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| Predicate | Object |
|---|---|
| rdf:type | |
| lifeskim:mentions | |
| pubmed:issue |
5
|
| pubmed:dateCreated |
1995-6-16
|
| pubmed:abstractText |
We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis show that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.
|
| pubmed:language |
eng
|
| pubmed:journal | |
| pubmed:citationSubset |
IM
|
| pubmed:status |
MEDLINE
|
| pubmed:issn |
0303-6812
|
| pubmed:author | |
| pubmed:issnType |
Print
|
| pubmed:volume |
33
|
| pubmed:owner |
NLM
|
| pubmed:authorsComplete |
Y
|
| pubmed:pagination |
489-520
|
| pubmed:dateRevised |
2006-11-15
|
| pubmed:meshHeading | |
| pubmed:year |
1995
|
| pubmed:articleTitle |
Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis.
|
| pubmed:affiliation |
Centre for Mathematical Biology, Mathematical Institute, Oxford, England.
|
| pubmed:publicationType |
Journal Article,
Comparative Study,
Research Support, Non-U.S. Gov't
|