Models of Controlled Biological Growth

受控生物生长模型

基本信息

批准号：
1714237
负责人：
Alberto Bressan
金额：
$ 34.5万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-07-01 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1714237&HistoricalAwards=false
关键词：
Models Controlled Biological Growth

项目摘要

In the process of their growth, tissues in plants and animals develop into distinctly recognizable shapes: leaves, flowers, bones, etc.; almost universally, the tissue growth appears to be controlled with remarkable accuracy. The principal aim of this research is developing new mathematical tools to understand this control mechanism. From this theoretical perspective, some key questions will be addressed: What physical parameters produce the different behavior of a climbing vine, compared with a tree stem? How does nature control the shape and size of leaves, or flowers, in plants of different species? The project will study various partial differential equations (PDE) modeling the growth of a biological tissue. These equations describe the balance between diffusion and adsorption of growth-inducing chemicals, volume expansion, and elastic deformation of the tissue. The focus will be on the emergence of distinctive shapes, and on how these shapes can be modified by varying the growth-affecting physical parameters. The project will focus on various models of tissue growth, described by systems of partial differential equations. These represent diffusion and absorption for morphogens within the tissue, bulk growth, and elastic deformation. Existence, uniqueness, and qualitative properties of solutions will be studied, also in an anisotropic setting and for stratified domains. The results to be obtained will expand the current theory of evolution problems on domains with moving boundaries. The research will also address new types of stationary problems, somewhat like eigenvalue problems but in a set-valued framework. For various classes of stratified domains, the Principal Investigator expects to discover families of locally invariant "morpho-stationary" configurations, depending on finitely many parameters. These will generate a rich variety of new geometric shapes, that will be studied both analytically and numerically.

在生长的过程中，动植物中的组织成长为明显的形状：叶子，花，骨骼等；几乎普遍地，组织的生长似乎以显着的精度控制。这项研究的主要目的是开发新的数学工具来了解这种控制机制。从这个理论的角度来看，将解决一些关键问题：与树茎相比，哪些物理参数会产生攀岩藤的不同行为？自然如何在不同物种的植物中控制叶子或花朵的形状和大小？该项目将研究建模生物组织生长的各种偏微分方程（PDE）。这些方程式描述了差异与成瘾化学物质，体积膨胀和组织的弹性变形之间的平衡。重点将放在独特形状的出现上，以及如何通过改变影响生长的物理参数来修改这些形状。该项目将集中于各种组织生长模型，该模型由部分微分方程的系统描述。这些代表了组织内形态剂的差异和苦难，散装生长和弹性变形。解决方案的存在，唯一性和定性特性也将在各向异性环境和分层域中进行研究。要获得的结果将扩大具有移动边界的域上的当前进化问题。这项研究还将解决新的固定问题类型，有些类似于特征值问题，但在设定值的框架中。对于各种类别的分层域，主要研究人员希望根据许多参数发现本地不变的“形态阶层”配置的家庭。这些将产生各种新的几何形状，这些几何形状将在分析和数值上进行研究。