A real-space renormalization group for jamming

Abstract

Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction $\varphi$, defined as the ratio of particle volume to system volume, is increased past a critical value ${\varphi }_c$, 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 $\varphi ={\varphi }_c$, 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 ${\varphi }_c$ and gives estimates of critical exponents in two and three dimensions.

Submitted to Granular Matter: Special Issue In Memoriam of Bob Behringer

References in corpus (8)

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• Glassy dynamics of kinetically constrained models
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