Zeljko Cupic

PSEUDO-STEADY STATES IN THE MODEL OF THE BRAY-LIEBHAFSKY OSCILLATORY REACTION

The main pseudo-steady states in the process of catalytic hydrogen peroxide decomposition are analysed. The dominant steady states during the monotonic and oscillatory evolution, well known experimentally, are defined by stoichiometric network analysis of the model for this process. The trajectories for the evolution of the system in the phase space in the vicinity of the unstable pseudo-steady state where oscillatory behaviour is obtained, are also calculated. The adjustment of the phase trajectory to the corresponding oscillation is proposed as an additional criterion for the selection of the kinetic parameters necessary for numerical simulation. The calculation procedure is general, independent of the model under consideration.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Stoichiometric Network Analysis as Mathematical Method for Examinations of Instability Region and Oscillatory Dynamics

y Z. y CupiG. Schmitz, Lj. Kolar-Ani´ c Abstract: Reaction systems in chemistry, physical chemistry, and biochemistry, which can be described by true or pseudo-stoichiometric relationships between species, and, therefore, rep- resented with stoichiometric models, are usually very complex. For the analysis of the models of these complex nonlinear reaction systems with more than three variables, which can be in different dynamic states like multistability, oscillatority or chaos, some general mathemati- cal methods such as the Stoichiometric network analysis (SNA) must be used. Although the SNA is a powerful method for systematic examination of complex reaction systems, identifi- cation of underlying reaction pathways, and stability analysis of dynamic states, this method is practically unknown among mathematicians. Therefore, a simple application of SNA to one five-dimensional model is given here.

Oscillators: Phenomenological mappings and analogies: First part: Mathematical analogy and chains

New analytical and numerical results of dynamics for both linear and nonlinear system with two degrees of freedom are presented. For a mechanical chain system with two degrees of freedom, oscillations are investigated analytically and numerically with corresponding comparing between free and forced oscillatory dynamics of linear and nonlinear system. Also, energy analysis and transient energy between the mass particles in the system are discussed. Using Mihailo Petrovics theory of the mathematical phenomenology elements, phenomenological mappings in vibrations, signals, resonances and dynamical absorptions in models with two degrees of freedom - the abstractions of a different real system dynamics are identified and presented. Mathematical description of a chain mechanical system with two mass particles coupled by linear and nonlinear elastic springs and with two degrees of freedom is given. By analysis of corresponding solutions for free and forced vibrations, series of related two-frequency regimes and resonant states, as well as dynamical absorption states, are identified. Besides, by mathematical analogy and phenomenological mappings, the analysis of series of dynamics of other two degrees of freedom models dynamics (torsional system, double pendulum system, double electrical circuit) is performed.

Analysis of transients in adsorption-desorption at the surface of plasmonic sensors: Nonlinear versus linear approach

Monolayer adsorption-desorption processes at the surface of plasmonic sensors are modeled, first in an exact way, as a nonlinear second-order reaction, and then, after some approximations justified from the practical point of view, as a first order linear reaction. The time evolution of the number of adsorbed molecules from the beginning of the process to the moment in which the system reaches its equilibrium is derived in both cases. A comparative analysis of transients and steady state response is performed for a plasmon sensor with gold surface for some saturated and cyclic hydrocarbons including benzene, as well as for carbon monoxide. The results show in which practical situations the simpler linear model can be used and when the nonlinear model of adsorption-desorption must be applied instead.

The poissonian nature of adsorption-desorption processes

We analyze the adsorption-desorption processes of particle adsorption on solid surfaces to check if these processes are Poissonian in order to adopt or disregard the vast mathematical heritage previously developed for Poissonian processes in all practical situations where these processes are essential: plasmonic and other adsorption-desorption sensors and sensing networks, microresonators and other MEMS RF devices, integrated optics, to name just a few. We use the stochastic analysis approach with the probability generating functions.

Experimentally observable transitions between dynamical states in complex reaction systems

Abstract Identification of trends and their correspondence with dynamical state transitions are briefly discussed on several reaction network models. The influence of different threshold values on the trend analysis and dynamical state analysis results is examined. Both methods are applied here to the results of the numerical simulation. For this purpose the models of three reaction systems are used: simple model of consecutive, first order, equilibrium reactions, partial oxidation of cyclohexane, and model of the oscillatory reaction Bray Liebhafsky. Detailed kinetic analysis confirmed that transient dynamical states may be identified through the symbolic representation of the sequence of trend episodes in experimentally obtainable time series. Stoichiometric Network Analysis of possible dynamical states was used to identify reaction pathways responsible for the sequences of trend episodes. Some technical problems were also addressed, connected with selection of the threshold value and dynamical state notion.