Cover
Half Title
Also of Interest
Chemical Complexity via Simple Models: Modelics
Copyright
Preface
Contents
Part I: General part
1. Introduction. How to describe complex processes using simple models: Modelics
1.1 Model...modeling...
1.2 Top-down and bottom-up
Bibliography
2. Categorization of models
2.1 Physical framework of model design
2.1.1 Models of transport
2.1.2 The batch reactor
2.1.3 The continuous stirred-tank reactor
2.1.4 The plug-flow reactor
2.1.5 The pulse reactor
2.2 How to simplify complex models? Principles of simplification
2.2.1 Physicochemical assumptions of simplification of chemico-mathematical models
2.2.1.1 Assumptions on substances
2.2.1.2 Assumptions on (processes) reactions and their parameters
2.2.1.3 Assumptions on transport-reaction characteristics
2.2.1.4 Assumptions on experimental procedures
2.2.1.5 Combining assumptions
2.3 Mathematical concepts of simplification in chemical kinetics
2.3.1 Mathematical status of the quasi-steady-state (QSS) approximation
2.3.2 Limits of simplification: optimal model
Bibliography
Part II: Chemical modelics
3. Basic models of chemical kinetics
3.1 Equations of chemical kinetics and a scheme of parametric analysis
3.1.1 Experimental background
3.1.2 Equations of chemical kinetics
3.1.3 Scheme of parametric analysis
3.2 Autocatalytic models
3.2.1 Autocatalytic trigger
3.2.2 Autocatalytic oscillators
3.2.3 Association reaction
3.3 Catalytic schemes of transformations
3.3.1 Catalytic triggers
3.3.2 Catalytic oscillators
3.4 Catalytic continuous stirred-tank reactor (CSTR)
3.4.1 Flow reactor with an autocatalytic trigger
3.4.2 Flow reactor with a catalytic trigger
3.4.3 Flow reactor with an autocatalytic oscillator
3.4.4 Flow reactor with a catalytic oscillator
3.4.5 Kinetic “chaos” induced by noise
3.5 Two-center mechanisms
3.5.1 Oscillator–trigger model
3.5.2 Oscillator–oscillator model
3.5.3 Model with a step of interaction of centers Z1 ⇄ Z2
3.5.4 Model with a diffusion change of interaction centers
3.6 Simplest models of CO oxidation on platinum
3.7 Nonideal kinetics
3.8 Savchenko’s model
Critical phenomena
Catalytic mechanism with two active centers
Synchronization of oscillations by surface diffusion (Savchenko’s model)
Dynamics of auto-oscillations development.
3.9 Model of the Belousov–Zhabotinsky reaction
Bibliography
4. Thermokinetic models
4.1 Continuous stirred-tank reactors (CSTR)
4.2 Zel’dovich–Semenov model
4.2.1 Reaction A → P
4.2.2 The oxidation reaction A + O2 → P
4.2.3 Reaction nA → P
4.2.4 Reaction A → P with arbitrary kinetics
4.2.5 Semenov diagram as a stability criterion
4.3 Aris–Amundson model
4.3.1 Reaction A → P
4.3.2 Reaction of the n-th order
4.3.3 The oxidation reaction
4.3.4 Reaction with arbitrary kinetics
4.3.5 Andronov–Hopf bifurcations
4.3.6 Safe and unsafe boundaries of regions of critical phenomena
4.4 Volter–Salnikov model
4.5 Models of a continuous stirred tank reactor and a tube reactor
4.5.1 Parametric analysis of a dimensional model
4.5.2 Relation between dimensionless and dimensional models
4.5.3 Determination of ignition boundaries
4.5.4 Continuous tube reactor
4.6 Combustion model of hydrocarbon mixture
Dimensional model
Dimensionless model
4.7 Thermocatalytic triggers and oscillators
4.7.1 The Eley–Rideal monomolecular mechanism
4.7.2 The Eley–Rideal bimolecular mechanism
4.7.3 The linear catalytic cycle
4.7.4 The Langmuir–Hinshelwood Mechanism
4.7.5 Autocatalytic schemes of transformations
4.7.6 Autocatalytic oscillator
4.8 Parallel scheme
4.9 Consistent scheme
4.10 One reversible reaction
4.11 Model of spontaneous combustion of brown-coal dust
4.12 Modeling of the nitration of amyl in a CSTR and a tube reactor
4.12.1 Parametric analysis of the mathematical model of a CSTR
4.12.2 Model of a tube reactor
Bibliography
5. Models of macrokinetics
5.1 Homogeneous–heterogeneous reaction
5.2 Model of an imperfectly stirred continuous reactor
5.3 Dissipative structures on the active surface
5.4 The model of sorption–reaction–diffusion
5.5 Macrokinetics of catalytic reactions on surfaces of various geometries
5.6 Nonlinear interaction between the active surface and bulk of a solid
5.7 Models of wave propagation reactions
5.8 Macroclusters on the catalyst surface at the CO oxidation on Pt
5.9 Model of coking the feed channels of the fuel
Bibliography
Part III: Modelics everywhere
6. Models of population dynamics: “prey–predator” models
6.1 “Prey–predator” model
6.1.1 Nonlinearity of reproduction
6.1.2 Competition in the prey population
6.1.3 Saturation of the predator
6.1.4 Competition for the predator
6.1.5 Competition of the prey and saturation of the predator
6.1.6 Nonlinearity of eating of the prey by the predator and saturation of the predator
6.1.7 Competition of the predator for the prey and saturation of the predator
6.1.8 Nonlinearity of reproduction of predator and competition of prey
6.1.9 Saturation of the predator, nonlinearity of eating of prey by the predator, and competition of the prey
6.1.10 Saturation of the predator, competition of the predator for the prey, and competition of prey
6.1.11 Three populations
6.1.12 One-predator–two-prey and one-prey–two-predator systems
6.1.13 Community: two-prey–one-predator
6.2 A mathematical model of immunology
6.3 One model of economic dynamics
6.4 Environmental management model
Bibliography
Conclusion
Index