A new asymptotic toolbox for nonlinear discrete systems and particle chains

用于非线性离散系统和粒子链的新渐近工具箱

• 批准号: DP190101190
• 负责人: Dr Christopher Lustri
• 金额: $ 26.88万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-02-04 至 2023-09-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190101190
• 关键词: new; asymptotic; toolbox; nonlinear; discrete

This project aims to pioneer a mathematical toolbox of new asymptotic techniques for discrete systems driven by vanishingly small influences. The purpose of these techniques is to permit the asymptotic study of discrete problems in which significant effects originate due to subtle causes that are invisible to existing asymptotic methods. Discrete systems play a significant role in modern applied mathematics, and it is vital that mathematical tools be designed in order to explore their behaviour. The aim of this project is to open new pathways for resolving open scientific problems, providing benefits such as understanding the energy dissipation of particle chains and granular lattices contained in small-scale technological components.

该项目的目的是为新的渐近技术的数学工具箱开创了由消失的小影响驱动的离散系统的新渐近技术工具箱。这些技术的目的是允许对离散问题进行渐近研究，在这些问题中，由于现有渐近方法是看不见的微妙原因引起的显​​着影响。离散系统在现代应用数学中起着重要的作用，并且必须设计数学工具以探索其行为至关重要。该项目的目的是为解决开放的科学问题开放新的途径，提供了诸如了解小型技术组件中包含的粒子链和颗粒晶格的能量耗散。