Mathematically inspired structure design in nanoscale thermal transport

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.