Chemical Waves and Patterns

✍ Scribed by A. T. Winfree (auth.), Raymond Kapral, Kenneth Showalter (eds.)

• Publisher: Springer Netherlands
• Year: 1995
• Tongue: English
• Leaves: 640
• Series: Understanding Chemical Reactivity 10
• Edition: 1
• Category: Library

✦ Synopsis

The concept of macroscopic waves and patterns developing from chemical reaction coupling with diffusion was presented, apparently for the first time, at the Main Meeting of the Deutsche Bunsengesellschaft fur Angewandte Physikalische Chemie, held in Dresden, Germany from May 21 to 24, 1906. Robert Luther, Director of the Physical Chemistry Laboratory in Leipzig, read his paper on the discovery and analysis of propagating reaction-diffusion fronts in autocatalytic chemical reactions [1, 2]. He presented an equation for the velocity of these new waves, V = a(KDC)1/2, and asserted that they might have features in common with propagating action potentials in nerve cell axons. During the discussion period, a skeptic in the audience voiced his objections to this notion. It was none other than the great physical chemist Walther Nernst, who believed that nerve impulse propagation was far too rapid to be akin to the propagating fronts. He was also not willing to accept Luther's wave velocity equation without a derivation. Luther stood his ground, saying his equation was "a simple consequence of the corresponding differential equation. " He described several different autocatalytic reactions that exhibit propagating fronts (recommending gelling the solution to prevent convection) and even presented a demonstration: the autocatalytic permanganate oxidation of oxalate was carried out in a test tube with the image of the front projected onto a screen for the audience.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
Lingering Mysteries about Organizing Centers in the Belousov—Zhabotinsky Medium and Its Oregonator Model....Pages 3-55
Spiral Wave Dynamics....Pages 57-92
A Theory of Rotating Scroll Waves in Excitable Media....Pages 93-118
Spiral Waves in Weakly Excitable Media....Pages 119-162
Spiral Meandering....Pages 163-189
Spiral and Target Waves in Finite and Discontinuous Media....Pages 191-217
Front Matter....Pages 219-219
Turing Patterns: From Myth to Reality....Pages 221-268
Onset and Beyond Turing Pattern Formation....Pages 269-295
The Chemistry behind the First Experimental Chemical Examples of Turing Patterns....Pages 297-322
Turing Bifurcations and Pattern Selection....Pages 323-363
The Differential Flow Instabilities....Pages 365-397
Front Matter....Pages 399-399
Wave Propagation and Wave Pattern Formation in Nonuniform Reaction-Diffusion Systems....Pages 401-418
Chemical Front Propagation: Initiation and Relative Stability....Pages 419-446
Pattern Formation on Catalytic Surfaces....Pages 447-483
Simple and Complex Reaction-Diffusion Fronts....Pages 485-516
Modeling Front Pattern Formation and Intermittent Bursting Phenomena in the Couette Flow Reactor....Pages 517-570
Front Matter....Pages 571-571
Probabilistic Approach to Chemical Instabilities and Chaos....Pages 573-608
Internal Noise, Oscillations, Chaos and Chemical Waves....Pages 609-634
Back Matter....Pages 635-641

✦ Subjects

Physical Chemistry