Experimental evidence of a Rayleigh-plateau instability in free falling granular jets

A granular jet falling out of a funnel shaped container, subjected to small vertical vibrations, develops an instability farther downstream as may happen for ordinary liquid jets. Our results show that this instability is reminiscent of the Rayleigh-Plateau capillary instability leading to breakup of the jet at large scales. The first stages of this instability are captured in detail allowing a determination of the dispersion relation. Surface tensions measured in this unstable regime (of the order of mN/m) are in agreement with previously reported measurements carried out at much smaller scales. This instability and the breakup of the jet can be inhibited when the effect of the surrounding medium (air) is reduced by enclosing the jet in an evacuated chamber, showing that the effective surface tension measured is the result of a strong interaction with the surrounding air.     

Pressure screening and fluctuations at the bottom of a granular column

We report sets of precise and reproducible measurements on the static pressure at the bottom of a granular column. We make a quantitative analysis of the pressure saturation when the column height is increased. We evidence a great sensitivity of the measurements with the global packing fraction and the eventual presence of shear bands at the boundaries. We also show the limit of the classical Janssen model and discuss these experimental results under the scope of recently proposed theoretical frameworks. Received 7 September 1998 and Received in final form 28 January 1999     

Anomalous wave reflection at the interface of two strongly nonlinear granular media

Granular materials exhibit a strongly nonlinear behavior affecting the propagation of energy and information. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. We report the first experimental observation of the dramatic change of solitary wave reflectivity from the interface of two granular media triggered by a magnetically induced precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. We explain this effect by the high gradient of particle velocity near the interface.     

Jamming and fluctuations in granular drag

We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of the contact surface between the grains and the dragged object, thus implying that the stress-induced collapse is nucleated in the bulk of the granular sample. We also find that while the fluctuations are periodic at small depths, they become "stepped" at large depths, a transition which we interpret as a consequence of the long-range nature of the force chains.     

Medium-modified average multiplicity and multiplicity fluctuations in jets

The energy evolution of average multiplicities and multiplicity fluctuations in jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark–gluon plasma. The leading contribution of the standard production of soft hadrons is enhanced by a factor while next-to-leading order (NLO) corrections are suppressed by , where the parameter N _s >1 accounts for the induced soft gluons in the medium. Our results for such global observables are cross-checked and compared with their limits in the vacuum.     

Turbulentlike fluctuations in quasistatic flow of granular media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.     

Shear stress fluctuations in the granular liquid and solid phases

We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distribution's skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.     

Stress fluctuations and macroscopic stick-slip in granular materials

This paper deals with the quasi-static regime of deformation of granular matter. It investigates the size of the Representative Elementary Volume (REV), which is the minimum packing size above which the macroscopic mechanical behaviour of granular materials can be defined from averaging. The first part uses typical results from recent literature and finds that the minimum REV contains in general 10 grains; this result holds true either for most experiments or for Discrete Element Method (DEM) simulation. This appears to be quite small. However, the second part gives a counterexample, which has been found when investigating uniaxial compression of glass spheres which exhibit stick-slip; we show in this case that the minimum REV becomes 10⁷ grains. This makes the system not computable by DEM. Moreover, similarity between the Richter law of seism and the exponential statistics of stick-slip is stressed. Received 8 March 2002 and Received in final form 12 July 2002     

Large force fluctuations in a flowing granular medium

We study fluctuations in the force at the boundary of a 2D granular flow. The forces are mainly impulsive at all flow rates. The probability distribution of impulses decays exponentially at large impulses, as do the forces in a static granular medium. At small impulses, the distribution evolves continuously with flow rate with no indication of the transition from collisional flow to intermittently jamming flows. However, the distribution of the time interval between collisions tends to a power law, P(tau) - tau(-3/2), showing a clear dynamical signature of the approach to jamming.     

Energy and power fluctuations in vibrated granular gases

Using two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study the fluctuations of its total kinetic energy, of the power injected into the gas by the moving boundary and of the power dissipated by inelastic collisions. We show that an effective number N _f of degrees of freedom that depends on the inelasticity of collisions can be extracted from the probability density function (PDF) of the fluctuations of the total kinetic energy E. is then an intensive variable contrary to the usually defined granular temperature . We then show that an intensive temperature can also be calculated from the probability of certain large deviations of the injected power. Finally, we show that the fluctuations of injected and dissipated power are related such that their ratio is inversely proportional to the square-root of the ratio of their correlation times. This allows to define a quantity homogenous to a temperature that is intensive and conserved in the process of energy dynamics from its injection by the driving piston to its dissipation by inelastic collisions.Received: 3 August 2004, Published online: 14 December 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Energy fluctuations in vibrated and driven granular gases

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results that have previously been observed numerically and that had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit suggests that they are also due to the finite size of the system.     

Volume fluctuations and geometrical constraints in granular packs

I study the structural organization and correlations in very large packings of equally sized spheres, reconstructed in three dimensions with x-ray computed tomography. I show that the geometrical structure can be conveniently studied as a packing of irregular tetrahedra with volume distribution that must decay exponentially with parameters controlled by the conditions of mechanical stability, nonoverlapping, and space filling. I argue that the system's structure can be described as constituted of two phases: (1) an "unconstrained" phase which freely shares the volume and (2) a "constrained" phase which assumes configurations accordingly with the geometrical constraints. It results that the granular system exploits heterogeneity maximizing freedom and entropy while constraining mechanical stability.     

Force fluctuations in a vertically pushed granular column

We present series of experiments on the resistance force encountered by a bottom piston pushing a vertical granular column confined in a two-dimensional cell. We show that, due to the presence of friction at the boundaries and between the grains, the signal shows many complex features. At slow driving velocities, we observe a transition to a stick-slip dynamic instability. Depending on the granular material used, the elementary stick-slip events may either be well characterized or largely distributed. We present a statistical study on the waiting time between events and the distribution of energy release as a function of the spring stiffness and the driving velocity. Received 5 August 1998 and Received in final form 22 October 1998     

Quantum fluctuations and the universal kinetic inductance of granular superconducting films

The same mean-field theory for an array of Josephson junctions that describes the onset of superconductivity at normal state resistance R_N^(c) yields the kinetic inductance, L, for R_N<R_N^(c). The predicted universal behavior of L, as a function of R_N/R_N^(c), provides a further test of the theory of quantum fluctuations.     

Mesoscopic theory of critical fluctuations in isolated granular gases

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed only by vorticity fluctuations that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out.     

Scaling and universality of critical fluctuations in granular gases

The total energy fluctuations of a low-density granular gas in the homogeneous cooling state near the threshold of the clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown to exhibit a power-law divergent behavior. Moreover, the probability distribution of the fluctuations presents data collapse as the system approaches the instability, for different values of the inelasticity. The function describing the collapse turns out to be the symmetric of the one found in several molecular equilibrium and nonequilibrium systems.     

Partons and jets at the LHC

I review some issues related to short distance QCD and its relation to the experimental program of the large hadron collider (LHC) now under construction in Geneva.