Ebook: Nonlinear Waves in Active Media

TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci­ ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

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The interdisciplinary contributions to this book deal with nonlinear wave motion in media with additional energy influx. Their aim is to bridge the gap between two widely used approaches: - diffusion-type models used in combustion theory, biophysics, and chemical kinetics, - evolution equations based on hyperbolic models describing transient processes in fluid dynamics, plasma physics and solid mechanics. Interesting problems discussed by contributors include jumping waves and domino effects, the influence of small-scale vortices on turbulent flows, new evolution equations, pattern formation and new mathematical models of biological media.

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The interdisciplinary contributions to this book deal with nonlinear wave motion in media with additional energy influx. Their aim is to bridge the gap between two widely used approaches: - diffusion-type models used in combustion theory, biophysics, and chemical kinetics, - evolution equations based on hyperbolic models describing transient processes in fluid dynamics, plasma physics and solid mechanics. Interesting problems discussed by contributors include jumping waves and domino effects, the influence of small-scale vortices on turbulent flows, new evolution equations, pattern formation and new mathematical models of biological media.
Content:
Front Matter....Pages I-X
Front Matter....Pages 1-1
Nonlinear Waves in Active Media: An Introduction....Pages 2-7
A Variable Coefficient Version of Zakharov and Shabat’s Method: With Applications to the Integration of Variable Coefficient Nonlinear Equations and to Perturbed Soliton Equations....Pages 8-16
Evolution Equations Compatible with Quasilinear Hyperbolic Models Involving Source-Like Terms....Pages 17-23
Steady Waves in Active Birelaxating Media....Pages 24-30
Asymmetric Solitary Waves in Active Media....Pages 31-37
Kinematical Theory of Autowave Patterns in Excitable Media....Pages 38-51
Dynamics of Spiral Waves in Nonequilibrium Media....Pages 52-59
The Formation of Structures in Gravitationally Unstable Media....Pages 60-66
Stability of Cellular Wave Structures in Oscillatory Pattern-Forming Systems near Onset....Pages 67-74
Front Matter....Pages 75-75
Group Theory for the Domino Effect....Pages 76-83
Wave Motion of Elongated Elastic Bodies Subjected to Nonlinear Flutter....Pages 84-91
Instabilities and Waves in Heterogeneous Systems....Pages 92-98
Energy Exchange Between Nonlinear Waves in Elastic Waveguides and External Media....Pages 99-104
Front Matter....Pages 105-105
Instability and Turbulence....Pages 106-113
Autowaves of Turbulence in Hydrodynamics....Pages 114-120
Amplification of Nonlinear Waves in the Medium with Temporal Fluctuations....Pages 121-126
Laser Stimulated Instabilities of Waves in a Subsurface Layer of a Liquid....Pages 127-132
Regular and Chaotic Dynamics of Coherently Pumped 3-Level Lasers....Pages 133-142
Simulation of Transient Waves in Active Magnetoelastic Solids....Pages 143-148
Duffing-like Behavior in Extended Turbulence Mode Models....Pages 149-155
Front Matter....Pages 105-105
Nonlinear Microscopic Model for Heterogeneous Medium with Discrete Sources....Pages 156-160
Front Matter....Pages 161-161
A Parameter Study of Focused Sound Fields in Active Media....Pages 162-169
Idiosyncracies of Cardiac Tissue as an Excitable Medium....Pages 170-175
Active Media with Discrete Sources and “Jumping Waves”....Pages 176-184
The Continuum Approach as Applied to Wave Phenomena in Physiological Systems....Pages 185-191
Spatio-temporal Complexity in Biological Systems....Pages 192-200
Front Matter....Pages 201-201
Structure of Unstable Gas Detonation Front....Pages 202-209
Observations on the Nature of Reaction Runaway in Reaction-Diffusion Systems....Pages 210-217
The Interaction of High Frequency Low Amplitude Acoustic Waves with Premixed Flames....Pages 218-231
Reaction-Diffusion Waves in a Simple Isothermal Chemical System....Pages 232-242
Amplification of Shock Waves in Nonequilibrium Gas-Liquid Systems....Pages 243-249
Nonlinear Waves in a Reacting Mixture....Pages 250-256
Numerical Simulation of Condensation Waves in Gases....Pages 257-265
Back Matter....Pages 267-275

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The interdisciplinary contributions to this book deal with nonlinear wave motion in media with additional energy influx. Their aim is to bridge the gap between two widely used approaches: - diffusion-type models used in combustion theory, biophysics, and chemical kinetics, - evolution equations based on hyperbolic models describing transient processes in fluid dynamics, plasma physics and solid mechanics. Interesting problems discussed by contributors include jumping waves and domino effects, the influence of small-scale vortices on turbulent flows, new evolution equations, pattern formation and new mathematical models of biological media.
Content:
Front Matter....Pages I-X
Front Matter....Pages 1-1
Nonlinear Waves in Active Media: An Introduction....Pages 2-7
A Variable Coefficient Version of Zakharov and Shabat’s Method: With Applications to the Integration of Variable Coefficient Nonlinear Equations and to Perturbed Soliton Equations....Pages 8-16
Evolution Equations Compatible with Quasilinear Hyperbolic Models Involving Source-Like Terms....Pages 17-23
Steady Waves in Active Birelaxating Media....Pages 24-30
Asymmetric Solitary Waves in Active Media....Pages 31-37
Kinematical Theory of Autowave Patterns in Excitable Media....Pages 38-51
Dynamics of Spiral Waves in Nonequilibrium Media....Pages 52-59
The Formation of Structures in Gravitationally Unstable Media....Pages 60-66
Stability of Cellular Wave Structures in Oscillatory Pattern-Forming Systems near Onset....Pages 67-74
Front Matter....Pages 75-75
Group Theory for the Domino Effect....Pages 76-83
Wave Motion of Elongated Elastic Bodies Subjected to Nonlinear Flutter....Pages 84-91
Instabilities and Waves in Heterogeneous Systems....Pages 92-98
Energy Exchange Between Nonlinear Waves in Elastic Waveguides and External Media....Pages 99-104
Front Matter....Pages 105-105
Instability and Turbulence....Pages 106-113
Autowaves of Turbulence in Hydrodynamics....Pages 114-120
Amplification of Nonlinear Waves in the Medium with Temporal Fluctuations....Pages 121-126
Laser Stimulated Instabilities of Waves in a Subsurface Layer of a Liquid....Pages 127-132
Regular and Chaotic Dynamics of Coherently Pumped 3-Level Lasers....Pages 133-142
Simulation of Transient Waves in Active Magnetoelastic Solids....Pages 143-148
Duffing-like Behavior in Extended Turbulence Mode Models....Pages 149-155
Front Matter....Pages 105-105
Nonlinear Microscopic Model for Heterogeneous Medium with Discrete Sources....Pages 156-160
Front Matter....Pages 161-161
A Parameter Study of Focused Sound Fields in Active Media....Pages 162-169
Idiosyncracies of Cardiac Tissue as an Excitable Medium....Pages 170-175
Active Media with Discrete Sources and “Jumping Waves”....Pages 176-184
The Continuum Approach as Applied to Wave Phenomena in Physiological Systems....Pages 185-191
Spatio-temporal Complexity in Biological Systems....Pages 192-200
Front Matter....Pages 201-201
Structure of Unstable Gas Detonation Front....Pages 202-209
Observations on the Nature of Reaction Runaway in Reaction-Diffusion Systems....Pages 210-217
The Interaction of High Frequency Low Amplitude Acoustic Waves with Premixed Flames....Pages 218-231
Reaction-Diffusion Waves in a Simple Isothermal Chemical System....Pages 232-242
Amplification of Shock Waves in Nonequilibrium Gas-Liquid Systems....Pages 243-249
Nonlinear Waves in a Reacting Mixture....Pages 250-256
Numerical Simulation of Condensation Waves in Gases....Pages 257-265
Back Matter....Pages 267-275
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