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Controlling transient and coupled diffusion with pseudoconformal mapping.

Gaole Dai1, Teng Qu2, Min Lei2

  • 1School of Physical Science and Technology, Nantong University, Nantong 226019, China.

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|August 7, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a geometric framework using pseudoconformal mapping to precisely control diffusion in complex, time-dependent systems. The method enables programmable diffusion across various physical fields, enhancing thermal management and energy conversion.

Keywords:
Fick’s lawspatiotemporal controlthermal metamaterialtransformation optics

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Area of Science:

  • Multiphysics transport phenomena
  • Applied geometry and topology
  • Computational modeling and simulation

Background:

  • Conventional diffusion control is limited to steady-state, single-field conditions.
  • Transient and coupled-field diffusion presents significant control challenges.
  • Existing methods struggle with complex material properties and dynamic environments.

Purpose of the Study:

  • To develop a general geometric framework for regulating diffusion in time-dependent and multiphysics-coupled systems.
  • To enable precise spatial and temporal control over diffusion processes.
  • To provide a geometry-driven approach for programmable diffusion.

Main Methods:

  • Utilized pseudoconformal mapping as a core geometric tool.
  • Preserved material isotropy and ensured smooth interface matching.
  • Applied the framework to radiative-conductive, advective-conductive, and thermoelectric systems.

Main Results:

  • Achieved precise spatial and temporal control of temperature, flux, and voltage distributions.
  • Demonstrated robust and flexible modulation of diffusion governed by Fick's second law and beyond.
  • Validated the framework's applicability and scalability through simulations and experiments.

Conclusions:

  • The proposed geometric framework offers a novel paradigm for programmable diffusion control.
  • Findings have potential impact across thermal management, energy conversion, and biomedical transport.
  • The method provides a scalable and versatile solution for complex diffusion challenges.