Alexander N. Gorban, Boris M. Kaganovich

Sergey P. Filippov, Alexandre V. Keiko

Vitaly A. Shamansky, Igor A. Shirkalin

Thermodynamic Equilibria

and Extrema

Analysis of Attainability Regions and

Partial Equilibria

Translated by Marina V. Ozerova,

Valentina P. Yermakova, and Alexandre V. Keiko

 

 

Preface ............................................................................... vii

 

Introduction ............................................................................ 1

I.1. Subject of Research ......................................................... 1

I.2. To the Use of Equilibrium Principle ..................................... 4

I.3. Modeling of Open and Closed Systems................................. 5

I.4. Ideal and Nonideal Systems ............................................... 7

I.5. Modeling of Homogeneous and Heterogeneous Systems....... 8

I.6. Almost Almighty Thermodynamics .................................... 11

I.7. Problem of Getting Maximum Knowledge from

Available Information....................................................... 14

I.8. Types of Descriptions: Stationary (Where Do We Stay?),

Dynamic (How Do We Run?), Geometrical

(Where Do We Run?)....................................................... 17

I.9. The Field of Battle: Balance Polyhedrons ........................... 18

I.10. Roughness and Reliability of Thermodynamics..................... 19

I.11. Thermodynamically Admissible Paths .................................. 20

I.12. Thermodynamic Functions ................................................ 22

I.13. A Thermodynamic Tree and Space of Admissible Paths....... 24

I.14. From Admissibility to Feasibility ........................................ 25

I.15. Constraints Imposed by the Reaction Mechanism.................. 26

I.16. Constraints on Exchange................................................... 28

I.17. Constraints on Parameters ................................................. 29

I.18. Constraints on the Regions of Process Running ................... 30

I.19. Stability and Sensitivity .................................................... 31

I.20. The Art of the Possible:
Idealized Models of Real Systems............ 33

I.21. The Art of the Possible:
Methods for Calculation of Estimates...................... 35

I.22. Models of Extreme Concentrations ...................................... 37

I.23. Thermodynamics of Combustion......................................... 39

I.24. Thermodynamics of the Atmosphere .................................... 41

I.25. Thermodynamic Modeling on Graphs................................... 43

 

1. Principles of Equilibrium and Extremality in Mechanics

and Thermodynamics............................................................ 47

1.1. Principles of Equilibrium and Extremality in Mechanics........ 47

1.2. Principles of Equilibrium and Extremality

in Thermodynamics.......................................................... 50

1.3. Thermodynamics and Models of Motion ................................ 56

1.4. Partial Thermodynamic Equilibria ........................................ 66

1.5. A Thermodynamic Analysis of the

Chemical Kinetics Equations............................................... 72

 

2. Extreme Thermodynamic Models in Terms of

Mathematical Programming ................................................... 102

2.1. Brief Information from Mathematical Programming .............. 102

2.2. The Model of Extreme Intermediate States (MEIS) ............... 109

2.3. Description of Different Types
of Thermodynamic Systems.................................................. 121

2.4. Mathematical Features of the Extreme

Thermodynamic Models .................................................... 132

2.5. Convex Analysis of the Thermodynamics Problems ........... 141

 

3. Thermodynamic Modeling on Graphs................................... 152

3.1. Problem Statement and History............................................ 152

3.2. Thermodynamic Tree ........................................................ 155

3.3. Thermodynamic Interpretations of

Hydraulic Circuit Theory ................................................... 159

3.4. Thermodynamic Interpretations of Hydraulic Circuit

Theory: Heterogeneous Circuits ......................................... 171

 

4. Methods and Algorithms of Searching for

Thermodynamic Equilibria..................................................... 189

4.1. E.G. Antsiferovs General Two-Stage Technique

of Searching for Extreme Concentrations................................ 189

4.2. Optimization of the Initial Composition of Reagents

in a Chemical System by the Simplex Embedding Method .......... 191

4.3. Calculations of Complete and Partial Equilibria

by the Affine Scaling Method.............................................. 194

4.4. Construction of Algorithms Using

the Thermodynamic Tree Idea ............................................. 200

4.5. Analysis of Feasibility and Stability of Partial Equilibria...... 208

 

5. Application of Extreme Models............................................... 213

5.1. Thermodynamics of Atmosphere.......................................... 213

5.2. Thermodynamics of Combustion.......................................... 224

5.3. Fuel Processing .............................................................. 244

 

Conclusion .............................................................................. 251

Supplement ............................................................................. 253

References............................................................................... 266

Name Index............................................................................. 275

Subject Index........................................................................... 277

 

 

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