MEIS analysis

The chemical composition of caramel color is not yet fully understood but some compounds identified in the low weight fraction are considered caramel markers. All caramel classes contain 5-hydroxymethyl)-2-furaldehyde (5-HMF). In caramel classes in and TV, 4-methyUmidazole (4-MeI) has been detected, while 2-acetyl-4(5)-tetrahydroxybutylimidazole (THI) was found only in class HI caramel colors. The analysis of five caramel III samples by SPE/HPLC-MS revealed concentrations between 28.3 and 46.8 iglg THI and 73.3 to 187.8 for 4-MeP (see Figure 5.2.3). 

The authors are indebted to Ms. Bao-kun Chen and Ms. Xue-mei Sui for their experimental assistance in polymerization and analysis and to Ms. Gui-shan Zhang for preparing the drawings. 

Mei N, Tamae K, Kunugita N, HiranoT, Kasai H (2003) Analysis of 8-hydroxydeoxguanosine 5 -mono-phosphate (8-OH-dGMP) as a reliable marker of cellular oxidative DNA damage after y-irradia-tion. Environ Mol Mutagen 41 332-338... 

We can specially show that the main principles of nonequilibrium thermodynamics (the Onsager relations, the Prigogine theorem, symmetry principle) and other theories of motion (for example, theory of dynamic systems, synergetics, thermodynamic analysis of chemical kinetics) are observed in the MEIS-based equilibrium modeling. In order to do that, we will derive these statements from the principles of equilibrium thermodynamics. 

Currently the authors are developing three classes of models of extreme intermediate states (MEIS) (1) with variable parameters (2) with variable flows, and (3) those describing spatially inhomogeneous systems. All these classes of the models are formulated and analyzed in terms of MP, which, in the authors opinion, can be defined as a mathematical theory of equilibrium states. It is natural to start the analysis of the created modifications with the MEIS with variable parameters, which is the closest in character to the traditional equilibrium thermodynamics models. 

Development of the "flow" MEIS with the form reminding the models of nonequilibrium thermodynamics seems to be a very promising direction in equilibrium modeling of physical and chemical systems. Application of these models opens prospects for simpler analysis and solution of many complex problems related to the calculations of processes considered to be irreversible in principle. Certainly the flows in MEIS are interpreted statically as the coordinates of states. Thermodynamic interpretations are naturally extended to the kinetic coefficients that relate these flows with forces. Correctness of such interpretations is confirmed by the application of MP, being the theory of equilibrium states, as the terms for MEIS description. 

The notion of thermodynamic tree (the graph, each point of which represents the set of thermodynamically equivalent states) was introduced by Gorban (1984) where he also revealed the possibilities of applying this notion for analysis of the chemical kinetics equations. In the work by Gorban et al. (2001, 2006) the authors consider the problems of employing thermodynamic tree to study the physicochemical systems using MEIS. 

Though in formulations of MEIS of type (7)-(12) or the particular form (53)-(57) the possibility of projecting the space of thermodynamic variables to a tree is not shown, the knowledge of principal possibility to reduce the set Dt(y) to the tree makes the analysis of capabilities and comparative merits of the model of extreme intermediate states essentially easier, clearer, and more convincing. 

Prior to discussion of modeling the complete mechanisms of chemical systems on the basis of MEIS (29)-(34), we will present capabilities of the approximate analysis of the efficiency of such mechanisms by MEIS (7)-(12) with variable parameters. This possibility was studied in Kaganovich and Filippov (1995 Kaganovich et al., 1993). Let us consider a process during which some initial composition a should be used to get the maximum quantity of products b. Let the point y in Figure 7 denote an initial state of the reactive system. The point m corresponds to the maximum thermodynamically admissible concentration of b. The points l and k represent states of a chemical system with the use of catalysts that provide... 

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

This Section deals with the problem of MEIS comparison with the models of motion that was studied in the previous Section. However, whereas comparison was performed there on the basis of purely theoretical analysis, here it was made on the examples of specific objects. Compared are the attainable completeness and significance of the results of computing experiments, and the possibility of using these results, accuracy of the obtained estimates for the sought characteristics of the modeled system, laboriousness of calculations and preparation of initial information. 

Here the comparative analysis of MEIS characteristics will be made on the example of the simplest mechanism x1 > x2, x2 — X3 that was considered in Section 3.5. But the applied model is supplemented with the... 

At the same time calculations on the modified MEIS are possible without additional kinetic models and do not require extra experimental data for calculations, which makes it possible to use less initial information and obviously reduces the time and labor spent for computing experiment. Furthermore, there arise principally new possibilities for the analysis of methods to mitigate emissions from pulverized-coal boilers, since at separate modeling of different mechanisms of NO formation the measures taken can result in different consequences for each in terms of efficiency. Consideration of kinetic constraints in MEIS will substantially expand the sphere of their application to study other methods of coal combustion (fluidized bed, fixed bed, etc.) and to model processes of forming other pollutants such as polyaromatic hydrocarbons, CO, soot, etc. 

The analysis of stationary and nonstationary flow distributions in multiloop hydraulic systems with lumped, regulated, and distributed parameters and in heterogeneous systems was given in (Gorban et al., 2001, 2006 Kaganovich et al., 1997). In the concluding section of Section 5 the abundant capabilities of the flow MEIS are illustrated by the simplest example of stationary isothermal flow distribution of incompressible fluid in the three-loop circuit. It is shown how the degrees of order (laminar or turbulent modes) on the branches of this circuit are determined from calculation of the final equilibrium. 

The efficiency of MEIS modifications was tested on the examples of modeling and analysis of fuel combustion and processing and flow distribution in multiloop hydraulic systems. 

The capabilities of MEIS and the models of kinetics and nonequilibrium thermodynamics were compared based on the theoretical analysis and concrete examples. The main MEIS advantage was shown to consist in simplicity of initial assumptions on the equilibrium of modeled processes, their possible description by using the autonomous differential equations and the monotonicity of characteristic thermodynamic functions. Simplicity of the assumptions and universality of the applied principles of equilibrium and extremality lead to the lack of need in special formalized descriptions that automatically satisfy the Gibbs phase rule, the Prigogine theorem, the Curie principle, and some other factors comparative simplicity of the applied mathematical apparatus (differential equations are replaced by algebraic and transcendent ones) and easiness of initial information preparation possibility of sufficiently complete consideration of specific features of the modeled phenomena. 

The second group of problems (5-8) is associated directly with MEIS construction. Here the main goal for the future is to expand directions of analysis of the formalized descriptions of transfer processes, whose necessity was underlined above. Of particular interest are the studies on interrelations between thermal, electric, and chemical phenomena (the cross effects). Greater attention to transfer processes should be paid in... 

Comparison of MEIS capabilities (equilibrium descriptions) with capabilities of kinetics, theory of dynamic systems, nonequilibrium thermodynamics, synergetics, thermodynamic finite time, and thermodynamic analysis of motion equations. 

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