Deciphering D’Alemberts Dream: New Tools for Uncovering Rules for Self-Organized Pattern Formation in Geomaterials
Techniques from Complex Networks are used to study the evolving topology and functional connectivity in various granular systems in both two and three dimensions. A generic process of self-organization in all samples is realized and is characterized by the co-evolutionary synergy between force chains and 3-cycles. Three-cycles provide force chains a twofold benefit: (i) they prop-up force chains in the way that a counterfort or buttress supports a wall, and (ii) they frustrate rolling at contacts which is a critical mechanism for buckling. All samples reflect an inherent structural hierarchy where cyclic (minimal cycles) and linear (force chains) motifs of various length scales serve as basic building blocks for self-organization.
KeywordsComplex network Minimal cycles Granular material Force chains Self-organization
We thank our collaborators for permission to include data from their simulations and experiment. This work was supported by US Army Research Office (W911NF-07-1-0370) and the Australian Research Council (DP0986876 and DP0772409). We also thank the Victorian Partnership for Advanced Computing for computing resources.
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