Diffusionics: Basic Theory and Theoretical Framework

Abstract

Diffusionics, distinct from traditional physical laws, focuses on designing material parameters to actively control diffusion fields. The introduction of transformation theory provides a novel method to achieve active control of diffusion transport, leading to the design of devices with unique functions such as cloaks, concentrators, and rotators. However, materials corresponding to the parameters designed by transformation theory are challenging to find in nature. Therefore, the spatial arrangement of one or multiple materials to effectively achieve the desired parameters has become an alternative approach, indirectly spurring the development of metamaterials. This article reviews the fundamental theories and theoretical framework in diffusion science. We first introduce the basic concept of transformation theory, followed by a review of alternative theories such as effective medium theory and scattering cancellation theory. To study topological phenomena in diffusion systems and space-time modulated systems, the foundations of quantum mechanics, namely matrix mechanics and wave mechanics, are employed. Lastly, the article summarizes some challenges in diffusion science theory, which may be addressed by other methods in the future, such as transformation field methods and machine learning approaches.