Stenull Olaf, Lubensky T C
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev Lett. 2014 Oct 10;113(15):158301. doi: 10.1103/PhysRevLett.113.158301. Epub 2014 Oct 6.
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.
彭罗斯镶嵌形成晶格，展现出五重对称性和各向同性弹性，其不均匀配位与堵塞系统中的力网络非常相似。在周期性边界条件下，它们的平均配位数恰好为4。我们研究了这些晶格的有理近似的弹性和振动特性作为单胞尺寸N(S)的函数，发现它们有量级为sqrt[N(S)]的零模和自应力状态，但它们所有的弹性模量都为零。在通过随机化位点位置获得的一般形式中，它们的弹性和振动特性类似于堵塞时颗粒系统的特性，具有非零的体积模量、消失的剪切模量和扁平的态密度。
