Penrose tilings as jammed solids.
Penrose tilings form lattices, exhibiting fivefold symmetry and isotropic elasticity, with inhomogeneous coordination much like that of the force networks in jammed systems. Under periodic boundary conditions, their average coordination is exactly four. We study the elastic and vibrational properties of rational approximants to these lattices as a function of unit-cell size N(S) and find that they have of order sqrt[N(S)] zero modes and states of self-stress and yet all their elastic moduli vanish. In their generic form, obtained by randomizing site positions, their elastic and vibrational properties are similar to those of particulate systems at jamming with a nonzero bulk modulus, vanishing shear modulus, and a flat density of states.
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Olaf
O
Stenull
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
T C
TC
Lubensky
D003460:Crystallization; D004548:Elasticity; D008962:Models, Theoretical