Energy dissipation and dispersion effects in granular media

Shock-induced dispersion patterns of powder with diverse physical properties

Under the strong pressure pulse induced by a shock wave, powders exhibit specific instability and dispersion patterns that develop into jets over time. We experimentally investigate how the physical properties of particles affect the dispersion of powders in both the compaction and subsequent expansion phases. Our investigation uses a laboratory-scale Hele-Shaw cell device and nano-energetic materials to generate the pressure pulse. Depending on the initial radius of the powder, distinct jetting patterns are initiated by instability in either the inner or outer boundary of the powder. The degree of particle cohesion also influences the instability, and its relationship with the morphology of the finger structure at the inner boundary is quantitatively assessed. The permeability of the powder, which depends on particle size, is another important factor determining the instability of the powder layer during the compaction phase and its inward flow in the expansion phase. Based on the experimental results, a scaling analysis is performed to identify the characteristic time scale of temporal changes in the outer boundary of the powder. The findings presented in this paper offer novel insights for improved predictions of shock-induced particle dispersion in industrial processes.

Experimental study of transport of a dimer on a vertically oscillating plate

It has recently been shown that a dimer, composed of two identical spheres rigidly connected by a rod, under harmonic vertical vibration can exhibit a self-ordered transport behaviour. In this case, the mass centre of the dimer will perform a circular orbit in the horizontal plane, or a straight line if confined between parallel walls. In order to validate the numerical discoveries, we experimentally investigate the temporal evolution of the dimer's motion in both two- and three-dimensional situations. A stereoscopic vision method with a pair of high-speed cameras is adopted to perform omnidirectional measurements. All the cases studied in our experiments are also simulated using an existing numerical model. The combined investigations detail the dimer's dynamics and clearly show that its transport behaviours originate from a series of combinations of different contact states. This series is critical to our understanding of the transport properties in the dimer's motion and related self-ordered phenomena in granular systems.

Pure rotation of a prism on a ramp

In this work, we study a prism with a cross section in polygon rolling on a ramp inclined at a small angle. The prism under gravity rolls purely around each individual edge, intermittently interrupted by a sequence of face collisions between the side face of the prism and the ramp. By limiting the prism in a planar motion, we propose a mathematical model to deal with the events of the impacts. With a pair of laser-Doppler vibrometers, experiments are also conducted to measure the motions of various prisms made of different materials and with different edge number. Not only are good agreements achieved between our numerical and experimental results, but also an intriguing physical phenomenon is discovered: the purely rolling motion is nearly independent of the prism's materials, yet it is closely related to the prism's geometry. Imagine that an ideal circular section can be approximately equivalent to a polygon with a large enough edge number N, the finding presented in this paper may help discover the physical mechanism of rolling friction.

Symmetry of interactions rules in incompletely connected random replicator ecosystems

The evolution of an incompletely connected system of species with speciation and extinction is investigated in terms of random replicators. It is found that evolving random replicator systems with speciation do become large and complex, depending on speciation parameters. Antisymmetric interactions result in large systems, whereas systems with symmetric interactions remain small. A co-dominating feature is within-species interaction pressure: large within-species interaction increases species diversity. Average fitness evolves in all systems, however symmetry and connectivity evolve in small systems only. Newcomers get extinct almost immediately in symmetric systems. The distribution in species lifetimes is determined for antisymmetric systems. The replicator systems investigated do not show any sign of self-organized criticality. The generalized Lotka-Volterra system is shown to be a tedious way of implementing the replicator system.

Impact–contact dynamics in a disc–ball system

This paper concerns a disc–ball system, in which a moving ball collides against a disc resting on a rough, fixed horizontal surface. The complexity in such a simple object is due to the presence of the line contact between the disc and the fixed plate, which significantly influences the impact-generated state of the disc. We deal with this problem in a uniform framework that encapsulates different structures of the mathematical model, including contacts, impacts, stick–slip in friction, as well as the transitions among different states of the variable-structure dynamics. We design specific experiments that provide useful information to help determine the macroscopic parameters in impact and friction. Other complicated cases concerned with the couplings between impacts and friction are theoretically and experimentally investigated. Excellent agreements between numerical and experimental results support our theoretical developments.

Three-dimensional impact: energy-based modeling of tangential compliance

Impact is indispensable in robotic manipulation tasks in which objects and/or manipulators move at high speeds. Applied research using impact has been hindered by underdeveloped computational foundations for rigid-body collision. This paper studies the computation of tangential impulse as two rigid bodies in the space collide at a point with both tangential compliance and friction. It extends Stronge’s spring-based planar contact structure to three dimensions by modeling the contact point as a massless particle able to move tangentially on one body while connected to an infinitesimal region on the other body via three orthogonal springs. Slip or stick is indicated by whether the particle is still or moving. Impact analysis is carried out using normal impulse rather than time as the only independent variable, unlike in previous work on tangential compliance. This is due to the ability to update the energies stored in the three springs. Collision is governed by a system of differential equations that are solvable numerically. Modularity of the impact model makes it easy to be integrated into a multibody system, with one copy at each contact, in combination with a model for multiple impacts that governs normal impulses at different contacts.

Granular medium impacted by a projectile: experiment and model

We present a minimal discrete model for the propagation of energy through a 3D granular medium impacted by a particulate projectile. In this model, energy is transferred from grain to grain via binary collision events. This description can be successfully applied to the analysis of the collision process of a single spherical particle (of diameter donto a half space of granular medium composed of similarly sized particles. The model reproduces remarkably well the experimental observations. Besides, the present model provides a clear picture of the mechanism of energy propagation. A continuum version of the model, where the energy propagation from bead to bead is characterized by a diffusion equation, is derived. The diffusion coefficient is found to be proportional to the ratio of d(2) to the characteristic collision time Tau(c) . The numerical value of the coefficient of proportionality is essentially governed by the geometry of the packing. This paper constitutes an extension of a previously published letter (J. Crassous, D. Beladjine, A. Valance, Phys. Rev. Lett. 99, 248001 (2007)).