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Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation

Bai, Fengshan and Spence, Alastair and Stuart, Andrew M. (1994) Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation. Physica D, 78 (3-4). pp. 155-165. ISSN 0167-2789. https://resolver.caltech.edu/CaltechAUTHORS:20170609-122809369

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Abstract

Time dependent solutions of the Cahn-Hilliard equation are studied numerically. In particular heteroclinic orbits, which connect different equilibrium solutions at t = -∞ and t = +∞, are sought. Thus boundary value problems in space-time are computed. This computation requires an investigation of the stability of equilibria, since projections onto the stable and unstable manifolds determine the boundary conditions at t = -∞ and t = +∞. This stability analysis is then followed by solution of the appropriate boundary value problem in space-time. The results obtained cannot be found by standard initial value simulations. By specifying the two steady states at t = ±∞ appropriately it is possible to find orbits reflecting a given degree of coarsening over the time evolution. This gives a clear picture of the dynamic coarsening admissible in the equation. It also provides an understanding of orbits on the global attractor for the equation.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0167-2789(94)90112-0DOIArticle
http://www.sciencedirect.com/science/article/pii/0167278994901120?via%3DihubPublisherArticle
Additional Information:© 1994 Elsevier B.V. Received 29 September 1993, Revised 1 May 1994. The work of Bai and Spence is supported by the UK Science Engineering Research Council. The work of Stuart is funded by the Office of Naval Research under contract N00014-92-J-1876 and the National Science Foundation under contract number DMS-9201727.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Office of Naval Research (ONR)N00014-92-J-1876
NSFDMS-9201727
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ28
Issue or Number:3-4
Record Number:CaltechAUTHORS:20170609-122809369
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170609-122809369
Official Citation:Fengshan Bai, Alastair Spence, Andrew M. Stuart, Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation, Physica D: Nonlinear Phenomena, Volume 78, Issue 3, 1994, Pages 155-165, ISSN 0167-2789, http://dx.doi.org/10.1016/0167-2789(94)90112-0. (http://www.sciencedirect.com/science/article/pii/0167278994901120)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78057
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 21:21
Last Modified:03 Oct 2019 18:04

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