Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension
Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the parti...
| Autores principales: | , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
American Institute of Physics Publishing
2015
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| _version_ | 1826314429911793664 |
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| author | Simpson, MJ Baker, RE |
| author_facet | Simpson, MJ Baker, RE |
| author_sort | Simpson, MJ |
| collection | OXFORD |
| description | Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here. |
| first_indexed | 2024-03-07T03:27:44Z |
| format | Journal article |
| id | oxford-uuid:b9a4c7dc-03f6-4b55-a3c8-517ad85af3c6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:33:58Z |
| publishDate | 2015 |
| publisher | American Institute of Physics Publishing |
| record_format | dspace |
| spelling | oxford-uuid:b9a4c7dc-03f6-4b55-a3c8-517ad85af3c62024-09-05T10:06:04ZExact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimensionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b9a4c7dc-03f6-4b55-a3c8-517ad85af3c6EnglishSymplectic Elements at OxfordAmerican Institute of Physics Publishing2015Simpson, MJBaker, REUnlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here. |
| spellingShingle | Simpson, MJ Baker, RE Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title | Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title_full | Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title_fullStr | Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title_full_unstemmed | Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title_short | Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension |
| title_sort | exact calculations of survival probability for diffusion on growing lines disks and spheres the role of dimension |
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