Dynamics on space-filling shapes

空间填充形状的动力学

• 批准号: DP210100129
• 负责人: Prof Nalini Joshi
• 金额: $ 35.3万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210100129
• 关键词: Dynamics; space; filling; shapes

Modern science derives its power from mathematical models and tools that enable us to predict their behaviours. The project aims to construct new models given by dynamical systems that move consistently from one tile to another in a lattice of higher-dimensional shapes called polytopes. The construction is expected to lead to new functions with properties that will provide extensions of current models of growth processes. The intended outcomes of the project include predictive tools that describe nonlinear special functions and information about their symmetry reductions. This should provide significant benefits, such as new mathematical knowledge, innovative techniques, and enhanced scientific capacity in Australia.

现代科学的力量来自数学模型和工具，使我们能够预测它们的行为。该项目旨在构建由动力系统给出的新模型，这些动力系统在称为多面体的高维形状的晶格中从一个瓦片一致地移动到另一个瓦片。该结构预计将导致新的功能与属性，将提供扩展目前的增长过程模型。该项目的预期成果包括描述非线性特殊函数及其对称性约简信息的预测工具。这将带来巨大的好处，如新的数学知识，创新技术和提高澳大利亚的科学能力。