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Summary

This book discusses mathematical models that are based on the concepts of classical equilibrium thermodynamics. They are intended for the analysis of possible results of diverse natural and production processes. Unlike the traditional models, these allow one to view the achievable set of partial equilibria with regards to constraints on kinetics, energy and mass exchange and to determine states of the studied systems of interest for the researcher. Application of the suggested models in chemical technology, energy and ecology is illustrated in the examples.

Table of Contents

Preface vii
Introduction 1(46)
I.1. Subject of Research
1(3)
I.2. To the Use of Equilibrium Principle
4(1)
I.3. Modeling of Open and Closed Systems
5(2)
I.4. Ideal and Nonideal Systems
7(1)
I.5. Modeling of Homogeneous and Heterogeneous Systems
8(3)
I.6. Almost Almighty Thermodynamics
11(3)
I.7. Problem of Getting Maximum Knowledge from Available Information
14(3)
I.8. Types of Descriptions: Stationary (Where Do We Stay?), Dynamic (How Do We Run?), Geometrical (Where Do We Run?)
17(1)
I.9. "The Field of Battle": Balance Polyhedrons
18(1)
I.10. Roughness and Reliability of Thermodynamics
19(1)
I.11. Thermodynamically Admissible Paths
20(2)
I.12. Thermodynamic Functions
22(2)
I.13. A Thermodynamic Tree and Space of Admissible Paths
24(1)
I.14. From Admissibility to Feasibility
25(1)
I.15. Constraints Imposed by the Reaction Mechanism
26(2)
I.16. Constraints on Exchange
28(1)
I.17. Constraints on Parameters
29(1)
I.18. Constraints on the Regions of Process Running
30(1)
I.19. Stability and Sensitivity
31(2)
I.20. The Art of the Possible: Idealized Models of Real Systems
33(2)
I.21. The Art of the Possible: Methods for Calculation of Estimates
35(2)
I.22. Models of Extreme Concentrations
37(2)
I.23. Thermodynamics of Combustion
39(2)
I.24. Thermodynamics of the Atmosphere
41(2)
I.25. Thermodynamic Modeling on Graphs
43(4)
1. Principles of Equilibrium and Extremality in Mechanics and Thermodynamics 47(55)
1.1. Principles of Equilibrium and Extremality in Mechanics
47(3)
1.2. Principles of Equilibrium and Extremality in Thermodynamics
50(6)
1.3. Thermodynamics and Models of Motion
56(10)
1.4. Partial Thermodynamic Equilibria
66(6)
1.5. A Thermodynamic Analysis of the Chemical Kinetics Equations
72(30)
2. Extreme Thermodynamic Models in Terms of Mathematical Programming 102(50)
2.1. Brief Information from Mathematical Programming
102(7)
2.2. The Model of Extreme Intermediate States (MEIS)
109(12)
2.3. Description of Different Types of Thermodynamic Systems
121(11)
2.4. Mathematical Features of the Extreme Thermodynamic Models
132(9)
2.5. Convex Analysis of the Thermodynamics Problems
141(11)
3. Thermodynamic Modeling on Graphs 152(37)
3.1. Problem Statement and History
152(3)
3.2. Thermodynamic Tree
155(4)
3.3. Thermodynamic Interpretations of Hydraulic Circuit Theory
159(12)
3.4. Thermodynamic Interpretations of Hydraulic Circuit Theory: Heterogeneous Circuits
171(18)
4. Methods and Algorithms of Searching for Thermodynamic Equilibria 189(24)
4.1. E.G. Antsiferov's General Two-Stage Technique of Searching for Extreme Concentrations
189(2)
4.2. Optimization of the Initial Composition of Reagents in a Chemical System by the Simplex Embedding Method
191(3)
4.3. Calculations of Complete and Partial Equilibria by the Affine Scaling Method
194(6)
4.4. Construction of Algorithms Using the Thermodynamic Tree Idea
200(8)
4.5. Analysis of Feasibility and Stability of Partial Equilibria
208(5)
5. Application of Extreme Models 213(38)
5.1. Thermodynamics of Atmosphere
213(11)
5.2. Thermodynamics of Combustion
224(20)
5.3. Fuel Processing
244(7)
Conclusion 251(2)
Supplement 253(13)
References 266(9)
Name Index 275(2)
Subject Index 277

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