Stewart / Ray / Conley Dynamics and Modelling of Reactive Systems

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 22-24, 1979
1. Auflage 2014
ISBN: 978-1-4832-6206-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 426 Seiten, Web PDF

Dynamics and Modelling of Reactive Systems contains the proceedings of the Advanced Seminar on Dynamics and Modeling of Reactive Systems, held at the University of Wisconsin on October 1979. The book presents papers that assess the level of understanding of the dynamics of chemically reacting systems. The topics discussed include the hierarchies of models in reactive systems; model reduction of chemically reacting systems; and some consequences of nonlinearity in the diffusion process. Time-periodic and spatially irregular patterns; important aspects in simulating the dynamics of aerosols; and the diffusion and reaction in carbon burning are covered as well. Engineers and applied mathematicians will find the book highly insightful.

Autoren/Hrsg.

Stewart, Warren E.

Ray, W. Harmon

Conley, Charles C.

Inhaltsverzeichnis

1;Front Cover;1
2;Dynamics and Modelling of Reactive Systems;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Contributors;10
7;Preface;12
8;Chapter 1. Hierarchies of Models in Reactive Systems;14
8.1;1. INTRODUCTION;14
8.2;2. The systems;15
8.3;3. The non-reactive cases;17
8.4;4. A single reactant;22
8.5;5. Comparison of steady states;27
8.6;6. Systems of first order reactions;31
8.7;7. Moments in the equivalent model;35
8.8;8. Consecutive irreversible reactions;37
8.9;Conclusions;42
8.10;References;44
9;Chapter 2. Model Reduction of Chemically Reacting Systems;50
9.1;1. INTRODUCTION;50
9.2;2. MODEL OF THE FIXED-BED REACTOR;52
9.3;3. MOVING REACTION ZONE;54
9.4;4. REDUCED MODEL OF THE FIXED-BED REACTOR;62
9.5;CONCLUSION;69
9.6;REFERENCES;70
10;Chapter 3. Chemical Oscillations, Multiple Equilibria, and Reaction Network Structure;72
10.1;1. INTRODUCTION;72
10.2;2. REACTION NETWORKS, KINETICS, AND THE INDUCED DIFFERENTIAL EQUATIONS;77
10.3;3. SYSTEMS EMBRACED BY THE MATHEMATICAL FRAMEWORK;87
10.4;4. SOME QUESTIONS;95
10.5;5. THE ZERO DEFICIENCY THEOREM;104
10.6;6. NETWORKS OF POSITIVE DEFICIENCY;117
10.7;7. NETWORKS OF DEFICIENCY ONE: SPECIAL THEORY;123
10.8;8. OUTLOOK;139
10.9;REFERENCES;142
11;Chapter 4. Steady-State Multiplicity and Uniqueness Criteria for Chemically Reacting Systems;144
11.1;INTRODUCTION ;144
11.2;A SINGLE REACTION IN A LUMPED PARAMETER SYSTEM;145
11.3;TWO SIMULTANEOUS FIRST-ORDER REACTIONS;151
11.4;TWO CONSECUTIVE OR PARALLEL FIRST-ORDER REACTIONS;157
11.5;A POROUS CATALYST WITH UNIFORM INTRAPARTICLE TEMPERATURE;162
11.6;CONCLUDING REMARKS;169
11.7;REFERENCES;171
12;Chapter 5. Density-Dependent Interaction-Diffusion Systems;174
12.1;0. INTRODUCTION;174
12.2;1. POROUS MEDIUM FLOW;175
12.3;2. SINGLE SPECIES POPULATION MODELS;178
12.4;3 . INTERACTING POPULATIONS;184
12.5;REFERENCES;188
13;Chapter 6. Strange Oscillations in Chemical Reactions—Observations and Models;190
13.1;1. INTRODUCTION;190
13.2;2. SOLID-CATALYZED REACTIONS;192
13.3;3. THE EXPERIMENTAL SYSTEM;192
13.4;4. THE MATHEMATICAL MODEL;195
13.5;5. RESULTS OF ANALYSIS AND SIMULATIONS;198
13.6;6. CONCLUDING REMARKS;202
13.7;REFERENCES;204
14;Chapter 7. Time Periodic and Spatially Irregular Patterns;208
14.1;References;221
15;Chapter 8. Liesegang Rings and a Theory of Fast Reaction and Slow Diffusion;224
15.1;1. INTRODUCTION;224
15.2;2. THE MECHANISM OF LIESEGANG RING FORMATION;226
15.3;3. A MATHEMATICAL FORMULATION OF THE THEORY;228
15.4;4. REDUCTION TO A SIMPLER PROBLEM;230
15.5;5. FAST REACTION AND SLOW DIFFUSION;231
15.6;6. APPLICATION TO THE THEORY OF LIESEGANG BANDS;235
15.7;REFERENCES;237
16;Chapter 9. Dynamics of Aerosols;238
16.1;1. INTRODUCTION;238
16.2;2. GENERAL DYNAMIC EQUATION FOR AEROSOLS;238
16.3;3. KINETIC COEFFICIENTS;249
16.4;4. DIMENSIONLESS FORM OF THE CONTINUOUS GDE;253
16.5;5. AEROSOL SIZE DISTRIBUTION EVOLUTION UNDER PURE GROWTH;258
16.6;6. SUMMARY;268
16.7;REFERENCES;270
17;Chapter 10. Impulse Propagation in Excitable Systems;272
17.1;I. Introduction;272
17.2;II. Traveling wave solutions and the dispersion relation;277
17.3;Ill. Pulse dispersion during propagation;283
17.4;IV. Approximate kinematics;292
17.5;V. Summary;299
17.6;REFERENCES;302
18;Chapter 11. Current Problems in Combustion Research;306
18.1;1. INTRODUCTION;306
18.2;2. THE EQUATIONS OF COMBUSTION;307
18.3;3. DISCUSSION OF THE EQUATIONS;311
18.4;4. EXAMPLES OF SPECIFIC PROBLEMS;320
18.5;5. CONCLUSIONS;325
18.6;REFERENCES;325
19;Chapter 12. Measurement and Estimation of Rate Constants;328
19.1;1. INTRODUCTION;328
19.2;2. THERMOCHEMICAL KINETICS;328
19.3;3. MEASUREMENT TECHNIQUES;335
19.4;4. DISCUSSION;341
19.5;REFERENCES;342
20;Chapter 13. Nonisobaric Flame Propagation;346
20.1;1. INTRODUCTION;346
20.2;2. THE ONE-DIMENSIONAL PROBLEM;346
20.3;3. SO WHAT;351
20.4;4. A MODIFIED PROBLEM;354
20.5;5. CONCLUDING REMARK;355
20.6;REFERENCES;355
21;Chapter 14. Diffusion and Reaction in Carbon Burning;366
21.1;ABSTRACT;366
21.2;1. PROLEGOMENA;366
21.3;2. A CONTINUOUS FLAME THEORY;370
21.4;3. STRUCTURE OF THE STEADY STATE;373
21.5;4. DYNAMICS;378
21.6;NOMENCLATURE;386
21.7;REFERENCES;387
22;Chapter 15. On the Closure and Character of the Balance Equations for Heterogeneous Two-Phase Flow;388
22.1;1. INTRODUCTION;388
22.2;2. DEFINITION OF MACROSCOPIC VARIABLES;389
22.3;3. SMOOTHNESS OF THE AVERAGE AND FLUCTUATIONS;391
22.4;4. COMMUTATION OF DERIVATIVE AND AVERAGE;391
22.5;5. FUNDAMENTAL ASSUMPTIONS;393
22.6;6. MACROSCOPIC BALANCE OF MASS;394
22.7;7. MACROSCOPIC BALANCE OF MOMENTUM;395
22.8;8. MACROSCOPIC BALANCE OF ENERGY;397
22.9;9. CLOSURE AND CONSTITUTIVE LAWS;402
22.10;10. CHARACTERISTICS OF BALANCE EQUATIONS;406
22.11;11. CONCLUDING REMARKS;417
22.12;REFERENCES;418
23;Index;422