Friction law and hysteresis in granular materials.

The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this phenomenon in simple granular materials. We show that velocity weakening, corresponding to a nonmonotonic behavior in the friction law, [Formula: see text], is present even if the dynamic and static microscopic friction coefficients are identical, but disappears for softer particles. We argue that this instability is induced by endogenous acoustic noise, which tends to make contacts slide, leading to faster flow and increased noise. We show that soft spots, or excitable regions in the materials, correspond to rolling contacts that are about to slide, whose density is described by a nontrivial exponent [Formula: see text] We build a microscopic theory for the nonmonotonicity of [Formula: see text], which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts [Formula: see text], and the sliding velocity, in terms of [Formula: see text] Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis rationalizes previously unexplained observations and makes experimentally testable predictions.

Patterns of selective serotonin reuptake inhibitor use and risk of falls and fractures in community-dwelling elderly people: the Three-City cohort.

In this population-based elderly cohort, participants using selective serotonin reuptake inhibitor (SSRI) antidepressants have an increased risk of falls and fractures notably when the treatment was continued over 4 years. Among the various SSRI types, citalopram only was at significant risk for falls and fluoxetine for fractures. INTRODUCTION: Increased risk of falls and fractures has been reported in elderly users of SSRIs. However, biases were insufficiently addressed notably temporality between exposure and outcome and confounding by residual depression. Our objective was to examine the associations between SSRIs and fall or fracture incidence focusing on their chronic use and different types of SSRIs. METHODS: The population-based cohort included participants aged 65 years and above, who had not fallen before inclusion (n = 6599) or were free of recent fracture (n = 6823) and were followed up twice over 4 years. New fall and fracture events were self-reported and defined as at least two falls and one fracture, respectively, during the previous 2 years. SSRI users were compared with those taking no antidepressants. Hazard ratios (HRs) were estimated using Cox models with delayed entry and adjusted for many confounders including residual depressive symptoms. RESULTS: Incidence of falls was 19.3 % over 4 years and that of fractures 9.5 %. After multi-adjustment, SSRI intake was significantly associated with a higher risk of falls (HR, 95 % CI = 1.58, 1.23-2.03) and fractures (HR, 95 % CI = 1.61, 1.16-2.24). The risks were significantly increased by 80 % in those continuing the treatment over 4 years. Citalopram intake only was at significant risk for falls and fluoxetine for fractures. CONCLUSIONS: In this large community-dwelling elderly sample, SSRI users were at higher risk of falls and fractures. This association was not due to reverse causality or residual depressive symptoms. Different SSRI drugs may have specific adverse effects on falls and fractures.

Theory of the jamming transition at finite temperature.

A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature T and pressure p. Variational arguments and effective medium theory identically predict a non-trivial temperature scale T(∗) ∼ p((2-a)/(1-a)) with a ≈ 0.17 such that low-energy vibrational properties are hard-sphere like for T ≳ T(∗) and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating T, p, and the packing fraction ϕ, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of T and ϕ. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

Discontinuous shear thickening without inertia in dense non-Brownian suspensions.

A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here, the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain-rate hysteresis and arises at somewhat lower densities, where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded.

Effect of friction on dense suspension flows of hard particles.

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient µ_{p} and the viscous number J, we build a phase diagram that identifies three regimes of flow: frictionless, frictional sliding, and rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficients and small viscous numbers (below J∼10^{-3}), we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support the idea that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.

Phase diagram for inertial granular flows.

Flows of hard granular materials depend strongly on the interparticle friction coefficient µ_{p} and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10^{-4}≲I≲10^{-1}: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as µ_{p} increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with µ_{p}, corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I≥10^{-2.5} that the growth of the macroscopic friction µ(I) with I is induced by an increase of collisional dissipation. This implies in that range that µ(I)-µ(0)∼I^{1-2b}, where b≈0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L∼I^{-b} and the density of sliding contacts χ∼I^{b}.

Unified theory of inertial granular flows and non-Brownian suspensions.

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases both for aerial granular flows dominated by inertia and for over-damped suspensions. Concomitantly, the length scale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete, scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies both to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall, we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For overdamped flows, more observations are needed to decide if friction is a relevant perturbation. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.

Elasticity of floppy and stiff random networks.

We study the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination (average number of springs per node) relative to that of a marginally rigid network deltaz: a floppy network has deltaz<0, while a stiff network has deltaz>0. Under the influence of an externally applied load, we observe that the response of both floppy and stiff networks is controlled by the critical point corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the heterogeneity of the response, and the network stiffening as a function of deltaz and derive these theoretically, thus allowing us to predict aspects of the mechanical response of glasses and fibrous networks.