposed OF KEDFs (e.g., the Huang-Carter (HC) KEDF) for semiconductors, while the computational efficiency remains at the level of the WGC99 KEDF (several hundred times faster than the HC KEDF). This accurate, fast, and transferable new KEDF holds considerable promise for large-scale OFDFT simulations of metallic through semiconducting materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Physics of Reconnection and MMS Mission

Reconnection is the most important process driving the Earth's magnetosphere. Key to the success of the MMS science plan is the coupling of theory and observation. Determining the kinetic processes occurring in the diffusion region and physical parameters that control the rate of magnetic reconnection are among primary objectives of the MMS mission. Analysis of the role played by particle inertial effects in the diffusion region where the plasma is unmagnetized will be presented. The reconnection electric field in he diffusion region is supported primarily by particle non-gyrotropic effects. At the quasi-steady stage the reconnection electric field serves to accelerate and heat the incoming plasma population to maintain the current flow in the diffusion region the pressure balance. The primary mechanism controlling the dissipation in the vicinity of the reconnection site is incorporated into the fluid description in terms of non-gyrotropic corrections to the. induction and energy equations. The results of kinetic and fluid simulations illustrating the physics of magnetic reconnection will be presented. We will dem~:tistrate that kinetic nongyrotropic effects can significantly alter the global magnetosphere evolution and location of reconnection sites.

Kuznetsova, M. M.↗

How Do Type Ia Supernova Nebular Spectra Depend on Explosion Properties? Insights from Systematic Non-LTE Modeling

We present a radiative transfer code to model the nebular phase spectra of supernovae (SNe) in non-LTE (NLTE). We apply it to a systematic study of SNe Ia using parameterized 1D models and show how nebular spectral features depend on key physical parameters, such as the time since explosion, total ejecta mass, kinetic energy, radial density profile, and the masses of {sup 56}Ni, intermediate-mass elements, and stable iron-group elements. We also quantify the impact of uncertainties in atomic data inputs. We find the following. (1) The main features of SN Ia nebular spectra are relatively insensitive to most physical parameters. Degeneracy among parameters precludes a unique determination of the ejecta properties from spectral fitting. In particular, features can be equally well fit with generic Chandrasekhar mass (M{sub ch}), sub-M{sub Ch}, and super-M{sub Ch} models. (2) A sizable (≳0.1 M{sub ⊙}) central region of stable iron-group elements, often claimed as evidence for M{sub Ch} models, is not essential to fit the optical spectra and may produce an unusual flat-top [Co iii] profile. (3) The strength of [S iii] emission near 9500 Å can provide a useful diagnostic of explosion nucleosynthesis. (4) Substantial amounts (≳0.1 M{sub ⊙}) of unburned C/O mixed throughout the ejecta produce [O iii] emission not seen in observations. (5) Shifts in the wavelength of line peaks can arise from line-blending effects. (6) The steepness of the ejecta density profile affects the line shapes, offering a constraint on explosion models. (7) Uncertainties in atomic data limit the ability to infer physical parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

Fragility correlates thermodynamic and kinetic properties of glass forming liquids

Graphical abstract: The suggested new fragility parameter correlates viscosity and configurational entropy. - Highlights: • A new fragility function, F=ΔT/ΔC{sub p}×C{sub p}{sup l}/T{sub g} has been proposed. • A three parameter viscosity function using the new F reproduces Angell fragility plot. • A new ΔC{sub p} function is derived which directly relates Adam–Gibbs function with the fragility based viscosity function. - Abstract: In our earlier communication we proposed a simple fragility determining function, ([NBO]/V{sub m}{sup 3}T{sub g}), which we have now used to analyze several glass systems using available thermal data. A comparison with similar fragility determining function, ΔC{sub p}/C{sub p}{sup l}, introduced by Chryssikos et al. in their investigation of lithium borate glasses has also been performed and found to be more convenient quantity for discussing fragilities. We now propose a new function which uses both ΔC{sub p} and ΔT and which gives a numerical fragility parameter, F whose value lies between 0 and 1 for glass forming liquids. F can be calculated through the use of measured thermal parameters ΔC{sub p}, C{sub p}{sup l}, T{sub g} and T{sub m}. Use of the new fragility values in reduced viscosity equation reproduces the whole range of viscosity curves of the Angell plot. The reduced viscosity equation can be directly compared with the Adam–Gibbs viscosity equation and a heat capacity function can be formulated which reproduces satisfactorily the ΔC{sub p} versus ln(T{sub r}) curves and hence the configurational entropy.

36 MATERIALS SCIENCE↗

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective

The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design and Performance of South Ukraine Nuclear Power Plant Mixed Cores

In 2010, 42 Westinghouse fuel assemblies (WFAs) were loaded into the core of South Ukraine Nuclear Power Plant (SUNPP) Unit 3 after four successful cycles with 6 Westinghouse Lead Test Assemblies. The scope of safety substantiating documents required for the regulatory approval of this mixed core was extended considerably, particularly with development and implementation of new methodologies and 3-D kinetic codes. Additional verification for all employed codes was also performed. Despite the inherent hydraulic non-uniformity of a mixed core, it was possible to demonstrate that all design and operating restrictions for three different types of fuel (TVS-M, TVSA and WFA) loaded in the core were conservatively met. This paper provides the main results from the first year of operation of the core loaded with 42 WFAs, the predicted parameters for the transition and equilibrium cycles with WFAs, comparisons of predicted versus measured core parameters, as well as the acceptable margin evaluation results for reactivity accidents using the 3-D kinetic codes. To date WFA design parameters have been confirmed by operation experience.

Abdullayev, A M↗

Kinetics teach that electronic coupling lowers the free-energy change that accompanies electron transfer

Significance Nature’s use of electronic coupling (H DA ) and free-energy (ΔG o ) gradients to vectorially control electron transport provides inspiration for artificial photosynthesis. Theoretical predictions indicate that H DA and ΔG o are not independent parameters, and are instead linked. Reported here is a broadly applicable kinetic approach that was utilized to demonstrate such behavior for four acceptor–bridge–donor compounds. When the electronic coupling was large and electron transfer was adiabatic, the free energy of the reaction |ΔG o | was less than that for nonadiabatic transfer. This finding should be taken into account in the design of hybrid materials for solar energy conversion and has broad implications to the many classes of electron-transfer reactions in biology and chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the thermal stability of physical vapor deposited oxide-hardened nanocrystalline gold thin films

We describe a correlation between electrical resistivity and grain size for PVD synthesized polycrystalline oxide-hardened metal-matrix thin films in oxide-dilute (<5 vol. % oxide phase) compositions. The correlation is based on the Mayadas-Shatzkes (M-S) electron scattering model, predictive of grain size evolution as a function of composition in the oxide-dilute regime for 2 μm thick Au-ZnO films. We describe a technique to investigate grain boundary (GB) mobility and the thermal stability of GBs based on in situ electrical resistivity measurements during annealing experiments, interpreted using a combination of the M-S model and the Michels et al. model describing solute drag stabilized grain growth kinetics. Using this technique, activation energy and pre-exponential Arrhenius parameter values of E{sub a} = 21.6 kJ/mol and A{sub o} = 2.3 × 10{sup −17} m{sup 2}/s for Au-1 vol. % ZnO and E{sub a} = 12.7 kJ/mol and A{sub o} = 3.1 × 10{sup −18} m{sup 2}/s for Au-2 vol. % ZnO were determined. In the oxide-dilute regime, the grain size reduction of the Au matrix yielded a maximum hardness of 2.6 GPa for 5 vol. % ZnO. A combined model including percolation behavior and grain refinement is presented that accurately describes the composition dependent change in electrical resistivity throughout the entire composition range for Au-ZnO thin films. The proposed correlations are supported by microstructural characterization using transmission electron microscopy and electron diffraction mapping for grain size determination.

36 MATERIALS SCIENCE↗

DRDMannTurb: A Python package for scalable, data-driven synthetic turbulence

Synthetic turbulence models (STMs) are used in wind engineering to generate realistic flow fields and are employed as inputs to industrial wind simulations. Examples include prescribing inlet conditions in large eddy simulations that model loads on wind turbines and tall buildings. We are interested in STMs capable of generating fluctuations based on prescribed second-moment statistics since such models can simulate environmental conditions that closely resemble on-site observations. To this end, the widely used Mann model (see Mann, 1994, 1998) is the inspiration for DRDMannTurb. The Mann model is described by three physical parameters: a magnitude parameter influencing the global variance of the wind field and corresponding to the Kolmogorov constant multiplied by the rate of viscous dissipation of the turbulent kinetic energy to the two-thirds, αϵ 2/3 , a turbulence length scale parameter L, and a nondimensional parameter Γ related to the lifetime of the eddies. A number of studies, as well as international standards (e.g., those by the International Electrotechnical Commission (IEC)), include recommended values for these three parameters with the goal of standardizing wind simulations according to observed energy spectra. Yet, having only three parameters, the Mann model faces limitations in accurately representing the diversity of observable spectra. This Python package enables users to extend the Mann model and more accurately fit field measurements through flexible neural network models of the eddy lifetime function. Following Keith et al. (2021), we refer to this class of models as Deep Rapid Distortion (DRD) models. DRDMannTurb also includes a general module implementing an efficient method for synthetic turbulence generation based on a domain decomposition technique. This technique is also described in Keith et al. (2021).

17 WIND ENERGY↗

HTO washout model: on the relationship between exchange rate and washout coefficient

Washout coefficient Λ is widely used as a parameter in washout models. These models describes overall HTO washout with rain by a first-order kinetic equation, while washout coefficient Λ depends on the type of rain event and rain intensity and empirical parameters a, b. The washout coefficient is a macroscopic parameter and we have considered in this paper its relationship with a microscopic rate K of HTO isotopic exchange in atmospheric humidity and drops of rainwater. We have shown that the empirical parameters a, b can be represented through the rain event characteristics using the relationships of molecular impact rate, rain intensity and specific rain water content while washout coefficient Λ can be represented through the exchange rate K, rain intensity, raindrop diameter and terminal raindrop velocity.

07 ISOTOPE AND RADIATION SOURCES↗

Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions

We study the corrections to the power spectra of curvature and tensor perturbations and the tensor-to-scalar ratio r in single field slow roll inflation with standard kinetic term due to initial conditions imprinted by a ''fast-roll'' stage prior to slow roll. For a wide range of initial inflaton kinetic energy, this stage lasts only a few e-folds and merges smoothly with slow-roll thereby leading to non-Bunch-Davies initial conditions for modes that exit the Hubble radius during slow roll. We describe a program that yields the dynamics in the fast-roll stage while matching to the slow roll stage in a manner that is independent of the inflationary potentials. Corrections to the power spectra are encoded in a ''transfer function'' for initial conditions T{sub α}(k), P{sub α}(k) = P{sup BD}{sub α}(k)T{sub α}(k), implying a modification of the ''consistency condition'' for the tensor to scalar ratio at a pivot scale k{sub 0}: r(k{sub 0}) = −8n{sub T}(k{sub 0}) [T{sub T}(k{sub 0})/T{sub R}(k{sub 0})]. We obtain T{sub α}(k) to leading order in a Born approximation valid for modes of observational relevance today. A fit yields T{sub α}(k) = 1+A{sub α}k{sup −p}cos [2πωk/H{sub sr}+φ{sub α}], with 1.5∼<p∼<2, ω ≅ 1 and H{sub sr} the Hubble scale during slow roll inflation, where curvature and tensor perturbations feature the same p,ω for a wide range of initial conditions. These corrections lead to both a suppression of the quadrupole and oscillatory features in both P{sub R}(k) and r(k{sub 0}) with a period of the order of the Hubble scale during slow roll inflation. The results are quite general and independent of the specific inflationary potentials, depending solely on the ratio of kinetic to potential energy κ and the slow roll parameters ε{sub V}, η{sub V} to leading order in slow roll. For a wide range of κ and the values of ε{sub V}; η{sub V} corresponding to the upper bounds from Planck, we find that the low quadrupole is consistent with the results from Planck, and the oscillations in r(k{sub 0}) as a function of k{sub 0} could be observable if the modes corresponding to the quadrupole and the pivot scale crossed the Hubble radius very few (2–3) e-folds after the onset of slow roll. We comment on possible impact on the recent BICEP2 results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transient kinetic insights into selective propene oxidation over industrial bismuth molybdate catalysts

Selective oxidation of propene to acrolein over industrial multicomponent bismuth molybdate (BMO) catalysts significantly depends on reaction conditions that include operating parameters and catalyst state. Here, this work investigates selective propene oxidation in the intrinsic kinetic paradigm of Temporal Analysis of Products (TAP) reactor by systematically varying catalyst redox state, temperature, and oxygen-to-propene feed ratio. A 93 % propene conversion with an acrolein yield of 80 % is achieved at elevated temperatures (450 °C) on oxidized catalysts under oxygen-rich conditions (O 2 :C 3 H 6 = 10). However, these conditions diminish acrolein-to-CO 2 selectivity due to enhanced total oxidation to CO 2 . In contrast, a reduced catalyst state, moderate temperature (350 °C), and lower oxygen feed (O 2 :C 3 H 6 = 1) nearly doubles the acrolein to-CO 2 selectivity, albeit at a lower acrolein yield (33 %). Transient kinetic studies together with a kinetic model that simplify the major product formation pathways in lumped non-elementary forms reveal that the availability of surface oxygen species plays a pivotal role in governing reaction pathways. Additionally, density functional theory (DFT) calculations on pure BMO catalysts inform the role of surface redox states on propene and oxygen activation barriers. Lattice oxygen at acrolein-selective sites drives both acrolein and CO 2 formation, while adsorbed oxygen at activation sites favors unselective CO 2 generation. This work establishes a critical relationship between transient product selectivity and surface oxygen availability, which is strongly influenced by catalyst redox state, feed ratio, and reaction temperature. These insights underscore the importance of dynamic reactor operation strategies and offer a foundation for designing next-generation propene oxidation processes with tunable acrolein selectivity.

42 - ENGINEERING↗

Modeling Radiolysis and Chemical Reactions during Dry Storage of Aluminum-clad Spent Nuclear Fuel

After aluminum-clad spent nuclear fuel (ASNF) is removed from the reactor, it is initially stored in spent fuel pools, which are specially designed water-filled basins that provide temporary cooling to reduce the temperature of the fuel assemblies and provide radiation shielding. ASNF continues to generate heat due to the radioactive decay of elements within the fuel, which persists for many years post-shutdown as the residual radioactive products decay into more stable elements. During the wet storage period, an oxyhydroxide layer composed of boehmite/bayerite forms on the surfaces of the aluminum cladding from exposure to water in the pools. Road-ready packaging for long-term disposition of the ASNF involves dry storage in helium backfilled DOE standard canisters (DSCs). When the ASNF is removed from water storage and dried, most of the water is removed, but some physisorbed and chemisorbed water remains in the oxyhydroxide layers. This residual water can produce hydrogen when exposed to radiation from the ASNF during dry storage. Predicting hydrogen accumulation over time in the DSCs is critical for long-term storage considerations. Previous modeling efforts have developed coupled computational fluid dynamics (CFD)-chemical models to simulate temperature, pressure, and gas phase concentrations within the DSCs. These models use the thermal field predicted by CFD as input to a radiolysis model for the gas phase and the surface oxyhydroxide layer chemistry. Given the long storage period of the DSCs and the impracticality of long-term experiments, a simulation-based approach is necessary to assess chemical evolution within the canisters. This study advances the development of a modeling framework designed to simulate the chemical evolution of spent fuel canisters. Both thermal and radiation-driven reactions are considered, with radiation kinetics quantified using G-values. Sensitivity analysis identifies key parameters influencing species composition. Reaction pathway diagrams offer insight into dominant species formation routes, enabling more effective comparisons between model predictions and experimental observations, particularly regarding the production of hydrogen. Results show that the model predicts significant hydrogen gas production with minimal oxygen generation, primarily due to hydrogen formation via boehmite pathways. These findings underscore the importance of accurately characterizing surface-bound species and radiolysis kinetics. A deeper understanding of these mechanisms is critical for evaluating the long-term safety of nuclear waste storage.

12 - MGMT OF RADIOACTIVE AND NON-RADIOACTIVE WASTE↗

Rate-equation modelling and ensemble approach to extraction of parameters for viral infection-induced cell apoptosis and necrosis

We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death). Several model parameters necessary for computer simulation were determined by reviewing and analyzing available published experimental data. By comparing experimental data to computer modelling results, we identify the parameters that are the most sensitive to the measured system properties and allow for the best data fitting. Our model allows extraction of parameters from experimental data and also has predictive power. Using the model we describe interesting time-dependent quantities that were not directly measured in the experiment and identify correlations among the fitted parameter values. Numerical simulation of viral infection progression is done by a rate-equation approach resulting in a system of “stiff” equations, which are solved by using a novel variant of the stochastic ensemble modelling approach. The latter was originally developed for coupled chemical reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗