Abstract
The well known diffusion equation is used to simulate the spread of a quantity over a flat surface (in 2D) or through space (in 3D). However, the standard diffusion equation cannot be used to model the spread of a quantity over a curved surface such as the surface of an of an object in 3D space. However, if the surface is approximated by a set of flat, triangular elements then the diffusion equation can be applied to each element in terms of local variables and then mapped into the global variables using a relatively simple change of variables. This leads to a diffusion type equation with a different diffusion tensor in each element. This equation can then be solved using a boundary-finite element method.
The method is then used to simulate the changes in the density of biological cells on a surface as they migrate due to changes in the concentration of a growth factor.
The method is then used to simulate the changes in the density of biological cells on a surface as they migrate due to changes in the concentration of a growth factor.
| Original language | English |
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| Title of host publication | Proceeding of the 14th UK Conference on Boundary Integral Methods UKBIM14 |
| Editors | Edmund Chadwick |
| Publisher | University of Salford |
| Chapter | 1 |
| Pages | 6-15 |
| Number of pages | 10 |
| ISBN (Electronic) | 9781917780025 |
| Publication status | Published - 7 Aug 2025 |
| Event | 14th United Kingdom Conference on Boundary Integral Methods - University of Salford, Salford, United Kingdom Duration: 7 Jul 2025 → 8 Sept 2025 https://ukbim14.wordpress.com/ |
Conference
| Conference | 14th United Kingdom Conference on Boundary Integral Methods |
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| Abbreviated title | UKBIM14 |
| Country/Territory | United Kingdom |
| City | Salford |
| Period | 7/07/25 → 8/09/25 |
| Internet address |