Evidence for a Diverging Length Scale in Granular packings at the Onset of Unjamming

Bulbul Chakraborty, Brandeis University, DMR 0905880

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Dry granular materials such as sand, rice grains, and even marbles can form a jammed, solid when confined by pressure or under their own weight under gravity. These solids has are held together by external forces (pressure or gravity) since there is no attraction between them, and they fall apart (unjam) in interesting ways when the external forces are removed. There are large fluctuations in stress as the overall pressure is reduced towards zero, a phenomenon that is reminiscent of critical points, for example, the gas-liquid critical point. A hallmark of critical points is that there is dominant length scale that controls the spatial and temporal fluctuations, and this length scale can be measured in standard scattering experiments, which measure 2-point correlations. Theory and simulations have provided evidence for a length scale that increases as a system approaches unjamming. It has, however, been very difficult to (a) establish that a lengthscale diverges as grains unjam, and (b) identify a purely static correlation function that picks up this length scale.

Recent work by Mailman and Chakraborty, demonstrates that a static correlation function, which probes sensitivity to boundary conditions, exhibits a diverging correlation length as a granular packing is decompressed. This length scale is the one that had been seen in earlier simulations, and had been argued to exist from theory. These results demonstrate the existence of a diverging length scale at the unjamming transition, and and suggests that stress heterogeneities in granular packings form a mosaic characterized by this length scale.

IMAGES: (Anticlockwise from bottom right) Illustration of the construction of the correlation function. Inside a sub-region of size ρ, contact force variables fluctuate satisfying a frozen mechanically stable boundary, and a correlation function (<<C(ρ))>>) is defined as an overlap between old and new force networks. Variation of correlation function with pressure. Inset illustrates slower decays for lower pressures. Main plot illustrates that one dominant length scale, <ρ0>g, controls the behavior of (<<C(ρ))>>) by establishing a scaling form . Diverging Length Scale. Main plot shows the increase of ρ0 with decreasing pressure for many realizations. Inset shows application of finite size scaling techniques to establish divergence of the average length, <ρ0>.

School on Glass Formers and Glasses

Bulbul Chakraborty, Brandeis University, DMR 0905880

04/20/23

Bulbul Chakraborty was a lecturer at the School on Glass Formers and Glasses that was held in Bangalore in January, 2010. The purpose of this school was to provide an opportunity for students to learn about the progress in the area of glassy systems, and the school preceded the KITP program on the Physics of Glasses. Because the school was in India, it provided (a) an opportunity for Indian students to interact with scientists from USA and Europe, and (b) it provided US students with a great opportunity the interact with the Indian science community.Both Mitch Mailman and Dapeng Bi, students working on this NSF-funded project were participants at this school.IMAGES: (Clockwise from Top Left) Bulbul Chakraborty lecturing at the school, School Group Photoraph, Mitch Mailman (first row, right) attending a lecture, School Social Event.