Fluctuations and correlations during the shear flow of elastic particles near the jamming transition Claus Heussinger, Pinaki Chaudhuri and Jean-Louis Barrat ∗ November 1, 2018 Abstract We present a numerical study of the flow of an as- sembly of frictionless, soft discs at zero tempera- ture, in the vicinity of and slightly above the jam- ming density. We find that some of the flow prop- erties, such as the fluctuations in the number of contacts or the shear modulus, display a critical like behaviour that is governed by the proximity to the jamming point. Dynamical correlations dur- ing a quasistatic deformation, however, are non critical and dominated by system size. At finite strain rates, these dynamical correlations acquire a finite, strain-rate dependent amplitude, that de- creases when approaching the jamming point from above. Manuscript submitted to the themed Issue on granular and jammed materials of Soft Matter as changing the inclination angle of the support) can lead to large scale structural rearrangements (“avalanches”) or even to the complete fluidization of the material. A few years ago, Liu and Nagel 1 have suggested a “phase-diagram” for this type of solid-liquid transition (“jamming”). At zero tem- perature the axes relate to the ways an unjamming transition can be triggered, either by increasing the external driving (e.g. shear stress) or by decreasing the density of the material. The present study will probe the vicinity of this ”unjamming line” using quasistatic and finite strain rate simulations of a model granular system. If one applies a shear stress, which is small and below a certain threshold (“yield-stress”), the ma- terial will respond as an elastic solid. Increasing the stress above the yield-stress, the particles will un- jam and start to flow. This flow behavior is called “plastic flow” as the material will not revert to its original shape when the stress is removed. In the following we will assume that the sys- tem can flow at arbitrary small strain-rates without showing flow-localization. That this is possible is by no means guaranteed, as in some instances co- existence of flowing and jammed states is observed . 2 We have not observed such a persistent strain localization in the simulations that are presented here. Plastic flow is observed in a large number of glassy materials, that are a priori very different from the athermal granular systems close to point J (see below) studied in this paper. However, all ma- terials display a rather universal behavior, that was illustrated already in early studies on the plastic- flow of metallic glasses. 3,4 These studies have given indications that in the flowing phase the main plas- tic activity is spatially localized to so called shear transformation zones. 5,6 These zones are non per- 1 The properties of granular materials, in particu- lar sand, are a constant source of fascination for children and adults alike, and are intrinsically re- lated to the ability of such systems to exist in either solid or fluid states, under very similar conditions. For the scientist this fascination may arise through the apparent contradiction between the rigidity of the individual grains and the fragility of the as- sembly as a whole. This means that, for exam- ple, small changes in the loading conditions (such 1 Introduction and back- ground arXiv:1001.0658v2 [cond-mat.mtrl-sci] 23 Jun 2010 ∗ Universit´e Lyon 1, Laboratoire de Physique de la Mati`ere Condens´ee et Nanostructures, CNRS, UMR 5586 Domaine Scientifique de la Doua F-69622 Villeurbanne Cedex, France