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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.

在生长过程中，植物和动物的组织发育成明显可识别的形状：叶、花、骨头等；几乎普遍地，组织生长似乎受到非常精确的控制。这项研究的主要目的是开发新的数学工具来理解这种控制机制。从这个理论角度来看，一些关键问题将得到解决：与树干相比，哪些物理参数会产生攀爬藤蔓的不同行为？大自然如何控制不同物种植物的叶子或花朵的形状和大小？该项目将研究模拟生物组织生长的各种偏微分方程（PDE）。这些方程描述了生长诱导化学物质的扩散和吸附、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，以及如何通过改变影响生长的物理参数来修改这些形状。该项目将重点研究由偏微分方程组描述的各种组织生长模型。这些代表组织内形态发生素的扩散和吸收、体积生长和弹性变形。将研究解决方案的存在性、唯一性和定性属性，也在各向异性设置和分层域中进行研究。获得的结果将扩展当前关于具有移动边界的领域的进化问题理论。该研究还将解决新型平稳问题，有点像特征值问题，但在集值框架中。对于各种类别的分层域，首席研究员希望根据有限多个参数发现局部不变的“形态平稳”配置族。这些将产生丰富多样的新几何形状，将对这些形状进行分析和数值研究。