Sandpile formation by revolving rivers

Continuous to intermittent flows in growing granular heaps

If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size X_{c}, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an "uphill front" that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments, controlling the distance between the apex of the sandpile and the container feeding it from above, we show that X_{c} grows linearly with the input flux, but scales as the square root of the feeding height. We explain these facts from a phenomenological model based on the experimental observation that the flowing granular phase forms a "wedge" on top of the static one, differently from the case of stationary heaps. Moreover, we demonstrate that our controlled experiments allow to predict the value of X_{c} for the common situation in which the feeding height decreases as the pile increases in size.

Sink versus tilt penetration into shaken dry granular matter: The role of the foundation

We study the behavior of cylindrical objects as they sink into a dry granular bed fluidized due to lateral oscillations. Somewhat unexpectedly, we have found that, within a large range of lateral shaking powers, cylinders with flat bottoms sink vertically, while those with a "foundation" consisting of a shallow ring attached to their bottom, tilt besides sinking. The latter scenario seems to dominate independently from the nature of the foundation when strong enough lateral vibrations are applied. We are able to explain the observed behavior by quasi-2D numerical simulations, which also demonstrate the influence of the intruder's aspect ratio. The vertical sink dynamics is explained with the help of a Newtonian equation of motion for the intruder. Our findings may shed light on the behavior of buildings and other manmade structures during earthquakes.

Exponential velocity profile of granular flows down a confined heap

Thick granular flows are essential to many natural and industrial phenomena. Experimentally, it has been well established that the grain velocity profile is linear from the free surface to a certain depth, after which it decreases exponentially in the so-called "creep region". In this paper we obtain an exponential velocity profile based on the force balance of a grain near a wall, where the Janssen effect and the non-locality of interactions between grains are considered. When experimental parameters such as flow angles and friction coefficients are introduced in our model, it is able to reproduce experimental creep velocity profiles previously reported in the literature.

Granular chaos and mixing: Whirled in a grain of sand

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Sculpting sandcastles grain by grain: self-assembled sand towers

We study the spontaneous formation of granular towers produced when dry sand is poured on a wet sand bed. When the liquid content of the bed exceeds a threshold value W*, the impacting grains have a nonzero probability to stick on the wet grains due to instantaneous liquid bridges created during the impact. The trapped grains become wet by the capillary ascension of water and the process continues, giving rise to stable narrow towers. The growth velocity is determined by the surface liquid content which decreases exponentially as the tower height augments. This self-assembly mechanism (only observed in the funicular and capillary regimes) could theoretically last while the capillary rise of water is possible; however, the structure collapses before reaching this limit. The collapse occurs when the weight of the tower surpasses the cohesive stress at its base. The cohesive stress increases as the liquid content of the bed is reduced. Consequently, the highest towers are found just above W*.

Nonuniformities in the angle of repose and packing fraction of large heaps of particles

We report a numerical investigation of the structural properties of very large three-dimensional heaps of particles produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the final heap structure.

Revolving rivers in sandpiles: from continuous to intermittent flows

In a previous paper [E. Altshuler, Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of "revolving rivers" for sandpile formation is reported: As a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a river of sand on one side flowing from the apex of the pile to the edge of the base. For small piles the river is steady, or continuous. For larger piles, it becomes intermittent. In this paper we establish experimentally the "dynamical phase diagram" of the continuous and intermittent regimes, and give further details of the piles' "topography," improving the previous kinematic model to describe it and shedding further light on the mechanisms of river formation. Based on experiments in Hele-Shaw cells, we also propose that a simple dimensionality reduction argument can explain the transition between the continuous and intermittent dynamics.

Uphill solitary waves in granular flows

We have experimentally observed uphill solitary waves in the surface flow on a granular material. A heap is constructed by injecting sand between two vertical glass plates separated by a distance much larger than the average grain size, with an open boundary. As the heap reaches the open boundary, solitary fluctuations appear on the flowing layer and move "up the hill" (i.e., against the direction of the flow). We explain the phenomenon in the context of stop-and-go traffic models.

Delayed transitions between fluid-like and solid-like granular states

Analysis of granular flows has been a significant theoretical challenge over the past several decades. These flows are difficult to analyze largely because they exhibit both solid-like and fluid-like behaviors side-by-side in single experiments. In this paper, we examine two experiments in which the co-existence between these states is especially marked and leads to unique patterns that may serve as signatures for underlying granular dynamics deserving of further scrutiny. In these experiments, we find that when fluidization of grains is prolonged--as can be expected to occur for example under reduced gravity environments or under conditions of strong kinetic forcing (e.g. during earthquakes)--grains can produce residual depositional patterns that are difficult to distinguish from fluvial deposits. This suggests that geological landforms under low gravity (for example on Mars) or influenced by strong forcing (for example during earthquakes) may behave in a fluid-like manner despite being entirely dry.

Devil's-staircase-like behavior of the range of random time series with record-breaking fluctuations

We propose insight into the analysis of the record-breaking fluctuations in random time series, which permits to distinguish between the self-organized criticality and the record dynamics (RD) scenarios of system evolution, using a finite time series realization. Performed analysis of the time series associated with the historical prices of different commodities has shown that the evolution of commodity markets is controlled by the record-breaking fluctuations as it is outlined by the RD. Furthermore, we found that the sizes of record-breaking fluctuations follow a fat-tailed distribution and the devil's-staircase-like records of price ranges are multiaffine and persistent, nevertheless, the high moments (q> q(C) >2) of their q-order height-height correlation functions behave logarithmically.