Aperiodic Workshop: Dynamics, Physics and Topology in Aperiodic Order

非周期研讨会：非周期顺序的动力学、物理和拓扑

• 批准号: EP/H017100/1
• 负责人: John Hunton
• 金额: $ 1.39万
• 依托单位: University of Leicester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH017100%2F1
• 关键词: Aperiodic; Workshop; Dynamics; Physics; Topology

The discovery of quasicrystals in the early 1980's overthrew long-established and cherished principles of crystallography -- that structural order in solid state physics should always mean translationally periodic order. It sparked scientific activities across a number of disciplines and revealed the need to rethink fundamental concepts of order and disorder. Moreover, it forged a novel and rich link between, on the one hand, classical topics in convex geometry and combinatorics -- the study of aperiodic tilings --, and solid state physics and material science on the other. A broader activity has subsequently developed with mathematical disciplines such as topological dynamics, algebraic topology and noncommutative geometry providing key tools and insights for the understanding of the mathematical physics of these materials. The general field of research has come to be known as aperiodic order. More recent research has found links between the mathematics of aperiodic order and other applied sciences, most notably biology and the structure of viruses.Though the field is somewhat under-represented in the UK, there are a number of UK based researchers who have contributed some of the strongest and most innovative advances to the field. These researchers and their groups have not always been well connected, working on initially disparate parts of the subject. The proposed workshop will take as emphasis the interaction of the dynamical, physical and topological aspects, together with an exploration of new links with the biological application of aperiodic patterns. The programme offers the best promise of building a larger UK research base which can continue to contribute at the highest level to the field, and will also attract the key researchers in the mathematics of aperiodic order to the UK.

在1980年代初期，准晶体发现了晶体学原则 - 固态物理学中的结构秩序应始终意味着翻译周期性的顺序。它引发了许多学科的科学活动，并揭示了有必要重新考虑秩序和混乱的基本概念。此外，它在一方面建立了一种新颖而丰富的联系，这是凸几何和组合学中的古典主题 - 对神经斜纹的研究，另一方面是对固态物理学和材料科学的研究。随后，更广泛的活动是通过数学学科（例如拓扑动力学，代数拓扑结构和非共同几何形状）开发的，这些几何形状提供了关键工具和见解，以理解这些材料的数学物理学。一般研究领域已被称为Aperiodic秩序。最新的研究发现，十位阶秩序的数学与其他应用科学（最著名的生物学和病毒结构）之间的联系。尽管该领域在英国的代表性不足，但许多英国的研究人员贡献了一些最强大，最具创新性的进步。这些研究人员及其小组并不总是良好的联系，最初是该主题的不同部分。拟议的研讨会将强调动力学，物理和拓扑方面的相互作用，以及对新链接的探索以及神经模式的生物应用。该计划提供了建立一个更大的英国研究基础的最佳希望，该研究基础可以继续为该领域做出最高水平的贡献，还将吸引主要的研究人员在Aperiodic Order的数学中进入英国。