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.

现代科学从数学模型和工具中获得了力量，使我们能够预测其行为。该项目旨在构建由动态系统给出的新模型，这些模型在称为polytopes的高维形状的晶格中始终如一地从一个瓷砖转移到另一个瓷砖。预计该构建将带来新的功能，其特性将提供当前增长过程模型的扩展。该项目的预期结果包括描述非线性特殊功能的预测工具以及有关其对称性减少的信息。这应该提供重大的好处，例如新的数学知识，创新技术和澳大利亚增强的科学能力。