scholarly journals Pattern formation by boundary forcing in convectively unstable, oscillatory media with and without differential transport

2005 ◽  
Vol 72 (2) ◽  
Author(s):  
Patrick N. McGraw ◽  
Michael Menzinger
2005 ◽  
Vol 15 (07) ◽  
pp. 2283-2293 ◽  
Author(s):  
REBECCA ELLISON ◽  
VIRGINIA GARDNER ◽  
JOEL LEPAK ◽  
MEGHAN O'MALLEY ◽  
JOSEPH PAULLET ◽  
...  

We investigate small two-dimensional arrays of locally coupled phase oscillators which are shown to exhibit a surprising variety of stable structures which include: single spiral waves, spiral pairs and spirals with secondary periodic core motion. This periodic core motion is not the core meander familiar to many models of active media, but is in fact induced by the boundary of the small domain. Such boundary motion was investigated by Sepulchre and Babloyantz [1993] for the complex Ginzburg–Landau equation and for the Brusselator model in a relaxation oscillation parameter regime. The current model confirms the findings in [Sepulchre & Babloyantz, 1993] and sheds new light on the origin of such motion. The model also exhibits other patterns, as well as a chaotic regime. We discuss the transition between patterns as the form of the coupling is changed as well as implications for pattern formation in general oscillatory media.


2016 ◽  
Vol 94 (1) ◽  
Author(s):  
Rehman Ali ◽  
Jeremy Harris ◽  
Bard Ermentrout

1993 ◽  
Vol 3 (6) ◽  
pp. 865-889 ◽  
Author(s):  
Norbert Schwenk ◽  
Hans Wolfgang Spiess
Keyword(s):  

2000 ◽  
Vol 629 ◽  
Author(s):  
Jean-Loup Masson ◽  
Peter F. Green

ABSTRACTResearchers have shown that thin, nonwetting, liquid homopolymer films dewet substrates, forming patterns that reflect fluctuations in the local film thickness. These patterns have been shown to be either discrete cylindrical holes or bicontinuous “spinodal-like” patterns. In this paper we show the existence of a new morphology. During the early stage of dewetting, discrete highly asymmetric holes appear spontaneously throughout the film. The nucleation rate of these holes is faster than their growth rate. The morphology of the late stage of evolution, after 18 days, is characterized by a bicontinuous pattern, distinct form conventional spinodal dewetting patterns. This morphology has been observed for a range of film thicknesses between 7.5 and 21nm. The structural evolution of this intermediate morphology is discussed.


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