Mathematically inspired structure design has emerged as a powerful approach for tailoring material properties, especially in nanoscale thermal transport, with promising applications both within this field and beyond. By employing mathematical principles, based on number theory, such as periodicity and quasi-periodic organizations, researchers have developed advanced structures with unique thermal behaviours. Although periodic phononic crystals have been extensively explored, various structural design methods based on alternative mathematical sequences have gained attention in recent years. This review provides an in-depth overview of these mathematical frameworks, focusing on nanoscale thermal transport. We examine key mathematical sequences, their foundational principles, and analyze the influence of thermal behavior, highlighting recent advancements in this field. Looking ahead, further exploration of mathematical sequences offers significant potential for the development of next-generation materials with tailored, multi-functional properties suited to diverse technological applications.

中文翻译：

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纳米级热传输中的数学启发结构设计


受数学启发的结构设计已成为定制材料特性的强大方法，尤其是在纳米级热传输中，在该领域内外都有广阔的应用前景。通过采用基于数论的数学原理，例如周期性和准周期组织，研究人员开发了具有独特热行为的先进结构。尽管周期性声子晶体已被广泛探索，但近年来基于替代数学序列的各种结构设计方法也受到了关注。本综述对这些数学框架进行了深入概述，重点介绍了纳米级热传输。我们研究了关键的数学序列及其基本原理，并分析了热行为的影响，重点介绍了该领域的最新进展。展望未来，对数学序列的进一步探索为开发具有适合各种技术应用的定制多功能特性的下一代材料提供了巨大的潜力。