- Title Information
- Title
- Localized Structures in the Multi-dimensional Swift-Hohenberg Equation
- Name:
Personal
- Name Part
- McCalla, Scott G
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
- 2011
- Physical Description
- Extent
- xiii, 110 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D. -- Brown University (2011)
- Name:
Personal
- Name Part
- Sandstede, Bjorn
- Role
- Role Term:
Text
- Director
- Name:
Personal
- Name Part
- Mallet-Paret, John
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Scheel, Arnd
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Abstract
- This goal of this thesis is to understand patterns in the Swift{Hohenberg equation. Thepatterns studied are localized, stationary and radially symmetric in dimensions one throughthree. The emphasis is placed on the existence of these structures through numericalevidence and analytic proofs.The bifurcation structure of localized stationary radial patterns of the Swift{Hohenbergequation is explored when a continuous parameter n is varied that corresponds to the underlyingspace dimension whenever n is an integer. In particular, this numerical investigationreveals how 1D pulses and 2-pulses are connected to planar spots and rings when n isincreased from 1 to 2. It also elucidates changes in the snaking diagrams of spots whenthe dimension is switched from 2 to 3.A previously unknown spot solution is additionally uncovered. The second half of thethesis is devoted to rigorously proving this spot's existence. The amplitude of the spotexhibits an unexpected scaling as the bifurcation parameter is reduced to zero. The spotis constructed by gluing two known solutions together, each scaling as the square root ofthe bifurcation parameter, but it has a much larger scaling. This behaviour is explainedas a result of the proof.
- Subject
- Topic
- Pattern Formation
- Subject
- Topic
- PDEs
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/893484")
- Topic
- Differential equations, Partial
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20111003
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Identifier:
DOI
- 10.7301/Z0VQ30X9
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations