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From plasticity to a renormalization group

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Ball, R. C. and Blumenfeld, R.. (2003) From plasticity to a renormalization group. Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical and Engineering Sciences, Vol.361 (No.1805). pp. 731-738. ISSN 1364-503X

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Official URL: http://dx.doi.org/10.1098/rsta.2002.1161

Abstract

The marginally rigid State is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. The coordination number is identified as a discriminating characteristic, and for rough-surfaced particles we show that the low values predicted are indeed approached ill 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 generalized 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 scaling up the equations, which leads us to attempt a renormalization-group calculation. Finally, we discuss how perturbations propagate through such systems, suggesting a distinction between the behaviour of rough and smooth grains.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Granular materials, Plasticity, Renormalization group
Journal or Publication Title:	Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical and Engineering Sciences
Publisher:	Royal Society of London
ISSN:	1364-503X
Date:	15 April 2003
Volume:	Vol.361
Number:	No.1805
Number of Pages:	8
Page Range:	pp. 731-738
Identification Number:	10.1098/rsta.2002.1161
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/L5975 (EPSRC)
Title of Event:	Meeting on Slow Dynamics in Soft Matter
Location of Event:	Royal Society, London, England
Date(s) of Event:	September 25-26, 2002
References:	[1] Smid J and Novosad J, in Proc Powtech. Conf. 1981, Ind. Chem. Eng. Symp. 63, D3V 1-12 (1981). Their data are also reproduced in [3] below. [2] Edwards SF and Oakshott RB, Physica D 38, 88-93 (1989). [3] Wittmer JP, Claudin P, Cates ME and Bouchaud J-P, Nature 382, 336-8 (1996). [4] RC Ball in: Structure and dynamics of materials in the mesoscopic domain, eds. M Lal, RA Mashelkar, BD Kulkani and VM Naik (IC Press, 1999). [5] R C Ball and R Blumenfeld, Phys. Rev. Lett. 88, 115505 (2002). [6] SF Edwards and D Grinev, Phys Rev Lett 82, 5397 (1999). [7] Ball RC, Grinev DV, Physica A 292, 167-174 (2001). [8] Wittmer JP, Claudin P, and Cates ME, J Physique I, 7, 39-80 (1997). [9] Tkachenko & Witten Phys Rev E 62, 2510 (2000). [10] R Farr, PhD Thesis, Cambridge University (1998).
URI:	http://wrap.warwick.ac.uk/id/eprint/9793