scholarly journals Imperfect Bifurcation Near a Double Eigenvalue: Transitions Between Nonsymmetric and Symmetric Patterns

1983 ◽  
Vol 43 (5) ◽  
pp. 1042-1060 ◽  
Author(s):  
T. Erneux ◽  
D. S. Cohen
Keyword(s):  
Double Eigenvalue ◽  
Imperfect Bifurcation ◽  
Symmetric Patterns

scholarly journals Phyllotaxis as geometric canalization during plant development

Development ◽  
2020 ◽  
Vol 147 (19) ◽  
pp. dev165878 ◽  
Author(s):  
Christophe Godin ◽  
Christophe Golé ◽  
Stéphane Douady
Keyword(s):  
Developmental Biology ◽  
Plant Development ◽  
Fundamental Question ◽  
Developmental Constraints ◽  
Local Interactions ◽  
Final Shape ◽  
Lateral Organs ◽  
Universal Constraint ◽  
Symmetric Patterns

ABSTRACTWhy living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first to provide an accessible overview of phyllotaxis, and second to argue that the spiral patterns in plants are progressively canalized from local interactions of nascent organs. The relative uniformity of the organogenesis process across all plants then explains the prevalence of certain patterns in plants, i.e. Fibonacci phyllotaxis.

An Improved Microphotometer Trace of Radially Symmetric Patterns

1947 ◽  
Vol 15 (10) ◽  
pp. 765-765 ◽  
Author(s):  
I. Lugoski Karle ◽  
D. Hoober ◽  
J. Karle
Keyword(s):  
Symmetric Patterns

Bifurcation to vortex solutions in superconducting films

1997 ◽  
Vol 8 (2) ◽  
pp. 125-148 ◽  
Author(s):  
T. BOECK ◽  
S. J. CHAPMAN
Keyword(s):  
Magnetic Field ◽  
Superconducting Films ◽  
Leading Order ◽  
Nonlinear Stability Analysis ◽  
Slab Geometry ◽  
Weakly Nonlinear ◽  
Double Eigenvalue ◽  
Wide Range ◽  
Vortex Solutions ◽  
Parameter Values

The bifurcation from a normally conducting state to a superconducting state in a decreasing magnetic field is studied for a slab geometry. The leading eigenvalue is a double eigenvalue, leading to a rich structure of possible behaviours. A weakly-nonlinear stability analysis is performed, and the possible responses of the material are classified. Finally, the leading-order equations are solved numerically for a wide range of parameter values to determine which of these behaviours will occur in practice.

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