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E-grāmata: Pole Solutions for Flame Front Propagation

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Pole Solutions for Flame Front PropagationPalielināt
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This book deals with solving mathematically the unsteady flame propagation equations. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to investigate analytically and numerically properties of the flame front propagation equations.

Introduction.- Pole-Dynamics in Unstable Front Propagation: The Case of the Channel Geometry.- Using of Pole Dynamics for Stability Analysis of Premixed Flame Fronts: Dynamical Systems Approach in the Complex Plane.- Dynamics and Wrinkling of Radially Propagating Fronts Inferred from Scaling Laws in Channel Geometries.- Laplacian Growth Without Surface Tension in Filtration Combustion: Analytical Pole Solution.- Summary.
1 General View of Pole Solutions in Flame Front Propagation
1(10)
2 Pole-Dynamics in Unstable Front Propagation: The Case of The Channel Geometry
11(44)
2.1 Introduction
11(2)
2.2 Equations of Motion and Pole-Decomposition in the Channel Geometry
13(2)
2.3 Linear Stability Analysis in Channel Geometry
15(6)
2.3.1 Fourier Decomposition and Eigenvalues
16(2)
2.3.2 Qualitative Understanding Using Pole-Analysis
18(1)
2.3.3 Dynamics Near Marginality
18(2)
2.3.4 Excitable System
20(1)
2.4 Initial Conditions, Pole Decomposition and Coarsening
21(6)
2.4.1 Pole Expansion: General Comments
21(2)
2.4.2 The Initial Stages of the Front Evolution: The Exponential Stage and the Inverse Cascade
23(3)
2.4.3 Inverse Cascade in the Presence of Noise
26(1)
2.5 Acceleration of the Premixed Flame Front, Pole Dynamics and Noise
27(18)
2.5.1 Noisy Simulations
28(3)
2.5.2 Calculation of the Number of Poles in the System
31(4)
2.5.3 Theoretical Discussion of the Effect of Noise
35(8)
2.5.4 The Acceleration of the Premixed Flame Front Because of Noise
43(2)
2.6 Comparison with Experiment for Premixed Flame in Channel
45(1)
2.7 Summary and Conclusions
46(9)
Appendix: Derivation of Michelson Sivashinsky Equation
47(8)
3 Using of Pole Dynamics for Stability Analysis of Premixed Flame Fronts: Dynamical Systems Approach in the Complex Plane
55(12)
3.1 Introduction
55(1)
3.2 Linear Stability Analysis in Channel Geometry
56(2)
3.3 Linear Stability in Terms of Complex Singularities
58(7)
3.3.1 The Modes Associated with the Giant Cusp
59(2)
3.3.2 Modes Related to Additional Poles
61(4)
3.4 Conclusions
65(2)
4 Dynamics and Wrinkling of Radially Propagating Fronts Inferred from Scaling Laws in Channel Geometries
67(18)
4.1 Introduction
67(1)
4.2 The Geometry of Developing Premixed Flame Fronts: Analysis with Pole Decomposition
68(9)
4.3 Comparison with Experiment for Expended Premixed Flames
77(6)
4.4 Conclusions
83(2)
5 Laplacian Growth Without Surface Tension in Filtration Combustion: Analytical Pole Solution
85(24)
5.1 Introduction
85(3)
5.2 Asymptotic Single Saffman-Taylor "finger" Formation Without Surface Tension
88(9)
5.2.1 Asymptotic Behaviour of the Poles in the Mathematical Plane
90(4)
5.2.2 Theorem About Coalescence of the Poles
94(1)
5.2.3 The Final Result
95(2)
5.3 Saffman-Taylor "finger" Formation with Half of the Channel Size
97(5)
5.4 Comparison Laplacian Growth with Experiment for Filtration Combustion
102(2)
5.5 Conclusions
104(5)
Appendix 1 Proof of Theorems
104(1)
Appendix 2 Filtration Combustion---Basic Equations
105(4)
6 Summary
109(2)
Bibliography 111(6)
Index 117
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