TY - JOUR
T1 - Frictional Rigidity Percolation
T2 - A New Universality Class and Its Superuniversal Connections through Minimal Rigidity Proliferation
AU - Liu, Kuang
AU - Henkes, S.
AU - Schwarz, J. M.
N1 - Publisher Copyright:
© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the «https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2019/4/10
Y1 - 2019/4/10
N2 - We introduce two new complementary concepts, frictional rigidity percolation and minimal rigidity proliferation, to help identify the nature of the frictional jamming transition as well as significantly broaden the scope of rigidity percolation. To probe frictional rigidity percolation, we construct rigid clusters using a (3,3) pebble game for sliding and frictional contacts first on a honeycomb lattice with next-nearest neighbors, and second on a hierarchical lattice. For both lattices, we find a continuous rigidity transition. Our numerically obtained transition exponents for frictional rigidity percolation on the honeycomb lattice are distinct from those of central-force rigidity percolation. We propose that localized motifs, such as hinges connecting rigid clusters that are allowed only with friction, could give rise to this new frictional universality class. And yet, the distinction between the exponents characterizing the spanning rigid cluster for frictional and central-force rigidity percolation is small, motivating us to look for a limit in which they are identical, i.e., a search for mechanisms of superuniversality. To achieve this goal, we construct a minimally rigid cluster generating algorithm invoking generalized Henneberg moves, dubbed minimal rigidity proliferation. For both frictional and central-force rigidity percolation, these clusters appear to be in the same universality class as connectivity percolation, suggesting superuniversality between all three transitions for such minimally rigid clusters. These combined results allow us, for the first time in rigidity percolation, to directly compare two universality classes on the same lattice and to highlight unifying and distinguishing concepts of rigidity transitions in disordered systems.
AB - We introduce two new complementary concepts, frictional rigidity percolation and minimal rigidity proliferation, to help identify the nature of the frictional jamming transition as well as significantly broaden the scope of rigidity percolation. To probe frictional rigidity percolation, we construct rigid clusters using a (3,3) pebble game for sliding and frictional contacts first on a honeycomb lattice with next-nearest neighbors, and second on a hierarchical lattice. For both lattices, we find a continuous rigidity transition. Our numerically obtained transition exponents for frictional rigidity percolation on the honeycomb lattice are distinct from those of central-force rigidity percolation. We propose that localized motifs, such as hinges connecting rigid clusters that are allowed only with friction, could give rise to this new frictional universality class. And yet, the distinction between the exponents characterizing the spanning rigid cluster for frictional and central-force rigidity percolation is small, motivating us to look for a limit in which they are identical, i.e., a search for mechanisms of superuniversality. To achieve this goal, we construct a minimally rigid cluster generating algorithm invoking generalized Henneberg moves, dubbed minimal rigidity proliferation. For both frictional and central-force rigidity percolation, these clusters appear to be in the same universality class as connectivity percolation, suggesting superuniversality between all three transitions for such minimally rigid clusters. These combined results allow us, for the first time in rigidity percolation, to directly compare two universality classes on the same lattice and to highlight unifying and distinguishing concepts of rigidity transitions in disordered systems.
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U2 - 10.1103/PhysRevX.9.021006
DO - 10.1103/PhysRevX.9.021006
M3 - Article
AN - SCOPUS:85073650887
SN - 2160-3308
VL - 9
JO - Physical Review X
JF - Physical Review X
IS - 2
M1 - 021006
ER -