Kinetic models / networks

Fig. 5.4. The kinetic network model for the discrete NRE model used by Zheng et al. [102] The state labels represent the conformation (letter) and temperature (subscript) for each replica. For example, F2U1 represents the state in which replica 1 is folded and at temperature T2, while replica 2 is unfolded at temperature T. Gray and black arrows correspond to folding and unfolding transitions, respectively, while the temperature at which the transition occurs is indicated by the solid and dashed lines (for T2 and Ti, repectively). The bold arrows correspond to temperature exchange transitions, with the solid and dashed lines denoting transitions with rate parameters a and wa, respectively...

The tricarboxylic acid (TCA) cycle (also known as the citric acid cycle and the Krebs cycle) is a collection of biochemical reactions that oxidize certain organic molecules, generating CO2 and reducing the cofactors NAD and FAD to NADH and FADH2 [147], In turn, NADH and FADH2 donate electrons in the electron transport chain, an important component of oxidative ATP synthesis. The TCA cycle also serves to feed precursors to a number of important biosynthetic pathways, making it a critical hub in metabolism [147] for aerobic organisms. Its ubiquity and importance make it a useful example for the development of a kinetic network model. 

We have successfully carried out the first phase of extending our original kinetic network model for calculating steady-state properties (3,4) to apply to transient experiments involving step changes in shear rate. The model is seen to possess the ability to describe these stress transients. In addition, a number of new rheological tests have been proposed as potential means to... 

J. J. Heijnen, Approximative kinetics formats used in metabolic network modeling. Biotechnol. Bioeng. 91(5), 535 545 (2005). 

The recurrent network models assume that the structure of the network, as well as the values of the weights, do not change in time. Moreover, only the activation values (i.e., the output of each processor that is used in the next iteration) changes in time. In the biochemical network one cannot separate outputs and weights. The outputs of one biochemical neurons are time dependent and enter the following biochemical neurons as they are. However, the coefficients involved in these biochemical processes are the kinetic constants that appear in the rate equations, and these constants are real numbers. The inputs considered in biochemical networks are continuous analog numbers that change over time. The inputs to the recurrent neural networks are sets of binary numbers. 

A number of mechanistic modeling studies to explain the fluid catalytic cracking process and to predict the yields of valuable products of the FCC unit have been performed in the past. Weekman and Nace (1970) presented a reaction network model based on the assumption that the catalytic cracking kinetics are second order with respect to the feed concentration and on a three-lump scheme. The first lump corresponds to the entire charge stock above the gasoline boiling range, the second... 

Kinetic Gelation Modeling of Crosslinked Network Structure.197... 

Despite its limitations, kinetic gelation modeling is still a very useful tool in simulating network structure in highly crosslinked systems. While kinetic gelation models have gained widespread use in the polymer science field, the application of these models to dental materials and their development appears to be an area appropriate for further exploration. 

Kawabata44 has panted out on the basis of a simple network model that of the two derivatives, bW/blt and bW/bI2, the former should be related primarily to intramolecular forces such as the entropy force which plays a major role in the kinetic theory of rubber elasticity, while the latter should be a manifestation of intramolecular interactions. He predicted the possibility that bW/bI2 assumes negative values in the region of small defamation. In fact, the prediction was confirmed experimentally by Becker and also by the present authos. 

The kinetic model developed in Sect. 2.4 for the phenol-formaldehyde reaction belongs to a wider class of kinetic networks made up of irreversible nonchain reactions. In this section, a general form of the mathematical model for this class of reactive systems is presented moreover, it is shown that the temperature attainable in the reactor is bounded and the lower and upper bounds are computed. 

In Chaps. 5 and 6 model-based control and early diagnosis of faults for ideal batch reactors have been considered. A detailed kinetic network and a correspondingly complex rate of heat production have been included in the mathematical model, in order to simulate a realistic application however, the reactor was described by simple ideal mathematical models, as developed in Chap. 2. In fact, real chemical reactors differ from ideal ones because of two main causes of nonideal behavior, namely the nonideal mixing of the reactor contents and the presence of multiphase systems. 

Depending on the purpose of the model and the status of the molecular knowledge of the network, either simplified kinetic core models or kinetic detailed models can be constructed. Core models are most useful for showing principles of regulation or dynamics [5, 37, 41, 63-66] or to study a network in more phenomenological terms when it is poorly characterized [67-70]. In what follows we only consider detailed kinetic models. 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

As the craze microstructure is intrinsically discrete rather than continuous, the connection between the variables in the cohesive surface model and molecular characteristics, such as molecular weight, entanglement density or, in more general terms, molecular mobility, is expected to emerge from discrete analyses like the spring network model in [52,53] or from molecular dynamics as in [49,50]. Such a connection is currently under development between the critical craze thickness and the characteristics of the fibril structure, and similar developments are expected for the description of the craze kinetics on the basis of molecular dynamics calculations. 

The pore connectivity r of two types of silica (highly porous beads, monolithic silicas) was calculated according to the pore network model proposed by Meyers and Liapis. Nt was proportional to the particle porosity in the case of highly porous beads. The differences in the pore connectivity for both types of silica were reflected in the mass transfer kinetics in liquid phase separation processes by measuring the theoretical plate height-linear velocity dependencies. In a future study, monolithic silicas possessing different macro- as well as mesopores will be investigated and compared with the presented results. 

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