Dynamic-to-Structural Phase Transitions in Heterogeneous Media via Dual Balancing Fields

Authors: Thai, Hau Dinh Affiliation: Independent Researcher , Description: This work introduces a unified operator framework for dynamic-to-structural phase transitions in heterogeneous media. A canonical dual-balancing operator is formulated in which each dynamic drive mechanism is paired with a counter-regulating mechanism under modulation control. A Lyapunov-based convergence theorem establishes structural stabilization toward equilibria and stable bounded invariant manifolds. Representative orbital and resonance examples are provided. Version 1.0 presents the foundational formulation intended for further theoretical development. ,