Controlling transient and coupled diffusion with pseudoconformal mapping.

Abstract

Diffusion in physical, chemical, and biological systems often occurs under transient conditions and involves coupling across multiple physical fields, challenging conventional control methods limited to steady-state, single-field settings. Here, we present a general geometric framework for regulating diffusion in time-dependent and multiphysics-coupled environments based on pseudoconformal mapping. This method preserves material isotropy and ensures smooth interface matching, enabling robust and flexible modulation of diffusion governed by Fick's second law and beyond. We apply this framework to radiative-conductive, advective-conductive, and thermoelectric systems, achieving precise spatial and temporal control of temperature, flux, and voltage distributions. The proposed strategy is validated through simulations and experiments, demonstrating its broad applicability and scalability. Our findings provide a geometry-driven paradigm to programmable diffusion control, with potential impact across thermal management, energy conversion, and biomedical transport systems.