2013 Fiscal Year Final Research Report
Singular limit analysis for aggregation generated by random motion
| Project/Area Number |
24654027
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Meiji University |
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Principal Investigator |
MIMURA Masayasu 明治大学, 先端数理科学研究科, 教授 (50068128)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 能動的集合 / 走化性 / individual-based model / 特異極限 / 流体力学極限 / 自己組織化 |
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| Research Abstract |
For understanding of active aggregation of biological populations which are formed in a self-organized way, two different types of models have been proposed in different fields; One is macroscopic models in the field of PDEs and the other is microscopic models in the fields of physics and mathematical biology. However, In order to reveal the mechanism of self-organization arising in aggregation, we need to understand the relation between these two models.
In this proposal, we focus on active aggregation of biological populations which secret aggregating pheromone by themselves. For the formation of aggregation, there are already a chemotaxis-diffusion model (macroscopic model) and independently an individual-based model (microscopic model). For a link of these models, we develop two limiting procedures, that is, a singular limit and a hydrodynamic limit and by complementarily using them, we succeed in revealing the relation between these two models.
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