Singular limit analysis for aggregation generated by random motion

随机运动产生聚合的奇异极限分析

• 批准号: 24654027
• 负责人: MIMURA Masayasu
• 金额: $ 1.16万
• 依托单位: Meiji University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-24654027/
• 关键词: 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

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.

为了理解以自组织方式形成的生物种群的主动聚集，不同领域提出了两种不同类型的模型；一种是偏微分方程领域的宏观模型，另一种是物理学和数学生物学领域的微观模型。然而，为了揭示聚集中产生的自组织机制，我们需要了解这两个模型之间的关系。在这个提议中，我们关注生物种群的主动聚集，它们自身秘密聚集信息素。对于聚集的形成，已经存在趋化扩散模型（宏观模型）和独立的基于个体的模型（微观模型）。对于这些模型的联系，我们开发了两个限制程序，即奇异极限和水动力极限，并通过互补使用它们，我们成功地揭示了这两个模型之间的关系。

项目成果

現象数理学入門

现象数学导论

• 发表时间: 2013
• 作者: 三村 昌泰その他11名

Traveling waves in a tumor growth model with contact inhibition, Nonlinear PDEs

具有接触抑制的肿瘤生长模型中的行波，非线性偏微分方程

• 发表时间: 2012

自己組織化のモデリング支援分析

自组装的建模辅助分析

• 作者: Masayasu Mimura;三村昌泰
• 通讯作者: 三村昌泰

Infinite dimensional relaxation oscillation in aggregation-growth systems

聚集增长系统中的无限维弛豫振荡

• 发表时间: 2012
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: S.-I. Ei;H. Izuhara;M. Mimura
• 通讯作者: M. Mimura

Model-aided Understanding of Self-Organization

模型辅助理解自组织

• 作者: Masayasu Mimura;三村昌泰;Masayasu Mimura;Masayasu Mimura;三村昌泰;三村昌泰;Masayasu Mimura
• 通讯作者: Masayasu Mimura