Compaction and mobility in randomly agitated granular assemblies

We study the compaction and mobility properties of a dense granular material under weak random vibration. By putting in direct contact millimetric glass beads with piezoelectric transducers we manage to inject energy to the system in a disordered manner with accelerations much smaller than gravity, resulting in a slow compaction dynamics and no convection. We characterize the mobility inside the medium by pulling through it an intruder grain at constant velocity. We present an extensive study of the relation between drag force and velocity for different vibration conditions and sizes of the intruder.Comment: 4 pages, 6 figures, to appear in the proceedings of Powders and Grains 200

Reorganization of a dense granular assembly: the `unjamming response function'

We investigate the mechanical properties of a static dense granular assembly in response to a local forcing. To this end, a small cyclic displacement is applied on a grain in the bulk of a 2D disordered packing under gravity and the displacement fields are monitored. We evidence a dominant long range radial response in the upper half part above the sollicitation and after a large number of cycles the response is `quasi-reversible' with a remanent dissipation field exhibiting long range streams and vortex-like symmetry.Comment: 5 pages, 5 figures, accepted version for publication in Phys. Rev.

Simulations of Pattern Formation in Vibrated Granular Media

We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first quantitative data from numerical simulations showing an interesting dependence of the pattern wavelength on the acceleration and the system size. Our results are related to recent experimental findings and theoretical predictions for gravity waves.Comment: 6 pages PS-file including figures, (version accepted at Europhys. Lett. 26.10.96

Simulations of dense granular flow: Dynamic Arches and Spin Organization

We present a numerical model for a two dimensional (2D) granular assembly, falling in a rectangular container when the bottom is removed. We observe the occurrence of cracks splitting the initial pile into pieces, like in experiments. We study in detail various mechanisms connected to the `discontinuous decompaction' of this granular material. In particular, we focus on the history of one single long range crack, from its origin at one side wall, until it breaks the assembly into two pieces. This event is correlated to an increase in the number of collisions, i.e. strong pressure, and to a momentum wave originated by one particle. Eventually, strong friction reduces the falling velocity such that the crack may open below the slow, high pressure `dynamic arch'. Furthermore, we report the presence of large, organized structures of the particles' angular velocities in the dense parts of the granulate when the number of collisions is large.Comment: Submitted to J. Phys.

Unjamming a granular hopper by vibration

We present an experimental study of the outflow of a hopper continuously vibrated by a piezoelectric device. Outpouring of grains can be achieved for apertures much below the usual jamming limit observed for non vibrated hoppers. Granular flow persists down to the physical limit of one grain diameter, a limit reached for a finite vibration amplitude. For the smaller orifices, we observe an intermittent regime characterized by alternated periods of flow and blockage. Vibrations do not significantly modify the flow rates both in the continuous and the intermittent regime. The analysis of the statistical features of the flowing regime shows that the flow time significantly increases with the vibration amplitude. However, at low vibration amplitude and small orifice sizes, the jamming time distribution displays an anomalous statistics

Observing the evaporation transition in vibro-fluidized granular matter

By shaking a sand box the grains on the top start to jump giving the picture of evaporating a sand bulk, and a gaseous transition starts at the surface granular matter (GM) bed. Moreover the mixture of the grains in the whole bed starts to move in a cooperative way which is far away from a Brownian description. In a previous work we have shown that the key element to describe the statistics of this behavior is the exclusion of volume principle, whereby the system obeys a Fermi configurational approach. Even though the experiment involves an archetypal non-equilibrium system, we succeeded in defining a global temperature, as the quantity associated to the Lagrange parameter in a maximum entropic statistical description. In fact in order to close our approach we had to generalize the equipartition theorem for dissipative systems. Therefore we postulated, found and measured a fundamental dissipative parameter, written in terms of pumping and gravitational energies, linking the configurational entropy to the collective response for the expansion of the centre of mass (c.m.) of the granular bed. Here we present a kinetic approach to describe the experimental velocity distribution function (VDF) of this non-Maxwellian gas of macroscopic Fermi-like particles (mFp). The evaporation transition occurs mainly by jumping balls governed by the excluded volume principle. Surprisingly in the whole range of low temperatures that we measured this description reveals a lattice-gas, leading to a packing factor, which is independent of the external parameters. In addition we measure the mean free path, as a function of the driving frequency, and corroborate our prediction from the present kinetic theory.Comment: 6 pages, 4 figures, submitted for publication September 1st, 200

Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure

Force indeterminacy in the jammed state of hard disks

Granular packings of hard discs are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force-realizations in the space of contact forces. Configurations are generated for given values of the friction coefficient, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a non-monotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact-network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.Comment: 4 pages, 3 figures. Minor changes, journal reference adde

Cluster, Classify, Regress: A General Method For Learning Discountinous Functions

This paper presents a method for solving the supervised learning problem in which the output is highly nonlinear and discontinuous. It is proposed to solve this problem in three stages: (i) cluster the pairs of input-output data points, resulting in a label for each point; (ii) classify the data, where the corresponding label is the output; and finally (iii) perform one separate regression for each class, where the training data corresponds to the subset of the original input-output pairs which have that label according to the classifier. It has not yet been proposed to combine these 3 fundamental building blocks of machine learning in this simple and powerful fashion. This can be viewed as a form of deep learning, where any of the intermediate layers can itself be deep. The utility and robustness of the methodology is illustrated on some toy problems, including one example problem arising from simulation of plasma fusion in a tokamak.Comment: 12 files,6 figure