Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis
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 co...
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| Format: | Journal article |
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1995
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| _version_ | 1797050365531652096 |
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| author | Ngwa, G Maini, P |
| author_facet | Ngwa, G Maini, P |
| author_sort | Ngwa, G |
| collection | OXFORD |
| description | 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 shows 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. |
| first_indexed | 2024-03-06T18:04:03Z |
| format | Journal article |
| id | oxford-uuid:00d17675-a188-48c5-badf-8bef415a265c |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:04:03Z |
| publishDate | 1995 |
| record_format | dspace |
| spelling | oxford-uuid:00d17675-a188-48c5-badf-8bef415a265c2022-03-26T08:31:34ZSpatio-temporal patterns in a mechanical model for mesenchymal morphogenesisJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:00d17675-a188-48c5-badf-8bef415a265cMathematical Institute - ePrints1995Ngwa, GMaini, PWe 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 shows 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. |
| spellingShingle | Ngwa, G Maini, P Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title | Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title_full | Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title_fullStr | Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title_full_unstemmed | Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title_short | Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis |
| title_sort | spatio temporal patterns in a mechanical model for mesenchymal morphogenesis |
| work_keys_str_mv | AT ngwag spatiotemporalpatternsinamechanicalmodelformesenchymalmorphogenesis AT mainip spatiotemporalpatternsinamechanicalmodelformesenchymalmorphogenesis |