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 non-monotonic behavior in the friction law $\mu(I)$, 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 $\theta_s$. We build a microscopic theory for the non-monotonicity of $\mu(I)$, which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts $\chi$ and the sliding velocity, in terms of $\theta_s$. Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis rationalizes previously unexplained observations and makes new experimentally testable predictions.Comment: 6 pages + 3 pages S

On the Granular Stress-Geometry Equation

Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that (i) the equation imposes that the voids cannot carry stress, (ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and (iii) the packing fabric plays an essential role.Comment: 6 page

Unifying Suspension and Granular flows near Jamming

Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we review a theoretical framework that gives a scaling description of stationary flows of frictionless particles. Our analysis applies both to suspensions and inertial flows of hard particles. We report numerical results in support of the theory, and show the phase diagram that results when friction is added, delineating the regime of validity of the frictionless theory.Comment: Short review to appear in Powders and Grains 201

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 $\mu_p$ 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 coefficient and small viscous numbers (below $J\sim 10^{-3}$) 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 that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.Comment: 8 page

Emergence of order in random languages

We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in particular the Random Language Model of E. DeGiuli, Phys. Rev. Lett., 122, 128301, 2019. This model is solved in the replica-symmetric ansatz, which is valid in the high-temperature, disordered phase. It is shown that in the phase in which languages carry information, the replica symmetry must be broken.Comment: 16 pages + 1 appendix; v2: references added and some explanations expanded. J. Phys. A: Math. Theor 201

A job with no boundaries: home eldercare work in Italy

In recent years a number of important studies have explored the new international division of reproductive labor, but those works have concentrated, for the most part, on one end of the life cycle: nannies and childcare. This article focuses on the other end of it, home eldercare work. Jobs falling under this label encompass a variety of work situations but the title suggests a job that is more homogeneous than the occupation actually is. This article explores, through the narratives of the workers and the exploration of this 24-hour job, what it means to work as a home eldercare assistant

The distribution of forces affects vibrational properties in hard sphere glasses

We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{\theta_e}$ the force distribution of such pairs and $\phi_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $\omega^*$, rising up to it as $D(\omega) \sim \omega^{2+a}$, and decaying above $\omega^*$ as $D(\omega)\sim \omega^{-a}$ where $a=(1-\theta_e)/(3+\theta_e)$ and $\omega$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle \delta R^2\rangle\sim1/\mu\sim (\phi_c-\phi)^{\kappa}$ where $\kappa=2-2/(3+\theta_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{\delta z}\sim (\phi_c-\phi)^{-b}$ where $b=(1+\theta_e)/(6+2\theta_e)$ and $\delta z=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $\theta_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $\kappa\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, whereas some observations differ, as rationalized by the present approach.Comment: 5 pages + 4 pages supplementary informatio

Procjena otpora glisera u mirnoj vodi

Cilj ovog rada je procjena ukupnog otpora glisera s prizmatičnom formom trupa. Razvijen je programski kod za procjenu ukupnog otpora ova dva režima plovidbe koji omogućava projektantu brzu prognozu ukupnog otpora u fazi pretprojekta. Korištena je metoda Savitsky za procjenu otpora za predglisirajuće i glisirajuće područje i metoda Savitsky-Brown za predglisirajuće područje plovidbe. Kod je testiran na modelima Serije 62 za koju postoje mjerenja provedena u bazenu Brodarskog instituta u Zagrebu. Ukupni otpor dobiven programskim kodom usporeñen je s rezultatima mjerenja ukupnog otpora. Iz dobivenih rezultata vidljivo je da metoda Savitsky nije pogodna za proračun otpora u području niskih vrijednosti Froudeovog broja na temelju istisnine 1 FnÑ 2 £ £ , jer odstupanje u rezultatima može iznositi do 45%, dok za područje većih vrijednosti Froudeovog broja Fn 2 Ñ > daje zadovoljavajuće slaganje s izmjerenim vrijednostima uz maksimalno odstupanje do 20%. Za područje niskih vrijednosti Froudeovog broja preporuča se primjena metode Savitsky-Brown kod koje su odstupanja do 10%