Master Equation For System Research Articles

A theoretical and kinetic study of key reactions between ammonia and fuel molecules, part III: H-atom abstraction from esters by ṄH2 radicals

Hydrogen atom abstraction reactions by ṄH2 radicals play a crucial role in determining the reactivity of ammonia/fuel binary blends. Esters are a typical component of environmentally friendly and economically promising biofuels. The feasibility of the ammonia/biofuel dual-fuel approach has been proven in practical engines. [Energy and Fuels 22 (2008) 2963] and [Int. J. Energy Res. 2023 (2023) 9920670]. ṄH2 radicals play a critical role in the combustion and pyrolysis chemistry of ammonia and N-containing-rich fuels. In ammonia/biofuels hybrid combustion, ṄH2 radicals can react with biofuel molecules in a reaction class that is particularly important especially when sufficient ammonia is blended in order to eliminate NOx emissions. To help unravel the chemistry of ammonia/biofuel blends, a systematic theoretical kinetic study of H-atom abstraction from eleven alky esters of CnH2n+1COOCH3 (n = 1–4), CH3COOCmH2m+1 (m = 1–4), and C2H5COOC2H5, by ṄH2 radicals is performed in this work. The geometry optimization, frequency, and zero-point energy calculations for all related species, as well as the hindrance potential energy surface for low frequency torsional modes in the reactants and transition states, were performed at the M06–2X/6–311++G(d,p) level of theory. Intrinsic reaction coordinate calculations were performed to validate the connections between the transition states and expected minima energy species. The energies of all of the species involved were calculated at the QCISD(T)/cc-pVXZ (X = D, T, Q) and MP2/cc-pVYZ (Y = T, Q) levels of theory and then extrapolated to the complete basis set. Rate constants of 39 reactions were calculated using the Master Equation System Solver (MESS) program in the temperature range of 500 – 2000 K. These rate constants for different H-atom abstraction sites are provided and can be extrapolated to larger esters. The kinetic effects from the functional group are also illustrated by performing detailed comparisons with the previous studies of ṄH2 radical reactions with alkanes, alcohols and ethers.

Theoretical kinetic study of key reactions between ammonia and fuel molecules, part I: Hydrogen atom abstraction from alkanes by ṄH2 radical

Cross reactions between ṄH2 radical and fuel molecules are essential in determining the reactivity for ammonia/fuel blends. A systematic theoretical chemical kinetic investigation of hydrogen atom abstraction by ṄH2 radical from C1–C6 alkanes, n-heptane, and isooctane has been performed in this study. The geometry optimization, frequency, and zero-point energy calculations for all species related to the title reactions were calculated at the M06-2X/6-311++G(d,p) level of theory. One-dimensional hindered rotor treatment has also been performed at the same level of theory to obtain the potential energy surface for the low frequency torsional modes. Single-point energy was obtained at the QCISD(T)/cc-pVDZ, QCISD(T)/cc-pVTZ, MP2/cc-pVDZ, MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory and then extrapolated to the complete basis set. Benchmark calculations for single point energy have also been carried out at the CCSD(T)-F12/cc-pVTZ, CCSD(T)-F12/cc-pVQZ, CCSD(T)-F12/aug-cc-pVTZ and CCSD(T)-F12/aug-cc-pVQZ levels of theory based on the geometries obtained at the CCSD(T)/cc-pVDZ level of theory for the reaction systems of methane + ṄH2 and ethane + ṄH2. The rate constants of 41 reactions in the temperature range 298.15–2000 K were calculated by using the Master Equation System Solver (MESS) with conventional transition state theory. Good agreement has been gained between our calculated results and the available theoretical and experimental data in the literature. Rate rules for different reaction sites have also been derived, and the average rate constants for primary, secondary, and tertiary sites were also reported on a per hydrogen atom basis. The impact of calculation data for the ammonia/alkane blends model has also been investigated. The calculated rate constants are valuable for the combustion kinetic model development for ammonia blending fuels.

Master equation model for solute transport in river basins: part II basin fluvial scale

At basin scale the physical phenomenon of diffusion involves the intricate spreading and dispersion of substances within complex systems as networks of interconnected channels, streams, and land surfaces. Understanding this process is crucial for many purposes as management and conservation of water resources. We extend the model application of our previous work (Part I, Rizzello et al. in Stoch Environ Res Risk Assess 37:3807–3817, 2023) from channel to basin scale. We use conservation of mass and momentum to formulate and apply the Master Equation system at basin scale. The results on simulated events highlight the transition of the model from channel scale to basin scale.

Machine learning rate constants of hydrogen abstraction reactions between ester and H atom

The rate constants of hydrogen abstraction reactions of alkyl ester by H atom are crucial for optimizing combustion reaction network and improving combustion efficiency of biodiesel. Due to the lack of experimental and theoretical rate coefficients data for some reactions - such as hydrogen abstraction of large biodiesel molecules by free radicals - machine learning provides a viable alternative to predict rate constants. In this study, three different machine learning (ML) methods - feedforward neural network (FNN), extreme gradient boosting (XGB) and XGB-FNN hybrid model - were used to predict rate constants of the reactions between alkyl ester and H atom. The rate constants of 41 reactions between H + CnH2n+1COOCmH2m+1 (n = 0–5, m = 1, 2) were calculated by the Master Equation System Solver (MESS) program over a temperature range of 300–2000 K for model training. The results showed that the XGB-FNN model with 8 descriptors has better overall performance than the other two ML methods. The average deviation of XGB-FNN model on the test set is 33.56% by performing leave one out (LOO) cross validations. The rate constants of the H + methyl decanoate (MD) reactions over a temperature range of 300∼2000 K were predicted by the XGB-FNN model, which follow well the modified three-parameter Arrhenius equation and agree well with theoretical values, indicating that the hybrid XGB-FNN model is robust in predicting the rate constants of alkyl ester and H atom in the temperature range of combustion. The present ML method in this study is supposed to be able to provide accurate and affordable rate constants prediction of larger systems, the molecular sizes of which are comparable to those of the dominant components of real biodiesel. That is important for the development of biodiesel kinetic models.

Formation of phosphorus monoxide through the [Formula: see text] reaction.

Phosphorus is a key and vital element for a diverse set of important biological molecules, being indispensable for life as we know. A deeper comprehension of its role in astrochemistry and atmospheric chemistry may aid in finding answers to how this element became available on Earth. The PO molecule is one of the main reservoirs of phosphorus in the interstellar medium (ISM), and a better understanding of the mechanisms and rate coefficients for its formation in the ISM is important for modelling its abundances. In this work, we perform multireference configuration interaction calculations on the formation of PO via the [Formula: see text] reaction, analyzing its potential energy surface and rate coefficients for the global reaction on both doublet and quartet states. We also perform DFT (M06-2X) and CCSD(T) calculations, in order to compare the results. We found that the OPO system possesses a high multiconfigurational character, making DFT and CCSD methodologies not suitable for its potential energy landscape calculation. The rate coefficients have been calculated using the master equation system solver (MESS) package, and the results compared to recent experimental data. It is shown that the quartet state contributes for temperatures higher than 700K. The computed rate coefficient can be described by a modified Arrhenius equation [[Formula: see text]] with [Formula: see text], [Formula: see text] and [Formula: see text] K.

Simulation of Oxygen Chemical Kinetics Behind Incident and Reflected Shocks via Master Equation

A model for simulating postshock conditions using only state-resolved kinetic data of ab initio accuracy is presented. The quasi-classical trajectory method is used to compute a vibrational-specific kinetic database that describes internal energy transfer and dissociation in a nonionizing oxygen mixture. The kinetic database is implemented in a system of master equations and coupled to conservation laws to simulate a series of conditions, including zero-dimensional adiabatic reservoir, one-dimensional postincident, and one-dimensional postreflected shock relaxation. The present results are in excellent agreement with temperature profiles produced by the direct molecular simulation method at a fraction of cost. For the first time, the state-resolved model is applied to model relaxation behind a reflected shock passing through a thermally nonequilibrium gas. Model validation is made via comparisons to the experiments of Ibraguimova et al. (Journal of Chemical Physics, Vol. 139, No. 3, 2013, Paper 034317) and Streicher et al. (Physics of Fluids, Vol. 33, No. 5, 2021, Paper 056107). It is shown that neglecting relaxation in the postincident shock region may lead to nonnegligible errors in determining initial postreflected shock translational and vibrational temperatures, particularly in cases where the test gas is not diluted with an inert species.

Exploring the kinetics and thermochemistry effects on C2-C6 alkene combustion chemistry by ȮH radical; Implications for Combustion Modeling and Simulation

A systematic theoretical study of C2 to C6 alkenes reacting with ȮH radical to explore the kinetics and thermochemistry effects are carried out in this work. The geometries and frequencies of 15 reactants, 15 pre-reaction complexes, 93 transition states, and 93 products are optimized at M06-2X/6-311++G(d,p) level of theory. The hindrance potentials for low-frequency torsional modes are treated at M06-2X/6–31 G level of theory. Single-point energies for all species involved in this work are calculated at spin-unrestricted CCSD(T)/CBS level of theory with basis-set correction from MP2/aug-cc-pVnZ (n = T and Q). High-pressure-limit rate constants for H-atom abstraction reaction channels and pressure-dependent rate constants for addition reaction channels are calculated by solving the Rice-Ramsperger Kassel-Marcus/Master Equation (RRKM/ME) implemented in the Master Equation System Solver (MESS) program, coupled with variational transition-state theory (VTST). Temperature-dependent thermochemical properties for all species and related radicals have been computed using a combination of composite methods to provide adequate accuracy results for modeling application. For straight-chain alkenes, the temperature range, in which the addition channel dominates, shifts to lower temperatures as the alkene gets longer. Hydrogen-atom abstractions from the allylic site of alkenes are the dominant reaction channels at high temperatures. The H-atom abstraction reactions from secondary alkylic and primary alkylic CH sites become more important as substituent groups become larger. High-pressure-limit and pressure-dependent rate constants calculated in this work have been extensively compared with the experimental and theoretical results available in the literature, and they show overall good agreement. The simulation results show that the calculated rate constants in this work have positive influences to the accuracy of simulation results at most reaction conditions. However, at some of the reaction conditions, thermochemical data have much more important influence to the simulation results at low temperature ranges. Rate constants obtained in this work and detailed branching ratio for each reaction can serve as a guidance in alkene combustion model development.

Splitting methods and short time existence for the master equations in mean field games

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite-dimensional equations stated in the space of probability measures. Our new approach simplifies and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.

A Spectral Theorem for the Semigroup Generated by a Class of Infinitely Many Master Equations

In this article we investigate the spectral properties of the infinitesimal generator of an infinite system of master equations arising in the analysis of the approach to equilibrium in statistical mechanics. The system under consideration thus consists of infinitely many first-order differential equations governing the time evolution of probabilities susceptible of describing jumps between the eigenstates of a differential operator with a discrete point spectrum. The transition rates between eigenstates are chosen in such a way that the so-called detailed balance conditions are satisfied, so that for a large class of initial conditions the given system possesses a global solution which converges exponentially rapidly toward a time independent probability of Gibbs type. A particular feature and a challenge of the problem under consideration is that in the infinite-dimensional functional space where the initial-value problem is well posed, the infinitesimal generator is realized as a non normal and non dissipative compact operator, whose spectrum therefore does not exhibit a spectral gap around the zero eigenvalue.

Cellular Signaling beyond the Wiener-Kolmogorov Limit.

Accurate propagation of signals through stochastic biochemical networks involves significant expenditure of cellular resources. The same is true for regulatory mechanisms that suppress fluctuations in biomolecular populations. Wiener-Kolmogorov (WK) optimal noise filter theory, originally developed for engineering problems, has recently emerged as a valuable tool to estimate the maximum performance achievable in such biological systems for a given metabolic cost. However, WK theory has one assumption that potentially limits its applicability: it relies on a linear, continuum description of the reaction dynamics. Despite this, up to now no explicit test of the theory in nonlinear signaling systems with discrete molecular populations has ever seen performance beyond the WK bound. Here we report the first direct evidence of the bound being broken. To accomplish this, we develop a theoretical framework for multilevel signaling cascades, including the possibility of feedback interactions between input and output. In the absence of feedback, we introduce an analytical approach that allows us to calculate exact moments of the stationary distribution for a nonlinear system. With feedback, we rely on numerical solutions of the system's master equation. The results show WK violations in two common network motifs: a two-level signaling cascade and a negative feedback loop. However, the magnitude of the violation is biologically negligible, particularly in the parameter regime where signaling is most effective. The results demonstrate that while WK theory does not provide strict bounds, its predictions for performance limits are excellent approximations, even for nonlinear systems.

Formation of a Morphogen Gradient - Acceleration by Quantum Walks

The establishment of graded concentration distributions of certain signalling molecules, called morphogens, is crucial for the successful embryonic development of multicellular organisms. The morphogen system that has been studied in the greatest detail is the Bicoid (Bcd) gradient established during the early embryonic development of fruit flies and provides the embryo cells with the necessary positional information for the proper implementation of the body plan of the organism. Both continuous as well as discrete-state classical random-walk models fail to provide a completely satisfactory explanation of the dynamics of Bcd gradient formation within the developmentally relevant timescales. By presuming the existence of an arbitrary chirality degree of freedom that characterizes each Bcd molecule, we here therefore develop a discrete-time quantum walk model of the process. Our approach is based on the recent suggestion that high temperatures and random interactions need not necessarily destroy many-body quantum coherence. In this way we are led to a system of non-classical master equations bearing an interference term that can be numerically solved on a computer. Our analysis predicts a large value of diffusion rate for the Bcd system in the very early nuclear division cycles that needs to be verified experimentally. Additionally, with the chirality and position degrees of freedom at our disposal entanglement shows up as a natural consequence in the system. Taking inspiration from a very recent demonstration of the existence of entanglement phenomenon in a hot, strongly-interacting atomic system, the discussion takes the point of view that the emergence of geometry in the embryo system is consequence of quantum entanglement that needs further understanding and analysis.

Chemical kinetics study of 1,3-butadiene + HȮ2; implications for combustion modeling and simulation

Detailed reaction kinetics for the system of 1,3-butadiene + hydroperoxyl radical (HȮ2) and its application in combustion modeling have been investigated in this work. Zero-point energy (ZPE) corrected potential energy surfaces (PESs) for the title reactions have been obtained using high-level ab initio electronic structure methods of ROCCSD(T)/CBS//BHandHLYP/6–311++G(d,p), and the energies relative to the reactants for all stationary points were used in the kinetic calculations. Pressure- and temperature-dependent rate constants for each individual reaction pathway have been calculated by solving the Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) implemented in the Master Equation System Solver (MESS) program. The bimolecular pathways forming vinyl oxirane, (CYOC)CC, and hydroxyl radical (ȮH) from the reactants are found to be dominant in the temperature range of 800–2000 K below 1 atm, and keep competitive when temperature is higher than 1000 K at 100 atm. At elevated pressures, the stabilizations of the two entrance channels forming radicals of 1-hydroperoxy-3-buten-2-yl (C4H61–3OOH4) and 3-butenyl-2-peroxy (C4H71-OO3) are more important than the formation of bimolecular products (CYOC)CC + ȮH at temperatures below 1000 K. Temperature-dependent thermochemical properties for important species on the PESs of 1,3-butadiene + HȮ2 have also been calculated. The kinetics and thermochemistry data for the title reaction system calculated in this work have been incorporated into AramcoMech 3.0 mechanism and their influence on the performance of AramcoMech 3.0 in simulating the combustion properties of 1,3-butadiene, including ignition delay times and species profiles against temperature or time, has been investigated. This is a first-time study on the reaction kinetics between HȮ2 radical and species including two double bonds.

Noninteracting many-particle quantum transport between finite reservoirs

We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time, and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the time scale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.

A single pulse shock tube study of pentene isomer pyrolysis

A single-pulse shock tube study of the four pentene isomers is carried out at 2 ± 0.16 bar and 900–1600 K. C1 to C6 species profiles were recorded using gas chromatography mass spectrometry analyses. The species are identified using mass spectrometry and quantified by flame ionization detection. High-pressure limiting and pressure-dependent rate constants for 2M1B, 2M2B and 3M1B + Ḣ were calculated using RRKM theory with a Master Equation (ME) analysis using the Master Equation System Solver, MESS. A mechanism was formulated based on rate rules and theoretical calculations. Comparisons between experimental results and model simulations are provided for all of the five pentene isomers investigated with satisfactory agreement. Furthermore, an insight is provided into the influence of molecular structure on the reactivity of pyrolysis chemistry. Interestingly, it is found that the HACA mechanism is much less prominent for benzene formation compared to the role of cyclopentadienyl radical recombination with methyl radicals and also the recombination of propargyl radicals.

State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N2-N System.

We present a detailed comparison of two high-fidelity approaches for simulating non-equilibrium chemical processes in gases: the state-to-state master equation (StS-ME) and the direct molecular simulation (DMS) methods. The former is a deterministic method, which relies on the pre-computed kinetic database for the N2-N system based on the NASA Ames ab initio potential energy surface (PES) to describe the evolution of the molecules' internal energy states through a system of master equations. The latter is a stochastic interpretation of molecular dynamics relying exclusively on the same ab initio PES. It directly tracks the microscopic gas state through a particle ensemble undergoing a sequence of collisions. We study a mixture of nitrogen molecules and atoms forced into strong thermochemical non-equilibrium by sudden exposure of rovibrationally cold gas to a high-temperature heat bath. We observe excellent agreement between the DMS and StS-ME predictions for the transfer rates of translational into rotational and vibrational energy, as well as of dissociation rates across a wide range of temperatures. Both methods agree down to the microscopic scale, where they predict the same non-Boltzmann population distributions during quasi-steady-state dissociation. Beyond establishing the equivalence of both methods, this cross-validation helped in reinterpreting the NASA Ames kinetic database and resolve discrepancies observed in prior studies. The close agreement found between the StS-ME and DMS methods, whose sole model inputs are the PESs, lends confidence to their use as benchmark tools for studying high-temperature air chemistry.

Remarks on Nash equilibria in mean field game models with a major player

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number N of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as N tends to infinity.

Ab Initio/Transition-State Theory Study of the Reactions of Ċ5H9 Species of Relevance to 1,3-Pentadiene, Part I: Potential Energy Surfaces, Thermochemistry, and High-Pressure Limiting Rate Constants.

In this study, the reactions of Ċ5H9 radicals are theoretically investigated, with a particular emphasis on hydrogen atom addition reactions to 1,3-pentadiene (C5H8) to form Ċ5H9 radicals, although the subsequent isomerization and decomposition reactions of the Ċ5H9 radicals are also of direct relevance to the radicals formed from the pyrolysis and oxidation of species including pentene and cyclopentane. Moreover, H-atom abstraction reactions by hydrogen atoms from 1,3-pentadiene are also investigated. The geometries and frequencies of 63 potential energy surface (PES) minima and 88 transition states are optimized at the ωB97XD/aug-cc-pVTZ level of theory. Spin-unrestricted open-shell single-point energies for all the species are calculated at the CCSD(T)/aug-cc-pVTZ level of theory with basis set corrections from MP2/aug-cc-pVXZ (where X = T and Q). A one-dimensional hindered rotor treatment is employed for torsional modes, with the M06-2X/6-311++G(D,P) method used to compute the potential energy as a function of the dihedral angle. The high-pressure limiting rate constants and the thermochemical properties for C5 species are calculated using the Master Equation System Solver (MESS) with conventional transition-state theory and comparisons made with existing available literature data. A hydrogen atom can add to the terminal carbon atom of 1,3-pentadiene to form the 2,4-Ċ5H9 radical and/or the internal carbon atoms to form 2,5-Ċ5H9, 1,4-Ċ5H9, and 1,3-Ċ5H9 radicals. Among the four entrance channels for Ḣ atom addition reactions, the formation of 2,4-Ċ5H9 and 1,3-Ċ5H9 radicals is more exothermic in comparison to the other Ċ5H9 isomers (2,5-Ċ5H9, 1,4-Ċ5H9) because of the resonantly stabilized allylic structure. Consequently, the formation of the former is generally dominant in terms of barrier heights. Ḣ atom addition reactions to 1,3-pentadiene are compared to available C3-C5 alkenes and dienes, with external addition calculated to be kinetically favored over internal addition. However, the correlation between heats of formation and energy barriers for Ḣ atom addition to 1,2-dienes is different from that for 1,3- and 1,4-dienes. Hydrogen atom addition and abstraction rate constants are also compared for 1,3-pentadiene, with addition found to be dominant. The subsequent unimolecular reactions on the Ċ5H9 PES are found to be highly complex with reactions taking place on a multiple-well multiple-channel PES. For clarity, the reaction mechanism and kinetics of each Ċ5H9 radical are discussed individually in terms of the computed enthalpy of the reaction and activation, the transition-state structure/reaction class, and also in terms of the combustion species for which the reactions are of potential importance. The reactions on the Ċ5H9 PES are divided into three reaction classes (H-shift isomerization, cycloaddition, and β-scission reactions), and the reactivity-structure-based estimation rules for energy barriers are derived for these three reaction classes and compared to literature results for alkyl radicals.

Vibrational energy transfer and dissociation in O2-N2 collisions at hyperthermal temperatures.

Simulation of vibrational energy transfer and dissociation in O2-N2 collisions is conducted using the quasi-classical trajectory method on an ab initio potential energy surface. Vibrationally resolved rate coefficients are obtained in a high-temperature region between 8000 and 20 000 K by means of the cost-efficient classical trajectory propagation method. A system of master equations is constructed using the new dataset in order to simulate thermal and chemical nonequilibrium observed in shock flows. The O2 relaxation time derived from a solution of the master equations is in good agreement with the Millikan and White correlation at lower temperatures with an increasing discrepancy toward the translational temperature of 20 000 K. At the same time, the N2 master equation relaxation time is similar to that derived under the assumption of a two-state system. The effect of vibrational-vibrational energy transfer appears to be crucial for N2 relaxation and dissociation. Thermal equilibrium and quasi-steady state dissociation rate coefficients in O2-N2 heat bath are reported.

Understanding the importance of the temperature dependence of viscosity on the crystallization dynamics in the Ge2Sb2Te5 phase-change material

The crystallization dynamics in the phase-change material Ge2Sb2Te5 is modelled using the more detailed Master equation method over a wide range of heating rates commensurate with published ultrafast calorimetry experiments. Through the attachment and detachment of monomers, the Master rate equation naturally traces nucleation and growth of crystallites with temperature history to calculate the transient distribution of cluster sizes in the material. Both the attachment and detachment rates in this theory are strong functions of viscosity, and thus, the value of viscosity and its dependence on temperature significantly affect the crystallization process. In this paper, we use the physically realistic Mauro−Yue−Ellison−Gupta−Allan viscosity model in the Master equation approach to study the role of the viscosity model parameters on the crystallization dynamics in Ge2Sb2Te5 under ramped annealing conditions with heating rates up to 4 × 104 K/s. Furthermore, due to the relatively low computational cost of the Master equation method compared to atomistic level computations, an iterative numerical approach was developed to fit theoretical Kissinger plots simulated with the Master equation system to experimental Kissinger plots from ultrafast calorimetry measurements at increasing heating rates. This provided a more rigorous method (incorporating both nucleation and growth processes) to extract the viscosity model parameters from the analysis of experimental data. The simulations and analysis revealed the strong coupling between the glass transition temperature and fragility index in the viscosity and crystallization models and highlighted the role of the dependence of the glass transition temperature on the heating rate for the accurate estimation of the fragility index of phase-change materials from the analysis of experimental measurements.

State-specific simulation of oxygen vibrational excitation and dissociation behind a normal shock

A complete vibration–vibration–translation (V–V–T) bound–bound transitions rates database for O2–O2 collisions is generated using the forced harmonic oscillator (FHO) model with temperature range between 1000 and 20,000K. The postshock process of oxygen vibrational excitation and dissociation is simulated by solving the system of master equations coupled with the one-dimensional compressible flow equations. The results agree well with existing shock tube data. The state-specific calculations show that inclusion of pure vibration–vibration (V–V) processes could reduce the discrepancy with experimental data and the quasi-steady-state (QSS) approximation is valid when dissociation starts to dominate.