Stressed Backbone and Elasticity of Random Central-Force Systems

Abstract

We use a new algorithm to find the stress-carrying backbone of "generic" site-diluted triangular lattices of up to 10 6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice (see Fig. 1). The percolation threshold is pc = 0.6975±0.0003, the correlation length exponent ν = 1.16 ± 0.03 and the fractal dimension of the backbone D b = 1.78 ± 0.02. The number of "critical bonds" (if you remove them rigidity is lost) on the backbone scales as L x , with x = 0.85 ± 0.05. The Young's modulus is also calculated.

Understanding the α‐helix to coil transition in polypeptides using network rigidity: Predicting heat and cold denaturation in mixed solvent conditions

“…39,40 Follow-up investigations have suggested that folding pathways are related to network rigidity, 41 and the folding transition is related to a rigidity transition. 42 These works have been made possible because of recent developments in graph algorithms [43][44][45][46][47][48] that calculate network rigidity.…”

Hierarchical models of rigidity percolation

“…A decisive theoretical progress was made in the 90's for generic [37] 2D rigidity, with the introduction of combinatorial algorithms [6,7], based on Laman's theorem [8]. These new algorithms allow for the study of much larger samples than before, as well as more precise estimates around the critical point [9].…”

Rigid Cluster Decomposition Reveals Criticality in Frictional Jamming

“…Frictional jamming is more puzzling: The hysteresis observed in the stress-strain rate curves of stresscontrolled flow simulations [5][6][7][8] and experiments [9] has lead to an interpretation as a first-order transition. Yet, signs of second-order criticality appear when treating the fraction of contacts at the Coulomb threshold as an additional parameter [10][11][12].To elucidate the frictional jamming transition from a microscopic viewpoint, we extend concepts and tools from rigidity percolation, i.e., the onset of mechanical rigidity in disordered spring networks [13][14][15][16], to frictional packings. The former is driven by the emergence of a system-spanning rigid cluster that can be mapped out (in 2d) using the pebble game [17], an improved constraint counting method that goes beyond meanfield by identifying redundant constraints.…”

“…To elucidate the frictional jamming transition from a microscopic viewpoint, we extend concepts and tools from rigidity percolation, i.e., the onset of mechanical rigidity in disordered spring networks [13][14][15][16], to frictional packings. The former is driven by the emergence of a system-spanning rigid cluster that can be mapped out (in 2d) using the pebble game [17], an improved constraint counting method that goes beyond meanfield by identifying redundant constraints.…”