Pattern formation and geometry of the manifold

The objective of the present work is to investigate how pattern formation in the Cahn–Hilliard system can be influenced by geometry of the manifold. This is in contrast to control methods in which the physical field is modified and the pattern formation of the original system changes in response to...

Full description

Saved in:
Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2011-03, Vol.16 (3), p.1424-1432
Main Authors: Haji, Amir Hossein, Mahzoon, Mojtaba, Javadpour, Sirus
Format: Article
Language:English
Subjects:
Cahn–Hilliard equation
Circumferences
Computer simulation
Control systems
Helical
Manifold
Manifolds
Mathematical models
Modulation
Pattern formation
Rolls
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The objective of the present work is to investigate how pattern formation in the Cahn–Hilliard system can be influenced by geometry of the manifold. This is in contrast to control methods in which the physical field is modified and the pattern formation of the original system changes in response to control inputs. The idea begins with the cylindrical manifold symmetry leading to circumferential rolls while the torus manifold can be used to produce and control helical rolls. The next step is to search for a weaker restriction on the geometry of the manifold in order to reduce its dimension. In particular a short amplitude sinusoidal modulation on a flat surface is studied. At the final step a sequential pattern formation is presented.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2010.06.019