Comment on "Spatial structure of states of self stress in jammed systems" by D. M. Sussman, C. P. Goodrich, and A. J. Liu, Soft Matter, 2016, 12, 3982.
basic_science · Level V
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- Also identified by DOI 10.1039/c6sm01111j.
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Abstract
Sussman, Goodrich and Liu recently introduced a novel definition of states of self stress in packing-derived networks, and reported that the lengthscale that characterizes these states depends on the network connectivity z and spatial dimension đ as (z - 2đ)<sup>-0.8</sup> in two dimensions, and as (z - 2đ)<sup>-0.6</sup> in three dimensions. Here we derive an explicit expression for these particular states of self stress, and show that they are equivalent to the force response to a local dipolar force in random networks of relaxed Hookean springs, previously shown to be characterized by the lengthscale l<sub>c</sub> ∼ (z - 2đ)<sup>-1/2</sup>. We conclude that the systems studied by Sussman et al. are insufficient in size to observe the correct scaling with connectivity of the characteristic lengthscale of states of self stress.