Statistical mechanics of frustrated assemblies and incompatible graphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929437304422400 |
|---|---|
| author | Ortiz-Tavárez, José M. Yang, Zhen Kotov, Nicholas Mao, Xiaoming |
| author_facet | Ortiz-Tavárez, José M. Yang, Zhen Kotov, Nicholas Mao, Xiaoming |
| contents | 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. Through numerical simulations, the theory reveals new characteristics of frustrated assemblies, including two distinct percolation transitions for structure and stress, a crossover between cumulative and non-cumulative frustration controlled by disorder, and a divergent length scale in their response. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistical mechanics of frustrated assemblies and incompatible graphs Ortiz-Tavárez, José M. Yang, Zhen Kotov, Nicholas Mao, Xiaoming Soft Condensed Matter Disordered Systems and Neural Networks Materials Science Statistical Mechanics Mathematical Physics 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. Through numerical simulations, the theory reveals new characteristics of frustrated assemblies, including two distinct percolation transitions for structure and stress, a crossover between cumulative and non-cumulative frustration controlled by disorder, and a divergent length scale in their response. |
| title | Statistical mechanics of frustrated assemblies and incompatible graphs |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Materials Science Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2407.18210 |