Work

Decoupling Conjugate Fields in Diffusion Systems via Field‐Line Coordinate Transformations

Year: 2026

Type: article

Abstract: In diffusive systems, conjugate fields such as scalar potentials and fluxes are intrinsically coupled through constitutive relations, fundamentally limiting their independent control. Here, we introduce a conjugate‐field decoupling mechanism based on field‐line coordinate transformations, which enables independent manipulation of these quantities within a single physical domain. By performing transformations along equipotential lines and current lines, we show that the geometric mapping of conjugate fields can be selectively preserved or reshaped, thereby lifting their intrinsic coupling constraint. As a result, we realize electric metamaterials in which current and voltage exhibit distinct functionalities, including cloaking, concentration, and rotation. Moreover, a symmetry‐protected functionality exchange emerges under rotated boundary conditions, revealing an underlying geometric duality between conjugate fields. Our work establishes a general paradigm for decoupling conjugate fields in diffusion systems and opens new avenues for multifunctional control in thermal, electrical, and mass transport phenomena.

Source: Small Structures

DOI: 10.1002/sstr.70642