Critical Scaling of Bagnold Rheology at the Jamming Transition of Frictionless Two Dimensional Disks

We carry out constant volume simulations of steady-state, shear driven, rheology in a simple model of bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We carry out a detailed critical scaling analysis of our resulting data for pressure $p$ and shear stress $\sigma$, in order to determine the critical exponent $\beta$ that describes the algebraic divergence of the Bagnold transport coefficients, as the jamming transition is approached from below. We show that it is necessary, for the strain rates considered in this work, to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data. Our resulting value $\beta\approx 5.0\pm 0.4$ is clearly larger than the theoretical prediction by Otsuki and Hayakawa, and is consistent with earlier numerical results by Peyneau and Roux, and recent theoretical predictions by DeGiuli et al. We have also considered the macroscopic friction $\mu\equiv \sigma/p$ and similarly find results consistent with Peyneau and Roux, and with DeGiuli et al. Our results confirm that the shear driven jamming transition in Bagnoldian systems is well described by a critical scaling theory (as was found previously for Newtonian systems), and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.Comment: 20 pages, 21 figures; revised manuscript according to published versio

Beyond linear elasticity: Jammed solids at finite shear strain and rate

The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point -- suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear startup experiments in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network. Our findings indicate that the mechanical response of jammed solids are generically nonlinear and rate-dependent on experimentally accessible strain and time scales.Comment: 10 pages, 9 figure

Neurofilament light chain in cerebrospinal fluid and prediction of disease activity in clinically isolated syndrome and relapsing-remitting multiple sclerosis

BACKGROUND AND PURPOSE: Improved biomarkers are needed to facilitate clinical decision-making and as surrogate endpoints in clinical trials in multiple sclerosis (MS). We assessed whether neurodegenerative and neuroinflammatory markers in cerebrospinal fluid (CSF) at initial sampling could predict disease activity during 2 years of follow-up in patients with clinically isolated syndrome (CIS) and relapsing–remitting MS. METHODS: Using multiplex bead array and enzyme-linked immunosorbent assay, CXCL1, CXCL8, CXCL10, CXCL13, CCL20, CCL22, neurofilament light chain (NFL), neurofilament heavy chain, glial fibrillary acidic protein, chitinase-3-like-1, matrix metalloproteinase-9 and osteopontin were analysed in CSF from 41 patients with CIS or relapsing–remitting MS and 22 healthy controls. Disease activity (relapses, magnetic resonance imaging activity or disability worsening) in patients was recorded during 2 years of follow-up in this prospective longitudinal cohort study. RESULTS: In a logistic regression analysis model, NFL in CSF at baseline emerged as the best predictive marker, correctly classifying 93% of patients who showed evidence of disease activity during 2 years of follow-up and 67% of patients who did not, with an overall proportion of 85% (33 of 39 patients) correctly classified. Combining NFL with either neurofilament heavy chain or osteopontin resulted in 87% overall correctly classified patients, whereas combining NFL with a chemokine did not improve results. CONCLUSIONS: This study demonstrates the potential prognostic value of NFL in baseline CSF in CIS and relapsing–remitting MS and supports its use as a predictive biomarker of disease activity

Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming

In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials1. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards’ original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. D.F. acknowledges support by EPSRC Programme Grant EP/I001352/1 and EPSRC grant EP/I000844/1. K.R. and B.C. acknowledge the support of NSF-DMR 1409093 and the W. M. Keck Foundation

On the apparent yield stress in non-Brownian magnetorheological fluids

We use simulations to probe the flow properties of dense two-dimensional magnetorheological fluids. Prior results from both experiments and simulations report that the shear stress σ scales with strain rate as σ ∼ 1-Δ, with values of the exponent ranging between 2/3 &lt; Δ ≤ 1. However it remains unclear what properties of the system select the value of Δ, and in particular under what conditions the system displays a yield stress (Δ = 1). To address these questions, we perform simulations of a minimalistic model system in which particles interact via long ranged magnetic dipole forces, finite ranged elastic repulsion, and viscous damping. We find a surprising dependence of the apparent exponent Δ on the form of the viscous force law. For experimentally relevant values of the volume fraction φ and the dimensionless Mason number Mn (which quantifies the competition between viscous and magnetic stresses), models using a Stokes-like drag force show Δ ≈ 0.75 and no apparent yield stress. When dissipation occurs at the contact, however, a clear yield stress plateau is evident in the steady state flow curves. In either case, increasing φ towards the jamming transition suffices to induce a yield stress. We relate these qualitatively distinct flow curves to clustering mechanisms at the particle scale. For Stokes-like drag, the system builds up anisotropic, chain-like clusters as Mn tends to zero (vanishing strain rate and/or high field strength). For contact damping, by contrast, there is a second clustering mechanism due to inelastic collisions.</p

Nonlocal elasticity near jamming in frictionless soft spheres

We use simulations of frictionless soft sphere packings to identify novel constitutive relations for linear elasticity near the jamming transition. By forcing packings at varying wavelengths, we directly access their transverse and longitudinal compliances. These are found to be wavelength dependent, in violation of conventional (local) linear elasticity. Crossovers in the compliances select characteristic length scales, which signify the appearance of nonlocal effects. Two of these length scales diverge as the pressure vanishes, indicating that critical effects near jamming control the breakdown of local elasticity. We expect these nonlocal constitutive relations to be applicable to a wide range of weakly jammed solids, including emulsions, foams, and granulates.Engineering Thermodynamic

Beyond linear elasticity: Jammed solids at finite shear strain and rate

The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point-suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear start-up tests in athermal soft sphere packings, the canonical model for jamming. By systematically varying the strain amplitude, strain rate, distance to jamming, and system size, we identify characteristic strain and time scales that quantify how and when the window of linear elasticity closes, and relate these scales to changes in the microscopic contact network.Accepted Author ManuscriptEngineering Thermodynamic