2025-04-07 ミシガン大学
The intricate geometries of shells made by single-celled plankton called coccolithophores inspired University of Michigan researchers to understand how mismatched building blocks can yield complex behaviors and desirable material properties. Image credit: F. M. Monteiro et al. Sci. Adv. (2016) DOI: 10.1126/sciadv.1501822 (Used under a CC BY-SA 4.0 license)
＜関連情報＞
- https://news.umich.edu/frustration-incorporated-revealing-a-natural-strategy-for-making-superior-materials/
- https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.147401
フラストレート集合体と相容れないグラフの統計力学 Statistical Mechanics of Frustrated Assemblies and Incompatible Graphs
José M. Ortiz-Tavárez, Zhen Yang, Nicholas Kotov, and Xiaoming Mao
Physical Review Letters Published 7 April, 2025
DOI: https://doi.org/10.1103/PhysRevLett.134.147401
Abstract
Geometrically frustrated assemblies where building blocks misfit have been shown to generate intriguing phenomena from self-limited growth, fiber formation, to structural complexity. We introduce a graph theory formulation of geometrically frustrated assemblies, capturing frustrated interactions through the concept of incompatible flows, providing a direct link between structural connectivity and frustration. This theory offers a minimal yet comprehensive framework for the fundamental statistical mechanics of frustrated assemblies, and connects it to tensor gauge theory formulations of amorphous solids. Through numerical simulations, the theory reveals new characteristics of frustrated assemblies, including two distinct percolation transitions for structure and incompatible flows, a crossover between cumulative and noncumulative frustration controlled by disorder, and a divergent length scale in their response.
