## I. Albert, J.G. Sample, A.J. Morss, S. Rajagopalan, A.-L. Barabási, P. Schiffer

# Granular drag on a discrete object: shape effects on jamming

#### Physical Review E 64, 061303 (2001)

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We study the drag force on discrete objects with circular cross section moving slowly through a spherical granular medium. Variations in the geometry of the dragged object change the drag force only by a small fraction relative to shape effects in fluid drag. The drag force depends quadratically on the object’s diameter as expected. We do observe, however, a deviation above the expected linear depth dependence, and the magnitude of the deviation is apparently controlled by geometrical factors.

## B. Kahng, I. Albert, P. Schiffer, A.-L. Barabási

# Modeling relaxation and jamming in granular media

#### Physical Review E 64, 051303 (2001)

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We introduce a stochastic microscopic model to investigate the jamming and reorganization of grains induced by an object moving through a granular medium. The model reproduces the experimentally observed periodic sawtooth fluctuations in the jamming force and predicts the period and the power spectrum in terms of the controllable physical parameters. It also predicts that the avalanche sizes, defined as the number of displaced grains during a single advance of the object, follow a power law P(s);s2t , where the exponent is independent of the physical parameters.

## I. Albert, P. Tegzes, R. Albert, J. G. Sample, A.-L. Barabási, T. Vicsek, B. Kahng, P. Schiffer

# Stick-slip fluctuations in granular drag

#### Physical Review E 64, 031307 (2001)

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We study fluctuations in the drag force experienced by an object moving through a granular medium. The successive formation and collapse of jammed states give a stick-slip nature to the fluctuations which are periodic at small depths but become ‘‘stepped’’ at large depths, a transition that we interpret as a consequence of the long-range nature of the force chains and the finite size of our experiment. Another important finding is that the mean force and the fluctuations appear to be independent of the properties of the contact surface between the grains and the dragged object. These results imply that the drag force originates in the bulk properties of the granular sample.

## R. Albert, H. Jeong, A.-L. Barabási

# Diameter of the world wide web

#### Nature 401, 130-131 (1999)

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Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web’s connectivity and consequently how effectively we can locate information on it.

## I. Albert, P. Tegzes, B. Kahng, R. Albert, J.G. Sample, M.A. Pfeifer, A.-L. Barabási, T. Vicsek, P. Schiffer

# Jamming and fluctuations in granular drag

#### Physical Review Letters 84, 5122–5125 (2000)

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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.

## P. Tegzes, R. Albert, M. Paskvan, A.-L. Barabási, T. Vicsek, P. Schiffer

# Liquid-induced transitions in granular media

#### Physical Review E 60, 5823–5826 (1999)

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We investigate the effect of interstitial liquid on the physical properties of granular media by measuring the angle of repose as a function of the liquid content. The resultant adhesive forces lead to three distinct regimes in the observed behavior as the liquid content is increased: a granular regime in which the grains move individually, acorrelated regime in which the grains move in correlated clusters, and a plastic regime in which the grains flow coherently. We discuss these regimes in terms of two proposed theories describing the effects of liquid on the physical properties of granular media.

## A.-L. Barabási, R. Albert, P. Schiffer

# The physics of sandcastles: maximum angle of stability in wet and dry granular media

#### Physica A 266, 366-371 (1999)

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We demonstrate that stability criteria can be used to calculate the maximum angle of stability, m, of a granular medium composed of spherical particles in three dimensions and circular discs in two dimensions. We apply the results to wet granular material by calculating the dependence of m on the liquid content of the material. The results are in good agreement with our experimental data.

## R. Albert, I. Albert, D. Hornbaker, P. Schiffer, A.-L. Barabási

# Maximum angle of stability in wet and dry spherical granular media

#### Physical Review E 56, R6271–R6274 (1997)

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We demonstrate that stability criteria can be used to calculate the maximum angle of stability u m of a granular medium composed of spherical particles in three dimensions and circular disks in two dimensions. The predicted angles are in good agreement with the experimental results. Furthermore, we determine the dependence of u m on cohesive forces, applying the results to wet granular material by calculating the dependence of u m on the liquid content of the material. We have also studied wet granular media experimentally and find good agreement between the theory and our experimental results.

## D. J. Hornbaker, R. Albert, I. Albert, A.-L. Barabási, P. Schiffer

# What keeps sandcastles standing?

#### Nature 387, 765 (1997)

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Any child playing on the beach knows that the physical properties of wet and dry sand are very different. Wet sand can be used to build sharp-featured sandcastles that would be unstable in dry sand. We have now quantified the effect of adding small quantities of liquid to a granular medium. Nanometre-scale layers of liquid on millimetre-scale grains dramatically increase the repose angle (the steepest stable slope that the substance can form) and allow the development of long-range correlations, or clumps.