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From plasticity to a normalisation group
 (undated)

RC Ball, (Department of Physics, University of Warwick) R.C.Ball@warwick.ac.uk
R Blumenfeld, (Cavendish Laboratory, University of Cambridge)

The Marginally Rigid State is a candidate paradigm for what makes granular material
a state of matter distinct from both liquid and solid. Coordination number is
identified as a discriminating characteristic, and for roughsurfaced particles we show
that the low values predicted are indeed approached in simple two dimensional
experiments. We show calculations of the stress transmission suggesting that this is
governed by local linear equations of constraint between the stress components.
These constraints can in turn be related to the generalised forces conjugate to the
motion of grains rolling over each other. The lack of a spatially coherent way of
imposing a sign convention on these motions is a problem for upscaling the
equations, which leads us to attempt a renormalisation group calculation. Finally we
discuss how perturba tions propagate through such systems, suggesting a distinction
between the behaviour of rough and of smooth grains.

