Nemlineáris és lineáris modellek a reakciókinetikában = Nonlinear and linear models in chemical kinetics

A kémiai folyamatok időbeni lefutását és a részfolyamatok sorrendjét részletes reakciómechanizmusokat tartalmazó modellekkel lehet vizsgálni. Ilyen reakciómechanizmusokat általánosan használnak égések leírására, légkörkémiában, valamint pirolízis folyamatok és biokémiai rendszerek vizsgálatára. A kémia valamennyi, itt felsorolt területén alkalmaztunk reakciókinetikai modelleket tudományos és gyakorlati szempontból is fontos jelenségek szimulációjára. Ezek a matematikai modellek erősen nemlineárisak, ami a vizsgálatukra új eszközök kifejlesztését kívánta meg. Számítottuk a modellek megoldásának érzékenységét a paraméterek változtatása hatására. Több esetben azt találtuk, hogy ezek az érzékenységi függvények hasonlóak egymáshoz, ami arra vezet, hogy a nemlineáris modell egyes körülményeknél lineárisan viselkedik. Új, az eddigieknél sokkal hatékonyabb eszközöket fejlesztettünk ki reakciómechanizmusok redukciójára, tehát az eredetinél sokkal kisebb, csaknem azonos szimulációs eredményeket adó modell megtalálására. Vizsgáltuk a paraméterek bizonytalanságának hatását a szimulációs eredmények bizonytalanságára. Elsőként foglalkoztunk annak vizsgálatával, hogy milyen kapcsolat van az Arrhenius-paraméterek bizonytalansága és az azokból számított reakciósebességi együttható hőmérsékletfüggő bizonytalansága között. Több elemi gázreakció esetén becsültük az Arrhenius-paraméterek együttes bizonytalanságát. A pályázat támogatásával 11 referált cikk, négy konferenciacikk és egy könyv jelent meg. A kutatási témában résztvevő hallgatók 9 TDK dolgozatot, 5 szakdolgozatot és egy PhD értekezést készítettek. | The temporal behaviour of chemical processes and the order of subprocesses can be simulated using mathematical models based on detailed reaction mechanisms. Such mechanisms are widely used for the description of combustion and atmospheric chemical processes and at the investigation of pyrolytic and biochemical systems. Reaction kinetic models, related to all these fields of chemistry, were applied for the simulation of processes of both academic and industrial importance. These models are strongly nonlinear and we developed a series of mathematical and computational tools for the investigation of them. The sensitivity of the model output to parameter changes was investigated. In several cases the similarity of the sensitivity functions was detected, which means that these models behave linearly at certain circumstances. New, more effective methods were developed for the reduction of reaction mechanisms. Mechanism reduction means the construction of a much smaller model that provides simulation results almost identical to the original one. The effect of the uncertainty of parameters on the uncertainty of simulation results was explored. The relation between the uncertainty of the Arrhenius parameters and the temperature dependent uncertainty of the rate coefficient was investigated. The joint uncertainty of the Arrhenius-parameters was determined for several gas-phase elementary reactions. Based on the support of the grant, 11 peer-reviewed articles, 4 conference papers and one book were published. The students participated in the research prepared 9 project (“TDK”) reports, 5 BSc or MSc theses and one PhD thesis

Lokális és globális érzékenység-analízis új alkalmazásai a kémiai kinetikában = New applications of local and global sensitivity analysis in chemical kinetics

Az OTKA pályázat keretében végzett kutatások részletes reakciómechanizmusok vizsgálatával foglalkoztak. A kémiai rendszerek meglehetősen szerteágazóak voltak: hidrogén, szénmonoxid és metán égése; metán pirolízise; számos tüzelőanyag (H2, CO, CH4, C2H4, C3H6) oxigénnel alkotott elegyének gyulladása polikristályos platinafelületen; fotokémiai reakciók vizsgálata szmogkamrában és szennyezett szabad levegőben; CCl4 megsemmisítése plazmában reduktív és oxidatív körülmények között; egy biokémiai kinetikai rendszer, a sarjadzó élesztő sejtosztódásának vizsgálata. Minden esetben a vizsgált kémiai folyamatot részletes reakciómechanizmussal írtuk le, ennek alapján szimulációkat végeztünk, és a kapott eredményeket mérési adatokkal hasonlítottuk össze. A mérések vagy a jellemző alkalmazás körülményeinél elvégeztük a reakciórendszerek analízisét. Igénybe vettük a mások által, vagy éppen általunk korábban kifejlesztett módszereket is, de egy sor mechanizmusvizsgálati módszert e kutatások során fejlesztettünk ki és elsőként alkalmaztunk. Ilyen módszerek például a lokális érzékenységi vektorok korrelációjának vizsgálata, a lángsebesség-érzékenységek globális bizonytalanság-analízise, vagy a komponenstér dinamikus dimenziója változásának és az érzékenységi függvények globális hasonlóságának összehasonlítása. A kutatások következtében számos új kémiai ismerethez jutottunk a vizsgált rendszerekről, és új reakciómechanizmus-vizsgáló eszközöket vezettünk be. | All investigations in the project were related to the analysis of detailed reaction mechanisms. A wide variety of chemical systems were investigated, which included the combustion of hydrogen, wet CO and methane; pyrolysis and oxidative pyrolysis of methane; ignition of fuel-oxygen mixtures on polycrystalline platinum catalyst, where the fuels were H2, CO, CH4, C2H4, and C3H6; photochemical ozone formation in smog chambers and in ambient air; decomposition of carbon tetrachloride in RF thermal plasma reactor at neutral and oxidative conditions; molecular regulation network of the cell cycle of budding yeast. In all cases the system was described by a set of chemical reaction steps, simulations were carried out and the reaction mechanism was investigated at the experimental conditions or the conditions of typical applications. The analyses of mechanisms were carried out using tools that had been developed earlier, but also several new tools for mechanism analysis was developed during the project. These new tools include the analysis of the correlation of the local sensitivity vectors, global uncertainty analysis of local sensitivity coefficients, and contrasting the shape of the local sensitivity functions with the change of the dynamical dimension during the simulations. As a result of the project, new chemical knowledge was obtained about the systems investigated and several new methods were introduced for the analysis of complex reaction mechanisms

MAC, a novel stochastic optimization method

A novel stochastic optimization method called MAC was suggested. The method is based on the calculation of the objective function at several random points and then an empirical expected value and an empirical covariance matrix are calculated. The empirical expected value is proven to converge to the optimum value of the problem. The MAC algorithm was encoded in Matlab and the code was tested on 20 test problems. Its performance was compared with those of the interior point method (Matlab name: fmincon), simplex, pattern search (PS), simulated annealing (SA), particle swarm optimization (PSO), and genetic algorithm (GA) methods. The MAC method failed two test functions and provided inaccurate results on four other test functions. However, it provided accurate results and required much less CPU time than the widely used optimization methods on the other 14 test functions

Uncertainty of the rate parameters of several important elementary reactions of the H2 and syngas combustion systems

Abstract Re-evaluation of the temperature-dependent uncertainty parameter f(T) of elementary reactions is proposed by considering all available direct measurements and theoretical calculations. A procedure is presented for making f(T) consistent with the form of the recommended Arrhenius expression. The corresponding uncertainty domain of the transformed Arrhenius parameters (ln A, n, E/R) is convex and centrally symmetric around the mean parameter set. The f(T) function can be stored efficiently using the covariance matrix of the transformed Arrhenius parameters. The calculation of the uncertainty of a backward rate coefficient from the uncertainty of the forward rate coefficient and thermodynamic data is discussed. For many rate coefficients, a large number of experimental and theoretical determinations are available, and a normal distribution can be assumed for the uncertainty of ln k. If little information is available for the rate coefficient, equal probability of the transformed Arrhenius parameters within their domain of uncertainty (i.e. uniform distribution) can be assumed. Algorithms are provided for sampling the transformed Arrhenius parameters with either normal or uniform distributions. A suite of computer codes is presented that allows the straightforward application of these methods. For 22 important elementary reactions of the H2 and syngas (wet CO) combustion systems, the Arrhenius parameters and 3rd body collision efficiencies were collected from experimental, theoretical and review publications. For each elementary reaction, kmin and kmax limits were determined at several temperatures within a defined range of temperature. These rate coefficient limits were used to obtain a consistent uncertainty function f(T) and to calculate the covariance matrix of the transformed Arrhenius parameters

Time scale and dimension analysis of a budding yeast cell cycle model

BACKGROUND: 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. RESULTS: 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. CONCLUSION: 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