scholarly journals Interpolation inequalities in pattern formation

2016 ◽  
Vol 271 (11) ◽  
pp. 3348-3392 ◽  
Author(s):  
Eleonora Cinti ◽  
Felix Otto
Keyword(s):  
Pattern Formation ◽  
Interpolation Inequalities

scholarly journals Sobolev-Kantorovich Inequalities

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Michel Ledoux
Keyword(s):  
Pattern Formation ◽  
Probability Density ◽  
Riemannian Manifolds ◽  
Wasserstein Distance ◽  
Sobolev Norm ◽  
Heat Flows ◽  
Interpolation Inequalities ◽  
Harnack Inequalities ◽  
Negatively Curved ◽  
Reference Measure

Abstract In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.

Pattern formation in the splay Freedericks transition of a nematic side-group polysiloxane

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

Pattern Formation in Thin Polymer Films: A New Morphology

2000 ◽  
Vol 629 ◽  
Author(s):  
Jean-Loup Masson ◽  
Peter F. Green
Keyword(s):  
Growth Rate ◽  
Pattern Formation ◽  
Early Stage ◽  
Structural Evolution ◽  
Distinct Form ◽  
Thin Polymer Films ◽  
Intermediate Morphology ◽  
Thin Polymer ◽  
Nonwetting Liquid ◽  
Cylindrical Holes

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.

Pattern Formation Survey on Non Uniformly Forced Swift-Hohenberg Equation

2019 ◽  
Author(s):  
Daniel Coelho ◽  
José da Rocha Miranda Pontes ◽  
Norberto Mangiavacchi
Keyword(s):  
Pattern Formation
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