Pattern Formation and Wave Propagation in Chemical Systems

1988 ◽  
pp. 105-126
Author(s):  
I. R. Epstein
Keyword(s):  
Wave Propagation ◽  
Pattern Formation ◽  
Chemical Systems

EQUIVALENT CNN CELL MODELS AND PATTERNS

2003 ◽  
Vol 13 (05) ◽  
pp. 1055-1161 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Genetic Algorithms ◽  
Wave Propagation ◽  
Pattern Formation ◽  
Discrete Time ◽  
Cell Model ◽  
Formation Mechanisms ◽  
Associative Memories ◽  
Cell Models ◽  
Canonical Models ◽  
Constrained Conditions

In this paper, canonical isolated CNN cell models are proposed by using implicit differential equations. A number of equivalent but distinct CNN cell models are derived from these canonical models. Almost every known CNN cell model can be classified into one or more groups via constrained conditions. This approach is also applied to discrete-time CNN cell models. Pattern formation mechanisms are investigated from the viewpoint of equivalent templates and genetic algorithms. A strange wave propagation phenomenon in nonuniform CNN cells is also presented in this paper. Finally, chaotic associative memories are proposed.

ELECTRIC FIELD INFLUENCE ON TRAVELING WAVE PROPAGATION AND STATIONARY PATTERN FORMATION

1995 ◽  
Vol 05 (03) ◽  
pp. 797-807 ◽  
Author(s):  
J. MOSQUERA ◽  
M. GÓMEZ-GESTEIRA ◽  
V. PÉREZ-MUÑUZURI ◽  
A.P. MUÑUZURI ◽  
V. PÉREZ-VILLAR
Keyword(s):  
Wave Propagation ◽  
Pattern Formation ◽  
Electric Field ◽  
Electric Fields ◽  
Traveling Wave ◽  
Traveling Fronts ◽  
Spatial Terms ◽  
Oregonator Model ◽  
Field Influence ◽  
Good Agreement

The electric field influence on pattern formation and traveling wave propagation is investigated in the framework of the Oregonator model. When an electric field is applied to a system that can suffer spatial instabilities, Turing and Turing-like patterns (traveling fronts that become stationary patterns when reaching a zero-flux boundary) are observed. On the other hand, when an electric field is applied to a system that cannot become unstable by spatial terms and where wavefronts are propagating in the absence of electric fields, the velocity of these wavefronts is modified and can even be reversed. This is in good agreement with previous experimental results.

scholarly journals Formins specify membrane patterns generated by propagating actin waves

2020 ◽  
Vol 31 (5) ◽  
pp. 373-385 ◽  
Author(s):  
Mary Ecke ◽  
Jana Prassler ◽  
Patrick Tanribil ◽  
Annette Müller-Taubenberger ◽  
Sarah Körber ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Pattern Formation ◽  
The Other ◽  
Cell Cortex ◽  
Actin Waves

Actin waves beneath the membrane of Dictyostelium cells separate two distinct areas of the cell cortex. Upon wave propagation, one type of area is converted into the other. We show that specific formins are recruited to different areas of the wave landscape and use these actin-polymerizing machines to analyze the dynamics of pattern formation.

Pattern formation in chemical systems

1995 ◽  
Vol 86 (1-2) ◽  
pp. 149-157 ◽  
Author(s):  
Raymond Kapral
Keyword(s):  
Pattern Formation ◽  
Chemical Systems

PATTERN FORMATIONS IN CHEMICAL SYSTEMS

2003 ◽  
Vol 06 (01) ◽  
pp. 3-14 ◽  
Author(s):  
JERZY MASELKO
Keyword(s):  
Numerical Simulation ◽  
Pattern Formation ◽  
Complex Pattern ◽  
Chemical Systems ◽  
Complex Patterns ◽  
Pattern Formations

The formation of complex patterns in chemical systems is discussed in the following cases: relations of pattern formation to thermodynamics theories; unusually complex pattern formation in very simple experimental chemical systems; and numerical simulation of patterns that develop in multicellular chemical systems. The paper concludes with a discussion on future technological applications.

scholarly journals Is the Skin an Excitable Medium? Pattern Formation in Erythema Gyratum Repens

2005 ◽  
Vol 6 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Stephen Gilmore ◽  
Kerry A. Landman
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Biochemical Basis ◽  
Bz Reaction ◽  
Chemical Systems ◽  
Inflammatory Dermatosis ◽  
Reaction Diffusion Model ◽  
Oscillatory Chemical ◽  
Spatio Temporal ◽  
Scaly Skin

Erythema gyratum repens (EGR) is a rare, inflammatory dermatosis of unknown aetiology. The morphology of the eruption is striking and displays rapidly evolving circinate and gyrate bands of erythematous and scaly skin. Although the aetiology of the pattern is unknown, it has previously been noted that the eruption shares morphologic features with the patterns of spatio-temporal chemical concentration profiles observed in the Belusov-Zhabotinski (BZ) reaction. Yet this morphologic correspondence has not been investigated further. Here we apply a simple non-linear reaction–diffusion model, previously used to describe the BZ reaction, as a template for pattern formation in EGR, and show how the mechanism may provide a biochemical basis for many of the dynamic and morphologic features of the rash. These results are supported by the results of a cellular automaton simulation approximating the dynamics of oscillatory chemical systems—the Hodgepodge machine—where the spatio-temporal patterns developed show astonishing similarities to the morphology of EGR.

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