Evidences of conformal invariance in 2d rigidity percolation

The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid connected component, or cluster. As a continuous phase transition it exhibits a scale invariant critical point, at which the rigid clusters are random fractals. We show, using numerical analysis, that these clusters are also conformally invariant, and we use conformal field theory to predict the form of universal finite size effects. Furthermore, although connectivity and rigidity percolation are usually though to belong to different universality classes and thus be of fundamentally different natures, we provide evidence of unexpected similarities between the statistical properties of their random clusters at criticality. Our work opens a new research avenue through the application of the powerful 2D conformal field theory tools to understand the critical behavior of a wide range of physical and biological materials exhibiting such a mechanical transition

Microrheology to probe non-local effects in dense granular flows

A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. (Phys. Rev. Lett., 106 (2011) 108301): a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by (Phys. Rev. Lett., 111 (2013) 238301) and derived from a gradient expansion of the rheology $\mu[I]$. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed.Comment: 6 pages, 5 figure

Athermal analogue of sheared dense Brownian suspensions

The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming.Comment: 6 figures, 6 page

Multi-component colloidal gels:interplay between structure and mechanical proprieties

We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solidsComment: 9 Pages, 5 figure

Computing the linear viscoelastic properties of soft gels using an Optimally Windowed Chirp protocol

We use molecular dynamics simulations to investigate the linear viscoelastic response of a model three-dimensional particulate gel. The numerical simulations are combined with a novel test protocol (the optimally windowed chirp or OWCh), in which a continuous exponentially varying frequency sweep windowed by a tapered cosine function is applied. The mechanical response of the gel is then analyzed in the Fourier domain. We show that (i) OWCh leads to an accurate computation of the full frequency spectrum at a rate significantly faster than with the traditional discrete frequency sweeps, and with a reasonably high signal-to-noise ratio, and (ii) the bulk viscoelastic response of the microscopic model can be described in terms of a simple mesoscopic constitutive model. The simulated gel response is in fact well described by a mechanical model corresponding to a fractional Kelvin-Voigt model with a single Scott-Blair (or springpot) element and a spring in parallel. By varying the viscous damping and the particle mass used in the microscopic simulations over a wide range of values, we demonstrate the existence of a single master curve for the frequency dependence of the viscoelastic response of the gel that is fully predicted by the constitutive model. By developing a fast and robust protocol for evaluating the linear viscoelastic spectrum of these soft solids, we open the path toward novel multiscale insight into the rheological response for such complex materials

A non-local rheology for granular flows across yield conditions

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square-root of the distance to the yield point, on both sides of that point.Comment: 5 pages, 4 figure

Dynamical compressibility of dense granular shear flows

It has been conjectured by Bagnold [1] that an assembly of hard non-deformable spheres could behave as a compressible medium when slowly sheared, as the average density of such a system effectively depends on the confining pressure. Here we use discrete element simulations to show the existence of transverse and sagittal waves associated to this dynamical compressibility. For this purpose, we study the resonance of these waves in a linear Couette cell and compare the results with those predicted from a continuum local constitutive relation

Correlated rigidity percolation and colloidal gels

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation

Actin modulates shape and mechanics of tubular membranes

International audienceThe actin cytoskeleton shapes cells and also organizes internal membranous compartments. In particular, it interacts with membranes for intracellular transport of material in mammalian cells, yeast, or plant cells. Tubular membrane intermediates, pulled along microtubule tracks, are formed during this process and destabilize into vesicles. While the role of actin in tubule destabilization through scission is suggested, literature also provides examples of actin-mediated stabilization of membranous structures. To directly address this apparent contradiction, we mimic the geometry of tubular intermediates with preformed membrane tubes. The growth of an actin sleeve at the tube surface is monitored spatiotemporally. Depending on network cohesiveness, actin is able to entirely stabilize or locally maintain membrane tubes under pulling. On a single tube, thicker portions correlate with the presence of actin. These structures relax over several minutes and may provide enough time and curvature geometries for other proteins to act on tube stability

Non-local rheology in dense granular flows -- Revisiting the concept of fluidity

Granular materials belong to the class of amorphous athermal systems, like foams, emulsion or suspension they can resist shear like a solid, but flow like a liquid under a sufficiently large applied shear stress. They exhibit a dynamical phase transition between static and flowing states, as for phase transitions of thermodynamic systems, this rigidity transition exhibits a diverging length scales quantifying the degree of cooperatively. Several experiments have shown that the rheology of granular materials and emulsion is non-local, namely that the stress at a given location does not depend only on the shear rate at this location but also on the degree of mobility in the surrounding region. Several constitutive relations have recently been proposed and tested successfully against numerical and experimental results. Here we use discrete elements simulation of 2D shear flows to shed light on the dynamical mechanism underlying non-locality in dense granular flows