Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes
On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death,...
| Main Authors: | , |
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| Format: | Journal article |
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American Physical Society
2011
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| _version_ | 1797057777497014272 |
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| author | Simpson, M Baker, R |
| author_facet | Simpson, M Baker, R |
| author_sort | Simpson, M |
| collection | OXFORD |
| description | On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description. |
| first_indexed | 2024-03-06T19:41:16Z |
| format | Journal article |
| id | oxford-uuid:20bef913-50b6-4684-99d8-ddaecc5f757a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:41:16Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:20bef913-50b6-4684-99d8-ddaecc5f757a2022-03-26T11:29:19ZCorrecting mean-field approximations for spatially-dependent advection-diffusion-reaction processesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:20bef913-50b6-4684-99d8-ddaecc5f757aMathematical Institute - ePrintsAmerican Physical Society2011Simpson, MBaker, ROn the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description. |
| spellingShingle | Simpson, M Baker, R Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title | Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title_full | Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title_fullStr | Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title_full_unstemmed | Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title_short | Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes |
| title_sort | correcting mean field approximations for spatially dependent advection diffusion reaction processes |
| work_keys_str_mv | AT simpsonm correctingmeanfieldapproximationsforspatiallydependentadvectiondiffusionreactionprocesses AT bakerr correctingmeanfieldapproximationsforspatiallydependentadvectiondiffusionreactionprocesses |