From Frustrated Assemblies to Functional Complexity: A Statistical Mechanics of Structure and Property

Many materials from nature derive their extraordinary properties not from perfection, but from structured complexity—hierarchical architectures, controlled combination of order and disorder, and collective constraints that shape how components assemble, organize, and ultimately respond. In this talk, I will present a unified framework that connects geometrically frustrated assembly, network structures, and material functionality. Building on a graph-theoretic formulation of incompatible interactions, we introduce a statistical mechanics that links structural connectivity, incompatible flows, and emergent response, revealing distinct percolation transitions, disorder-controlled crossovers between cumulative and non-cumulative frustration, and anomalous scalings. I will then show how these concepts generalize beyond assembly to property engineering in nanoscale and mesoscale materials, where complexity itself becomes a design parameter. The framework provides microscopic principles for programming mechanics, transport, wave propagation, and multifunctionality in networks assembled from imperfect components—suggesting new routes toward scalable, biomimetic, and highly adaptive materials.