- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Asymptotic and numerical analysis of the Allen-Cahn...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Asymptotic and numerical analysis of the Allen-Cahn equation with a mass constraint Stafford, Douglas James
Abstract
The Allen-Cahn equation with a mass constraint is analyzed asymptotically and numerically in a two-dimensional domain. This problem models the phase separation of a binary mixture in the presence of a mass constraint. Solutions develop internal layers, or interfaces, that propagate depending on the curvature of the interfaces while keeping the area they enclose constant. Small interfaces attached to the boundary of the domain are shown to move along the boundary in the direction of increasing boundary curvature. The motion of the interfaces is simulated numerically to verify these asymptotic results. The slow motion behavior of a semi-circular interface intersecting aflat boundary segment is also analyzed. The projection method is used to derive an explicit ordinary differential equation for the location of the center of such a semi-circular interface.
Item Metadata
Title |
Asymptotic and numerical analysis of the Allen-Cahn equation with a mass constraint
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1997
|
Description |
The Allen-Cahn equation with a mass constraint is analyzed asymptotically and numerically
in a two-dimensional domain. This problem models the phase separation of a binary mixture
in the presence of a mass constraint. Solutions develop internal layers, or interfaces, that
propagate depending on the curvature of the interfaces while keeping the area they enclose
constant. Small interfaces attached to the boundary of the domain are shown to move along
the boundary in the direction of increasing boundary curvature. The motion of the interfaces
is simulated numerically to verify these asymptotic results. The slow motion behavior of a
semi-circular interface intersecting aflat boundary segment is also analyzed. The projection
method is used to derive an explicit ordinary differential equation for the location of the center
of such a semi-circular interface.
|
Extent |
2910740 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2009-03-24
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0079972
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
1997-11
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.