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

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

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

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

Eksperimentalno određivanje otpora serije brzih poludeplasmanskih katamarana

Problem određivanja ukupnog otpora katamarana daleko je složeniji od istog problema prisutnog kod jednotrupnih brodova. Složenosti hidrodinamičkog sadržaja ukupnog otpora katamarana doprinosi i pojava interferencije trupova koja može biti i viskozna i valna. Na temelju rezultata ispitivanja četiri modela katamarana provedenih u Brodarskom institutu u Zagrebu određen je faktor forme primjenom metode Prohaske. Određene su komponente ukupnog otpora ispitane serije katamarana primjenom metode Froudea i metode Insela i Mollanda. Dobiveni rezultati su ekstrapolirani na katamarane u naravnoj veličini i izračunate su vrijednosti ukupnog otpora. Relativne pogreške između vrijednosti dobivenih metodom Froudea i metodom Insela i Mollanda prikazane su dijagramom. Na temelju ukupnog otpora katamarana odabrana je najpovoljnija forma katamarana sa stajališta otpora

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%

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 $T^*\sim p^{(2-a)/(1-a)}$ with $a \approx 0.17$ such that low-energy vibrational properties are hard-sphere like for $T \gtrsim T^*$, and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating $T$, $p$, and the packing fraction $\phi$, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of $T$ and $\phi$. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.Comment: 8 pages + 3 pages S

Približna metoda proračuna ukupnog otpora glisera

U radu su opisani problemi određivanja ukupnog otpora glisirajućih formi u mirnoj vodi te načini određivanja ukupnog otpora istih. Pored rezultata modelskih ispitivanja najčešći načini su upotreba približnih proračuna ukupnog otpora glisera. Izrađen je programski alat za proračun ukupnog otpora i trima glisirajućih formi u programu excel. Programski alat se temelji na matematičkom modelu koji je razvio profesor Radojčić za proračun otpora, trima, oplakane površine i duljine oplakane površine glisirajućih formi primjenom regresijske analize na rezultate ispitivanja sistematskih Serija 62. Matematički model je funkcija četiri parametra trupa i opterećenja (parametar opterećenja, omjer duljine i širine zgiba, uzdužni položaj težišta mase i kut nagiba dna). Alat omogućuje brzi proračun ukupnog otpora i trima na osnovu ulaznih parametara glisirajućih formi u svrhu odabira najboljeg projekta u fazi predprojekta. Izrađeni alat je testiran na dostupnim eksperimentalnim podacima iz literature

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