Jamming phase diagram for frictional particles

The non-equilibrium transition from a fluid-like state to a disordered solid-like state, known as the jamming transition, occurs in a wide variety of physical systems, such as colloidal suspensions and molecular fluids, when the temperature is lowered or the density increased. Shear stress, as temperature, favors the fluid-like state, and must be also considered to define the system 'jamming phase diagram' [1-4]. Frictionless athermal systems [1], for instance, can be described by the zero temperature plane of the jamming diagram in the temperature, density, stress space. Here we consider the jamming of athermal frictional systems [8-13] such as granular materials, which are important to a number of applications from geophysics to industry. At constant volume and applied shear stress[1, 2], we show that while in absence of friction a system is either fluid-like or jammed, in the presence of friction a new region in the density shear-stress plane appears, where new dynamical regimes are found. In this region a system may slip, or even flow with a steady velocity for a long time in response to an applied stress, but then eventually jams. Jamming in non-thermal frictional systems is described here by a phase diagram in the density, shear-stress and friction space

Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model

We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we notice the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging as occurs in the spin glass phase. Due to a finite equilibration time, the system displays in this region the pattern of interrupted aging.Comment: 19 pages, 8 figure

Experimental study of the compaction dynamics for 2D anisotropic granular materials

We present an experimental study of the compaction dynamics for two-dimensional anisotropic granular systems. Compaction dynamics is measured at three different scales : (i) the macroscopic scale through the packing fraction $\rho$, (ii) the mesoscopic scale through both fractions of aligned grains $\phi_{a}$ and ideally ordered grains $\phi_{io}$, and (iii) the microscopic scale through both rotational and translational grain mobilities $\mu_{r,t}$. The effect of the grain rotations on the compaction dynamics has been measured. At the macroscopic scale, we have observed a discontinuity in the late stages of the compaction curve. At the mesoscopic scale, we have observed the formation and the growth of domains made of aligned grains. From a microscopic point of view, measurements reveal that the beginning of the compaction process is essentially related to translational motion of the grains. The grains rotations drive mainly the process during the latest stages of compaction.Comment: 8pages, 11 figure

Glass transition in granular media

In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the ``jamming transition''. In particular, using Edwards' approach, by analytical calculations at a mean field level, we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. Interestingly, the nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers.Comment: 7 pages, 4 figure

A fast algorithm for backbones

A matching algorithm for the identification of backbones in percolation problems is introduced. Using this procedure, percolation backbones are studied in two- to five-dimensional systems containing 1.7x10^7 sites, two orders of magnitude larger than was previously possible using burning algorithms.Comment: 8 pages, 6 .eps figures. Uses epsfig and ijmpc.sty (included). To appear in Int. J. Mod. Phys.

Site Percolation and Phase Transitions in Two Dimensions

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. We show that this result is valid for a wide class of bidimensional systems undergoing a continuous magnetization transition. We provide numerical evidence for discrete as well as for continuous spin models, including SU(N) lattice gauge theories. The critical percolation exponents do not coincide with the ones of the thermal transition, but they are the same for models belonging to the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures, references and comments adde

Relaxation properties in a lattice gas model with asymmetrical particles

We study the relaxation process in a two-dimensional lattice gas model, where the interactions come from the excluded volume. In this model particles have three arms with an asymmetrical shape, which results in geometrical frustration that inhibits full packing. A dynamical crossover is found at the arm percolation of the particles, from a dynamical behavior characterized by a single step relaxation above the transition, to a two-step decay below it. Relaxation functions of the self-part of density fluctuations are well fitted by a stretched exponential form, with a $\beta$ exponent decreasing when the temperature is lowered until the percolation transition is reached, and constant below it. The structural arrest of the model seems to happen only at the maximum density of the model, where both the inverse diffusivity and the relaxation time of density fluctuations diverge with a power law. The dynamical non linear susceptibility, defined as the fluctuations of the self-overlap autocorrelation, exhibits a peak at some characteristic time, which seems to diverge at the maximum density as well.Comment: 7 pages and 9 figure

Static and dynamic heterogeneities in irreversible gels and colloidal gelation

We compare the slow dynamics of irreversible gels, colloidal gels, glasses and spin glasses by analyzing the behavior of the so called non-linear dynamical susceptibility, a quantity usually introduced to quantitatively characterize the dynamical heterogeneities. In glasses this quantity typically grows with the time, reaches a maximum and then decreases at large time, due to the transient nature of dynamical heterogeneities and to the absence of a diverging static correlation length. We have recently shown that in irreversible gels the dynamical susceptibility is instead an increasing function of the time, as in the case of spin glasses, and tends asymptotically to the mean cluster size. On the basis of molecular dynamics simulations, we here show that in colloidal gelation where clusters are not permanent, at very low temperature and volume fractions, i.e. when the lifetime of the bonds is much larger than the structural relaxation time, the non-linear susceptibility has a behavior similar to the one of the irreversible gel, followed, at higher volume fractions, by a crossover towards the behavior of glass forming liquids.Comment: 9 pages, 3 figure