Traveling Waves in the Belousov–Zhabotinskii Reaction

1980 ◽  
Vol 38 (3) ◽  
pp. 422-444 ◽  
Author(s):  
R. G. Gibbs
Keyword(s):  
Traveling Waves ◽  
Belousov Zhabotinskii Reaction

THE DIFFERENTIAL GEOMETRY OF SCROLL WAVES

1991 ◽  
Vol 01 (04) ◽  
pp. 723-744 ◽  
Author(s):  
JOHN J. TYSON ◽  
STEVEN H. STROGATZ
Keyword(s):  
Traveling Waves ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Topological Constraint ◽  
Linking Number ◽  
Physical Chemical ◽  
Statics And Dynamics ◽  
Scroll Wave ◽  
Chemical And Biological Systems ◽  
Belousov Zhabotinskii Reaction

Traveling waves of excitation organize physical, chemical, and biological systems in space and time. In the biological context they serve to communicate information rapidly over long distances and to coordinate the activity of tissues and organs. An example of particular beauty, complexity and importance is the three-dimensional rotating scroll wave observed in the Belousov–Zhabotinskii reaction and in the ventricle of the heart. A scroll wave rotates around a filamentous phase singularity that weaves through the three-dimensional medium. At any instant of time the geometry of the scroll wave can be reduced to the spatial arrangement of a ribbon whose edges are the singular filament and the tip of the scroll wave. This ribbon, when it closes on itself, must satisfy the topological constraint L = Tw + Wr, where L is the linking number of the two edges of the ribbon, Tw is the total twist of the ribbon, and Wr is the writhing number of the singular filament. We discuss the origin of this equation and its implications for scroll wave statics and dynamics.

Stability of traveling waves in the Belousov-Zhabotinskii reaction

1990 ◽  
Vol 41 (10) ◽  
pp. 5418-5430 ◽  
Author(s):  
David A. Kessler ◽  
Herbert Levine
Keyword(s):  
Traveling Waves ◽  
Belousov Zhabotinskii Reaction

Dispersion of traveling waves in the belousov-zhabotinskii reaction

1988 ◽  
Vol 30 (1-2) ◽  
pp. 177-191 ◽  
Author(s):  
J.D. Dockery ◽  
J.P. Keener ◽  
J.J. Tyson
Keyword(s):  
Traveling Waves ◽  
Belousov Zhabotinskii Reaction

Belousov–Zhabotinskii type oscillation reaction with glycerol and kinetics of reactions between the system components

1987 ◽  
Vol 52 (10) ◽  
pp. 2375-2382 ◽  
Author(s):  
Ľubica Adamčíková ◽  
Peter Ševčík
Keyword(s):  
Oscillation System ◽  
Chemical Oscillations ◽  
Oscillation Reaction ◽  
Reaction Solution ◽  
System Components ◽  
Probable Source ◽  
Belousov Zhabotinskii Reaction ◽  
Kinetics Of ◽  
Hydrolysis Of ◽  
Type Oscillation

Glycerol causes chemical oscillations in Belousov-Zhabotinskii reaction in a closed system as well as in a reaction solution bubbled with nitrogen. Since the oxidation of glycerol with bromate ions does not proceed autocatalytically and bromine in the oxidation state 0 or +1 in the absence of light does not react with glycerol, hydrolysis of bromine is the probable source of bromide ions in the studied oscillation system.

Double-Diffusive Convection in Traveling Waves in the Iodate−Sulfite System Explained

1996 ◽  
Vol 100 (40) ◽  
pp. 16209-16212 ◽  
Author(s):  
John A. Pojman ◽  
Andrea Komlósi ◽  
Istvan P. Nagy
Keyword(s):  
Traveling Waves ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Double Diffusive
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