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arXiv · 1903.02405

A real-space renormalization group for jamming

Abram H. Clark
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Abstract

Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction $ϕ$, defined as the ratio of particle volume to system volume, is increased past a critical value $ϕ_c$, a liquid-solid phase transition occurs, and grains are no longer able to rearrange. Previous studies have shown evidence of spatial correlations that diverge near $ϕ= ϕ_c$, but there has been no explicit spatial renormalization group (RG) scheme that has captured this transition. Here, I present a candidate for such a scheme, using a block-spin-like transformation of a randomly vacated lattice of grains. I define a real-space RG transformation based on local mechanical stability. This model displays a critical packing fraction $ϕ_c$ and gives estimates of critical exponents in two and three dimensions.

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Abram H. Clark. 2019-09-09. A real-space renormalization group for jamming. https://doi.org/10.1007/s10035-019-0937-z

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