A PHYSICOCHEMICAL BASIS FOR PATTERN AND RHYTHM,

Abstract

The physical system under investigation is a membrane or thread, within which various chemical species are reacting and diffusing along the length. At the same time the participating species are exchanging with the surrounding media. The number of species is left open. The rate equations specifying accumulation of each species in terms of production, influx by diffusion, and input by exchange with surroundings are linearized about the uniform, steady-state solution and then cast into matrix form. Solutions are obtained which may grow, decay, remain stationary in time, or oscillate. Examples of one, two, and three participating species are discussed. In addition, the effects of geometry, such as cylindrical or spherical surfaces as the medium, are discussed briefly. Turing(1952) considered chemical patterns on a closed loop and, cursorily, on a sphere. His work motivated the present research. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1967
Accession Number
AD0652550

Entities

People

  • John I. Gmitro
  • L. E. Scriven

Organizations

  • University of Minnesota

Tags

DTIC Thesaurus Topics

  • Diffusion
  • Equations
  • Geometry
  • Mathematics
  • Membranes
  • Production
  • Stationary
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Plasma Physics / Magnetohydrodynamics
  • Theoretical Analysis.