Analytic representation of oscillations, excitability, and traveling waves in a realistic model of the Belousov–Zhabotinskii reaction

1977 ◽  
Vol 66 (3) ◽  
pp. 905-915 ◽  
Author(s):  
John J. Tyson
Keyword(s):  
Traveling Waves ◽  
Realistic Model ◽  
Analytic Representation ◽  
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

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

A Realistic Model for the 1992-96 Tidal Waves

1997 ◽  
Author(s):  
Srinivas Tadepalli ◽  
Costas Emmanuel Synolakis
Keyword(s):  
Realistic Model ◽  
Tidal Waves
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