Stenull and Lubensky Reply.

for the randomized rational approximates to a fivefold Penrose tiling were carried out on samples that are of order of the typical sizes treated in numerical studies of jammed systems with ε 1⁄4 10−2, ε being the magnitude of the maximum random deviation of the x and y components of the site coordinates. It did not occur to us to look either at larger systems or at larger random displacements, the latter because we wanted to avoid phantom bond crossings. We were, therefore, somewhat surprised to see the preceding Comment by Moukarzel and Naumis [1] (MN) providing evidence that the bulk modulus eventually turns around and tends to zero with increasing sample NS size and/or amplitude ε of random displacements. We carried out further simulations to provide either further support for MN’s results or evidence that they might be wrong. These simulations were done for ε 1⁄4 10−4, 10−3, 10−2, 0.1, 0.5, and for rational approximates ranging from 1=1 to 55=34. Our new results agree qualitatively with MN’s in that the bulk modulus we calculate first rises with NS and/or ε and then eventually falls off as these variables become large. Our data collapses well on a single curve when B is plotted as a function of εNS, see Fig. 1. It does not collapse so well when B is plotted as a function of ε2N S as MN’s does. We do not have an explanation for this discrepancy. Though these new results invalidate our conclusion that the randomized Penrose tilings and jamming systems share common behavior for all sample sizes, including ones with NS → ∞, we stand by our assertion that randomized Penrose tilings are useful model systems for jammed matter for the range of parameters we considered.