Stripes ordering in self-stratification experiments of binary and ternary granular mixtures

The self-stratification of binary and ternary granular mixtures has been experimentally investigated. Ternary mixtures lead to a particular ordering of the strates which was not accounted for in former explanations. Bouncing grains are found to have an important effect on strate formation. A complementary mechanism for self-stratification of binary and ternary granular mixtures is proposed.Comment: 4 pages, 5 figures. submitted for pubication, guess wher

Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations

We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites (''wells'') separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t) follow the same scaling Ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases

How people interact in evolving online affiliation networks

The study of human interactions is of central importance for understanding the behavior of individuals, groups, and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links, and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We show that an accurate estimation of these probabilistic tendencies can be achieved only by following the time evolution of the network. Inferences about the reason for the existence of links using statistical analysis of network snapshots must therefore be made with great caution. Here, we start by characterizing every single link when the tie was established in the network. This information allows us to describe the probabilistic tendencies of tie formation and extract meaningful sociological conclusions. We also find significant differences in behavioral traits in the social tendencies among individuals according to their degree of activity, gender, age, popularity, and other attributes. For instance, in the particular data sets analyzed here, we find that women reciprocate connections 3 times as much as men and that this difference increases with age. Men tend to connect with the most popular people more often than women do, across all ages. On the other hand, triangular tie tendencies are similar, independent of gender, and show an increase with age. These results require further validation in other social settings. Our findings can be useful to build models of realistic social network structures and to discover the underlying laws that govern establishment of ties in evolving social networks

Learning and generation of long-range correlated sequences

We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We demonstrate that the average power-law behavior is learnable, namely, the sequence generated by the trained network obeys the same statistical behavior. The interplay between a correlated weight matrix and the sequence generated by such a network is explored. A weight matrix with a power-law correlation function along the vertical direction, gives rise to a sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review

The Role of Friction in Compaction and Segregation of Granular Materials

We investigate the role of friction in compaction and segregation of granular materials by combining Edwards' thermodynamic hypothesis with a simple mechanical model and mean-field based geometrical calculations. Systems of single species with large friction coefficients are found to compact less. Binary mixtures of grains differing in frictional properties are found to segregate at high compactivities, in contrary to granular mixtures differing in size, which segregate at low compactivities. A phase diagram for segregation vs. friction coefficients of the two species is generated. Finally, the characteristics of segregation are related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.Comment: 9 pages, 6 figures, submitted to Phys. Rev.

Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder

The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and supported by numerical simulations. This scaling theory is mapped onto the vibrational case at small frequencies. It is shown that for small frequencies, unexpectateley the localization length is smaller for correlated than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure

Scaling detection in time series: diffusion entropy analysis

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called Diffusion Entropy Analysis (DEA). We adopt artificial Gauss and L\'{e}vy time series, as prototypes of ordinary and anomalus statistics, respectively, and we analyse them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of L\'{e}vy statistics.Comment: 21 pages,10 figures, 1 tabl

Granular spirals on erodible sand bed submitted to a circular fluid motion

An experimental study of a granular surface submitted to a circular fluid motion is presented. The appearance of an instability along the sand-water interface is observed beyond a critical radius $r_c$. This creates ripples with a spiral shape on the granular surface. A phase diagram of such patterns is constructed and discussed as a function of the rotation speed $\omega$ of the flow and as a function of the height of water $h$ above the surface. The study of $r_c$ as a function of $h$, $\omega$ and $r$ parameters is reported. Thereafter, $r_c$ is shown to depend on the rotation speed according to a power law. The ripple wavelength is found to decrease when the rotation speed increases and is proportional to the radial distance $r$. The azimuthal angle \az of the spiral arms is studied. It is found that \az scales with $h\omega r$. This lead to the conclusion that \az depends on the fluid momentum. Comparison with experiments performed with fluids allows us to state that the spiral patterns are not the signature of an instability of the boundary layer.Comment: 7 pages, 10 figures, 1 table, using RevTeX4, submitted for publication (2002

Phase transitions in the steady state behavior of mechanically perturbed spin glasses and ferromagnets

We analyze the steady state regime of systems interpolating between spin glasses and ferromagnets under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. A crossover from a second order to first order ferromagnetic transition as a function of the spin coupling distribution is found. The flat measure over blocked states introduced by Edwards for granular media is used to explain this scenario. Annealed calculations of the Edwards entropy are shown to qualitatively explain the nature of the phase transitions. A Monte-Carlo construction of the Edwards measure confirms that this explanation is also quantitatively accurate

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $\mu$ between two particles is increased.Comment: 6 pages, 9 figures, submitted to Phys. Rev.