Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems

1995 ◽  
Vol 33 (8) ◽  
Author(s):  
LauraE. Stephenson ◽  
DavidJ. Wollkind
Keyword(s):  
Pattern Formation ◽  
Nonlinear Stability ◽  
Model Systems ◽  
Turing Pattern ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Stability Analyses ◽  
Activator Inhibitor

Linear and Weakly Nonlinear Stability Analyses of Cooperative Car-Following Models

2014 ◽  
Vol 15 (5) ◽  
pp. 2001-2013 ◽  
Author(s):  
Julien Monteil ◽  
Romain Billot ◽  
Jacques Sau ◽  
Nour-Eddin El Faouzi
Keyword(s):  
Nonlinear Stability ◽  
Weakly Nonlinear ◽  
Car Following ◽  
Stability Analyses

Weakly Nonlinear Stability Analyses of Prototype Reaction-Diffusion Model Equations

SIAM Review ◽  
1994 ◽  
Vol 36 (2) ◽  
pp. 176-214 ◽  
Author(s):  
David J. Wollkind ◽  
Valipuram S. Manoranjan ◽  
Limin Zhang
Keyword(s):  
Diffusion Model ◽  
Nonlinear Stability ◽  
Reaction Diffusion ◽  
Weakly Nonlinear ◽  
Stability Analyses ◽  
Reaction Diffusion Model ◽  
Model Equations

scholarly journals Nonlinear stability analyses of pattern formation on solid surfaces during ion-sputtered erosion

2005 ◽  
Vol 41 (8-9) ◽  
pp. 939-964 ◽  
Author(s):  
A. Pansuwan ◽  
C. Rattanakul ◽  
Y. Lenbury ◽  
D.J. Wollkind ◽  
L. Harrison ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Nonlinear Stability ◽  
Solid Surfaces ◽  
Stability Analyses

scholarly journals The origin of hysteresis in the flag instability

2011 ◽  
Vol 691 ◽  
pp. 583-593 ◽  
Author(s):  
Christophe Eloy ◽  
Nicolas Kofman ◽  
Lionel Schouveiler
Keyword(s):  
Numerical Simulations ◽  
Hysteresis Loop ◽  
Nonlinear Stability ◽  
Slender Body ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Stability Analyses ◽  
Aeroelastic Instability ◽  
Large Hysteresis ◽  
Cantilevered Plate

AbstractThe flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, the discrepancy is addressed. First, weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and, second, new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

Nucleation of superconductivity in decreasing fields. II

1994 ◽  
Vol 5 (4) ◽  
pp. 469-494 ◽  
Author(s):  
S. J. Chapman
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Nonlinear Stability ◽  
Bifurcation Point ◽  
Superconducting State ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Stability Analyses

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg–Landau theory. Linear and weakly nonlinear stability analyses are performed near the bifurcation point, and the implications of the results for each of three examples is considered.

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