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Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle ${\theta }_W>\pi ∕2$, the average tangential velocity $R\bar{\omega }$ of the disk scales with the typical wedge vibration velocity $v_b$, and is in general a nonmonotonic function of the overall tilt angle ${\theta }_T$ of the wedge. The present work focuses on wedges with ${\theta }_W=2\pi ∕3$, which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field u(r, t) (vortices) and in the density field n (r, t)(clusters), driven by unstable fluctuations, δa = {δn, δu}. Their spatial correlations, <δa(r, t)δa(r′,t)>, as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as ; there occur transitions to macroscopic shearing states, etc.

The Cahn–Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.

We investigate experimentally and via computer simulations the segregation pattern of binary granular mixtures in a vibrated container with bottlenecks. During the vibration the granular motion is more violent at the bottlenecks than at the bellies. Particles with more mobility congregate to the necks, while those with less mobility congregate to the bellies. We use discrete element simulations to reproduce the main characteristics of the experimental observations.

The physical mechanism of earthquake remains a challenging issue to be clarified. Seismologists used to attribute shallow earthquake to the elastic rebound of crustal rocks. The seismic energy calculated following the elastic rebound theory and with the data of experimental results upon rocks, however, shows a large discrepancy with measurement — a fact that has been dubbed as “the heat flow paradox”. For the intermediate-focus and deep-focus earthquakes, both occurring in the region of the mantle, there is not reasonable explanation either. This paper will discuss the physical mechanism of earthquake from a new perspective, starting from the fact that both the crust and the mantle are discrete collective system of matters with slow dynamics, as well as from the basic principles of physics, especially some new concepts of condensed matter physics emerged in the recent years. (1) Stress distribution in earth’s crust: Without taking the tectonic force into account, according to the rheological principle of “everything flows”, the normal stress and transverse stress must be balanced due to the effect of gravitational pressure over a long period of time, thus no differential stress in the original crustal rocks is to be expected. The tectonic force is successively transferred and accumulated via stick-slip motions of rock blocks to squeeze the fault gouge and then exerted upon other rock blocks. The superposition of such additional lateral tectonic force and the original stress gives rise to the real-time stress in crustal rocks. The mechanical characteristics of fault gouge are different from rocks as it consists of granular matters. The elastic moduli of the fault gouges are much less than those of rocks, and they become larger with increasing pressure. This peculiarity of the fault gouge leads to a tectonic force increasing with depth in a nonlinear fashion. The distribution and variation of the tectonic stress in the crust are specified. (2) The strength of crust rocks: The gravitational pressure can initiate the elasticity–plasticity transition in crust rocks. By calculating the depth dependence of elasticity–plasticity transition and according to the actual situation analysis, the behaviors of crust rocks can be categorized in three typical zones: elastic, partially plastic and fully plastic. As the proportion of plastic portion reaches about 10% in the partially plastic zone, plastic interconnection may occur and the variation of shear strength in rocks is mainly characterized by plastic behavior. The equivalent coefficient of friction for the plastic slip is smaller by an order of magnitude, or even less than that for brittle fracture, thus the shear strength of rocks by plastic sliding is much less than that by brittle breaking. Moreover, with increasing depth a number of other factors can further reduce the shear yield strength of rocks. On the other hand, since earthquake is a large-scale damage, the rock breaking must occur along the weakest path. Therefore, the actual fracture strength of rocks in a shallow earthquake is assuredly lower than the average shear strength of rocks as generally observed. The typical distributions of the average strength and actual fracture strength in crustal rocks varying with depth are schematically illustrated. (3) The conditions for earthquake occurrence and mechanisms of earthquake: An earthquake will lead to volume expansion, and volume expansion must break through the obstacle. The condition for an earthquake to occur is as follows: the tectonic force exceeds the sum of the fracture strength of rock, the friction force of fault boundary and the resistance from obstacles. Therefore, the shallow earthquake is characterized by plastic sliding of rocks that break through the obstacles. Accordingly, four possible patterns for shallow earthquakes are put forward. Deep-focus earthquakes are believed to result from a wide-range rock flow that breaks the jam. Both shallow earthquakes and deep-focus earthquakes are the energy release caused by the slip or flow of rocks following a jamming–unjamming transition. (4) The energetics and impending precursors of earthquake: The energy of earthquake is the kinetic energy released from the jamming–unjamming transition. Calculation shows that the kinetic energy of seismic rock sliding is comparable with the total work demanded for rocks’ shear failure and overcoming of frictional resistance. There will be no heat flow paradox. Meanwhile, some valuable seismic precursors are likely to be identified by observing the accumulation of additional tectonic forces, local geological changes, as well as the effect of rock state changes, etc.

We treat the earth crust and mantle as large scale discrete matters based on the principles of granular physics and existing experimental observations. Main outcomes are: A granular model of the structure and movement of the earth crust and mantle is established. The formation mechanism of the tectonic forces, which causes the earthquake, and a model of propagation for precursory information are proposed. Properties of the seismic precursory information and its relevance with the earthquake occurrence are illustrated, and principle of ways to detect the effective seismic precursor is elaborated. The mechanism of deep-focus earthquake is also explained by the jamming–unjamming transition of the granular flow. Some earthquake phenomena which were previously difficult to understand are explained, and the predictability of the earthquake is discussed. Due to the discrete nature of the earth crust and mantle, the continuum theory no longer applies during the quasi-static seismological process. In this paper, based on the principles of granular physics, we study the causes of earthquakes, earthquake precursors and predictions, and a new understanding, different from the traditional seismological viewpoint, is obtained.

In this paper, the vertically vibrated binary granular mixtures at atmospheric pressure are studied experimentally. We find a nonstationary segregation state, of which the structure changes with time cyclically. The period of the cyclic segregation is measured and its variation with the vibration conditions is shown. The transition between the segregation states is also discussed, and a phase diagram on the plot of frequency against acceleration amplitude is given. In order to observe the effect of air flow in the segregation process, an alternative container with ventilated bottom is designed. Our experiments show that both regions of the Brazil nut segregation state and the cyclic segregation state shrink obviously by use of the latter container and disappear completely if the whole system is placed in vacuum. These results testify that the air pressure plays a positive role in both the Brazil nut effect and cyclic segregation.

Force chains play an important role in linking the macro- and micro-mechanisms of powder in high velocity compaction (HVC). Force chain lengths, as an important quantitative characteristic, can describe the geometry of force chains. In this study, force chain lengths and their relation to other force chain characteristics in HVC were investigated by discrete element method. Results revealed that force chain length decreased and it can be related to the densification process of ferrous powder in HVC. Moreover, long force chains extended from top to bottom and may play a major role in supporting load, although the percentage of long force chains was low. Probability density functions of force chain lengths further showed the exponential decay. The proportion of short force chains increased and the proportion of long force chains decreased. Long force chains had high strength and can be aligned to the direction of the external load, but force chain lengths did not have clear relation to straightness. These relations were confirmed by Pearson correlation coefficients.

Two-dimensional segregation effect in vertically vibrated binary granular mixtures with same size is studied by molecular dynamic simulation. The results show that the lighter and mixed state, in which the lighter particles tend to rise and form a pure layer on top of the system while the heavier particles and some of the lighter ones stay at the bottom and form a mixed layer, also exists in the two-dimensional system. The validity of the scheme of the lighter and mixed state is testified by comparing the distribution profiles implied by the scheme with that of the real simulated state. We further propose to use twice the ratio of the thickness of the top layer to that of the whole system as an order parameter to describe the degree of the segregation quantitatively, and present a method that can accurately calculate the order parameter in the simulation. By use of the order parameter, we show that the order parameter is a convex monotonic function of the density ratio between the heavier and lighter particles.

When a rod is vertically withdrawn from a granular layer, oblique force chains can be developed by effective shearing. In this study, the force-chain structure in a rod-withdrawn granular layer was experimentally investigated using a photoelastic technique. The rod is vertically withdrawn from a two-dimensional granular layer consisting of bidisperse photoelastic disks. During the withdrawal, the development process of force chains is visualized by the photoelastic effect. By systematic analysis of photoelastic images, force chain structures newly developed by the rod withdrawing are identified and analyzed. In particular, the relation between the rod-withdrawing force $F_{\mathrm{\text{w}}}$, total force-chains force $F_{\mathrm{\text{t}}}$, and their average orientation $𝜃$ are discussed. We find that the oblique force chains are newly developed by withdrawing. The force-chain angle $𝜃$ is almost constant (approximately $20^{\circ }$ from the horizontal), and the total force $F_{\mathrm{\text{t}}}$ gradually increases by the withdrawal. In addition, $F_{\mathrm{\text{t}}}sin𝜃$ shows a clear correlation with $F_{\mathrm{\text{w}}}$.

We study jamming in granular mixtures from the novel point of view of extended hydrodynamics. Using a hard sphere binary mixture model we predict that a few large grains are expected to get caged more effectively in a matrix of small grains compared to a few small grains in a matrix of larger ones. A similar effect has been experimentally seen in the context of colloidal mixtures.

The initiation and steady-state dynamics of granular shear flow are investigated experimentally in a Couette geometry with independently moveable outer and inner cylinders. The motion of particles on the top surface is analyzed using fast imaging. During steady state rotation of both cylinders at different rates, a shear band develops close to the inner cylinder for all combinations of speeds of each cylinder we investigated. Experiments on flow initiation were carried out with one of the cylinders fixed. When the inner cylinder is stopped and restarted after a lag time of seconds to minutes in the same direction, a shear band develops immediately. When the inner cylinder is restarted in the opposite direction, shear initially spans the whole material, i.e. particles far from the shear surface are moving significantly more than in steady state.

We discuss two athermal types of dynamics suitable for spin-models designed to model repeated tapping of a granular assembly. These dynamics are applied to a range of models characterized by a 3-spin Hamiltonian aiming to capture the geometric frustration in packings of granular matter.

We briefly describe how mean-field glass models can be extended to the case where the bath and friction are non-thermal. Solving their dynamics, one discovers a temperature with a thermodynamic meaning associated with the slow rearrangements, even though there is no thermodynamic temperature at the level of fast dynamics. This temperature can be shown to match the one defined on the basis of a flat measure over blocked (jammed) configurations. Numerical checks on realistic systems suggest that these features may be valid in general.

The contact network of a frictionless polydisperse granular packing is isostatic in the limit of low applied pressure. It is argued here that, on disordered isostatic networks, displacement–displacement and stress–stress static Green functions are described by random multiplicative processes and have a truncated power-law distribution, with a cut-off that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the abovementioned anomalous properties disappear because Green functions now have a bounded distribution. Thus, the low-pressure, isostatic, limit is a critical point.

We discuss the application of synchrotron X-ray microtomography (XMT) to granular matter, foams, crumpled membranes, and paper. XMT provides rapid, high-resolution, fully three-dimensional characterization of each of these classes of material. In some cases, subsequent three-dimensional image processing allows the virtual reconstruction of the disordered material as a specified assemblage of idealized basic structural units. This allows measurement of otherwise inaccessible correlation functions and can also be used as the starting point for data-initiated simulations.

The elastic properties of granular materials can be enormously nonlinear as compared with the properties of non-porous materials. Experiments on isotropic compression of a granular assembly of spheres show that the shear μ, and bulk k, moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz–Mindlin elasticity theory. Moreover, the ratio between the experimental bulk and shear moduli is found to be constant but with a value larger than the theoretical prediction. Numerical simulations resolve the question as to whether the problem lies with the treatment of the grain-grain contact or with the elastic framework. We find that the problem lies principally with the latter; the affine assumption (which underlies the elastic formulation) is found to be valid for k but to breakdown seriously for μ. This explains why the experimental and numerical values of μ(p) are much smaller than the elastic predictions. In this paper we review recent progress on the understanding of this problem based on microscopic simulations, elasticity theory and more innovative ideas such as jamming, fragility and thermodynamics of granular materials.

The processing of fine-grained particles with diameters between 1 and 10 microns is difficult due to strong van-der-Waals attraction forces. In order to improve the handling properties, the fine-grained particles, i.e. host-particles, are coated with various nanoparticles, i.e. guest-particles. The mixing of fine-grained powders is influenced by particl-particle interactions. If these forces are distinctively used, both interactive and ordered mixtures can be produced. These particle mixtures consist of composite-particles that have new physical properties. These modified properties depend strongly on the coating process, the diameter- and mass-relationship of the guest- and the host-particles. The properties of the composite-particles can systematically be adjusted to the requirements of industrial applications. For example, a laboratory bubbling fluidized bed can be used to describe the conveying behavior of the functionalized host-particles. Applications for the functionalized particles are in the pharmaceutical and the powder coating industries, e.g. enhanced dry powder inhalers and thin lacquer films. The present research compares three different mixing/coating processes. The composite-particles are characterized by TEM, SEM and with their fluidization characteristics. The coating process itself is monitored by the electrostatic charge of the particles.

We discuss two athermal types of dynamics suitable for spin-models designed to model repeated tapping of a granular assembly. These dynamics are applied to a range of models characterized by a 3-spin Hamiltonian aiming to capture the geometric frustration in packings of granular matter.

We briefly describe how mean-field glass models can be extended to the case where the bath and friction are non-thermal. Solving their dynamics, one discovers a temperature with a thermodynamic meaning associated with the slow rearrangements, even though there is no thermodynamic temperature at the level of fast dynamics. This temperature can be shown to match the one defined on the basis of a flat measure over blocked (jammed) configurations. Numerical checks on realistic systems suggest that these features may be valid in general.

The initiation and steady-state dynamics of granular shear flow are investigated experimentally in a Couette geometry with independently moveable outer and inner cylinders. The motion of particles on the top surface is analyzed using fast imaging. During steady state rotation of both cylinders at different rates, a shear band develops close to the inner cylinder for all combinations of speeds of each cylinder we investigated. Experiments on flow initiation were carried out with one of the cylinders fixed. When the inner cylinder is stopped and restarted after a lag time of seconds to minutes in the same direction, a shear band develops immediately. When the inner cylinder is restarted in the opposite direction, shear initially spans the whole material, i.e. particles far from the shear surface are moving significantly more than in steady state.