权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Function theory in multiply-connected domains & applications to physical systems

多重连通域中的函数论

基本信息

批准号：
EP/C545036/1
负责人：
Darren Crowdy
金额：
$ 43.54万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FC545036%2F1
关键词：
Function theory multiply connected domains

项目摘要

Multiply-connected domains are what mathematicians call regions with holes . In physics, the holes can correspond to lots of different things such as air bubbles in fluids or regions of swirling motion (for example, storm systems or hurricanes) in the atmosphere or different clusters of bacteria competing for a common food supply. Thus, the mathematical concept of a multiply-connected domain occurs in many different places in the study of everyday phenomena. To understand such phenomena, it is necessary to study and understand mathematical models of them. This requires a knowledge of mathematical functions and techniques specially tailored to the multiply-connected domains in which these phenomena are taking place. Unfortunately, mathematicians in the past who have developed the mathematics of functions in multiply-connected domains have not done a very good job of translating the significance of their results to scientists interested in describing and studying everyday phenomena such as bubbles in fluids or the motion of storm systems. Yet, recent work by the PI has shown that if one can successfully translate these mathematical results and demonstrate their applicability to these various everyday phenomena, powerful new techniques become available to those scientists who study them, making their jobs much easier and leading to new Insights. This research proposes to continue in this crusade to develop and apply the mathematical results of classicalfunction theory and complex analysis to real-life problems.

多重连通域就是数学家所说的有洞区域。在物理学中，这些洞可以对应许多不同的事物，例如流体中的气泡或大气中的旋转运动区域（例如风暴系统或飓风）或竞争共同食物供应的不同细菌簇。因此，在日常现象的研究中，多重连通域的数学概念出现在许多不同的地方。为了理解这些现象，有必要研究和理解它们的数学模型。这需要专门针对发生这些现象的多重连接域定制的数学函数和技术知识。不幸的是，过去在多重连通域中发展了函数数学的数学家并没有很好地将他们的结果的意义转化为对描述和研究日常现象（例如流体中的气泡或风暴系统的运动）感兴趣的科学家。然而，PI 最近的工作表明，如果能够成功地转化这些数学结果并证明它们对这些各种日常现象的适用性，那么研究它们的科学家就可以使用强大的新技术，使他们的工作变得更加轻松并带来新的见解。这项研究建议继续发展经典函数理论和复分析的数学成果并将其应用于现实生活中的问题。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Diffusion-limited aggregation on curved surfaces

DOI：
10.1209/0295-5075/91/46005
发表时间：
2010-08-01
期刊：
EPL
影响因子：
1.8
作者：
Choi, J.;Crowdy, D.;Bazant, M. Z.
通讯作者：
Bazant, M. Z.

Multiple steady bubbles in a Hele-Shaw cell

DOI：
10.1098/rspa.2008.0252
发表时间：
2009-02
期刊：
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
影响因子：
0
作者：
D. Crowdy
通讯作者：
D. Crowdy

Exact solutions for the evolution of ellipsoidal inclusions in porous media

多孔介质中椭圆体包裹体演化的精确解