Feedback-induced phase transitions in active heterogeneous conductors

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Classical laws like Ohm's and Darcy's assume linear relationships between current and resistance.
• Active conducting media exhibit dynamic feedback where resistance and flow influence each other over time.
• Understanding these feedback mechanisms is crucial for explaining natural patterning and engineering novel architectures.

Purpose of the Study:

• To develop a minimal model for active conducting media with feedback coupling.
• To investigate the effects of flow-seeking and flow-avoiding behaviors on system heterogeneity.
• To provide a theoretical framework for pattern formation in active media.

Main Methods:

• Numerical simulations of a minimal feedback model.
• Continuum mean field theory application.
• Analysis of local and nonlocal feedback rules for matter addition/removal.

Main Results:

• Flow-avoiding feedback induces tunneling or channel-building phase separation, leading to heterogeneity.
• Flow-seeking feedback results in immuring or wall-building phase separation.
• The model demonstrates how simple feedback rules generate complex spatial patterns.

Conclusions:

• The study offers a qualitative explanation for patterning in natural active conducting media.
• The findings suggest methods for designing complex architectures in engineered systems using simple rules.
• Feedback mechanisms are key to understanding and controlling the evolution of active media.