Chemical Waves and Patterns

  • Raymond Kapral
  • Kenneth Showalter

Part of the Understanding Chemical Reactivity book series (UCRE, volume 10)

Table of contents

  1. Front Matter
    Pages i-x
  2. Spiral Waves

    1. Front Matter
      Pages 1-1
    2. Stefan C. Müller, Theo Plesser
      Pages 57-92
    3. John J. Tyson, James P. Keener
      Pages 93-118
    4. Alexander S. Mikhailov, Vladimir S. Zykov
      Pages 119-162
    5. Dwight Barkley
      Pages 163-189
    6. J. A. Sepulchre, A. Babloyantz
      Pages 191-217
  3. Turing and Turing-Like Patterns

    1. Front Matter
      Pages 219-219
    2. J. Boissonade, E. Dulos, P. De Kepper
      Pages 221-268
    3. Qi Ouyang, Harry L. Swinney
      Pages 269-295
    4. P. Borckmans, G. Dewel, A. De Wit, D. Walgraef
      Pages 323-363
    5. Michael Menzinger, Arkady B. Rovinsky
      Pages 365-397
  4. Chemical Wave Dynamics

    1. Front Matter
      Pages 399-399
    2. Eugenia Mori, Xiaolin Chu, John Ross
      Pages 419-446
    3. M. Eiswirth, G. Ertl
      Pages 447-483
    4. Stephen K. Scott, Kenneth Showalter
      Pages 485-516
  5. Fluctuations and Chemical Waves

    1. Front Matter
      Pages 571-571
    2. G. Nicolis, F. Baras, P. Geysermans, P. Peeters
      Pages 573-608
    3. Raymond Kapral, Xiao-Guang Wu
      Pages 609-634
  6. Back Matter
    Pages 635-641

About this book


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.


Diffusion bifurcation biology chaos chemistry development dynamics experiment imaging techniques noise physics porous media stability wave wave propagation

Editors and affiliations

  • Raymond Kapral
    • 1
  • Kenneth Showalter
    • 2
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada
  2. 2.Department of ChemistryWest Virginia UniversityMorgantownUSA

Bibliographic information