Methane is the major component of natural gas, which is one of the most widely used fuels. A large number of shock tube (ST) and rapid compression machine (RCM) ignition delay measurements are available in the literature for validating its detailed combustion mechanisms. A large set of experimental data was collected for methane combustion: ignition studies in STs (4939 data points in 574 datasets) and in RCMs (582/69). In total, 5521 data points in 643 datasets from 76 publications were collected, covering wide ranges of temperature T, pressure p, equivalence ratio φ, and diluent concentration. For a quantitative assessment of methane combustion models, a least-squares function is used to show the agreement between measurements and simulations. Thirteen recent methane combustion mechanisms were tested against these experimental data, and the dependence of their predictions on the types of experiments and the various experimental conditions was investigated. The mechanism comparison results show that most mechanisms could well reproduce the experimental ignition delay times (IDTs) measured in STs. IDTs measured in RCMs and STs at low temperatures (below 1000 K) could also be well predicted by several mechanisms. SanDiego-2014, Caltech-2015, Aramco-II-2016, and Glarborg-2018 were found to be the most accurate mechanisms for the simulation of methane combustion under ST experimental conditions, while Aramco-II-2016 had the smallest prediction error under RCM conditions. Local sensitivity analysis was carried out to determine the effect of reactions on the simulation results obtained under given experimental conditions and to identify the critical reaction steps for improving the methane combustion models.

Ammonia is a potential fuel for the storage of thermal energy. Experimental data were collected for homogeneous ammonia combustion: ignition delay times measured in shock tubes (247 data points in 28 datasets from four publications) and species concentration measurements from flow reactors (194/22/4). The measurements cover wide ranges of temperature T, pressure p, equivalence ratio φ and dilution. The experimental data were encoded in ReSpecTh Kinetics Data Format version 2.2 XML files. The standard deviations of the experimental datasets used were determined based on the experimental errors reported in the publications and also on error estimations obtained using program MinimalSplineFit. Simulations were carried out with eight recently published mechanisms at the conditions of these experiments using the Optima++ framework code, and the FlameMaster and OpenSmoke++ solver packages. The performance of the mechanisms was compared using a sum-of-square error function to quantify the agreement between the simulations and the experimental data. Ignition delay times were well reproduced by five mechanisms, the best ones were Glarborg-2018 and Shrestha-2018. None of the mechanisms were able to reproduce well the profiles of NO, N₂O and NH₃ concentrations measured in flow reactors.

A state-of-the-art chemical mechanism is introduced to properly describe chemical processes inside a harmonically excited spherical bubble placed in water and saturated with oxygen. The model uses up-to-date Arrhenius-constants, collision efficiency factors and takes into account the pressure-dependency of the reactions. Duplicated reactions are also applied, and the backward reactions rates are calculated via suitable thermodynamic equilibrium conditions. Our proposed reaction mechanism is compared to three other chemical models that are widely applied in sonochemistry and lack most of the aforementioned modelling issues. In the governing equations, only the reaction mechanisms are compared, all other parts of the models are identical. The chemical yields obtained by the different modelling techniques are taken at the maximum expansion of the bubble. A brief parameter study is made with different pressure amplitudes and driving frequencies at two equilibrium bubble sizes. The results show that due to the deficiencies of the former reaction mechanisms employed in the sonochemical literature, several orders of magnitude differences of the chemical yields can be observed. In addition, the trends along a control parameter can also have dissimilar characteristics that might lead to false optimal operating conditions. Consequently, an up-to-date and accurate chemical model is crucial to make qualitatively and quantitatively correct conclusions in sonochemistry.

The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth. We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network.

Optimisation of detailed combustion mechanisms means that the corresponding kinetic model is fitted to experimental data via optimising their important rate and thermodynamic parameters within their domain of uncertainty. Typically, several dozen parameters are fitted to several hundred to several thousand data points. Many numerical optimisation methods have been used, but the efficiency of these methods has not been compared systematically. In this work, parameters of an H₂/O₂/NO_x mechanism (214 reaction steps of 35 species) were fitted to 1552 indirect (ignition delay times measured in shock tubes and concentrations measured in flow reactors) and 755 direct measurements. Three test cases were investigated: (1) fitting the Arrhenius parameters of 2 reaction steps to 732 data points; (2) fitting the Arrhenius parameters of 4 reaction steps to 1077 data points; (3) fitting the Arrhenius parameters of 10 reaction steps to 2307 data points. All 3 cases were investigated in 2 ways: fitting the A-parameters only and fitting all Arrhenius parameters (5, 11 and 29 parameters, respectively). A series of global (FOCTOPUS, genetic algorithm, simulated annealing, particle swarm optimisation, covariance matrix adaptation evolutionary strategy (CMA-ES)) and local (simplex, pattern search, interior-point, quasi-Newton, BOBYQA, NEWUOA) optimisation methods were tested on these cases, some of them in two variants. The methods were compared in terms of the final error function value and number of error function evaluations. The main conclusions are that the FOCTOPUS resulted in the lowest final error value in all cases, but this method required relatively many error function evaluations. As the task became more difficult, more and more methods failed. A variant of the BOBYQA method looked stable and efficient in all cases.