Discovery Projects - Grant ID: DP210100129

充满空间的形状上的动态。现代科学的力量来自数学模型和工具，这些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提供的新模型，这些动力系统在称为多面体的高维形状网格中从一块瓷砖移动到另一块瓷砖。这一建设预计将带来新的功能，其性质将提供当前增长过程模型的扩展。该项目的预期成果包括描述非线性特殊函数的预测工具以及关于其对称性约化的信息。这应该会带来显著的好处，例如新的数学知识、创新的技术和增强澳大利亚的科学能力。

Dynamics on 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.