Crackling Noise in Fractional Percolation -- Randomly distributed discontinuous jumps in explosive percolation

Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation clusters of any size merge until a giant component dominates the entire system. Here we establish `fractional percolation' where the coalescence of clusters that substantially differ in size are systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed - characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets.Comment: non-final version, for final see Nature Communications homepag

Arrest stress of uniformly sheared wet granular matter

We conduct extensive independent numerical experiments considering frictionless disks without internal degrees of freedom (rotation etc.) in two dimensions. We report here that for a large range of the packing fractions below random-close packing, all components of the stress tensor of wet granular materials remain finite in the limit of zero shear rate. This is direct evidence for a fluid-to-solid arrest transition. The offset value of the shear stress characterizes plastic deformation of the arrested state {which corresponds to {\em dynamic yield stress} of the system}. {Based on an analytical line of argument, we propose that the mean number of capillary bridges per particle, $\nu$, follows a non-trivial dependence on the packing fraction, $\phi$, and the capillary energy, \vareps. Most noticeably, we show that $\nu$ is a generic and universal quantity which does not depend on the driving protocol.} Using this universal quantity, we calculate the arrest stress, $\sigma_a$, analytically based on a balance of the energy injection rate due to the external force driving the flow and the dissipation rate accounting for the rupture of capillary bridges. The resulting prediction of $\sigma_a$ is a non-linear function of the packing fraction $\phi$, and the capillary energy \vareps. This formula provides an excellent, parameter-free prediction of the numerical data. Corrections to the theory for small and large packing fractions are connected to the emergence of shear bands and of contributions to the stress from repulsive particle interactions, respectively.Comment: 7 pages, g figure

Attracted Diffusion-Limited Aggregation

In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the fractal dimension of the aggregated patterns as a function of the attraction strength \alpha. For the patterns grown in both two and three dimensions, the fractal dimension shows a significant dependence on the attraction strength for small values of \alpha, and approaches to that of the ordinary two-dimensional (2D) DLA in the limit of large \alpha. For non-attracting case with \alpha=1, our results in three dimensions reproduce the patterns of 3D ordinary DLA, while in two dimensions our model leads to formation of a compact cluster with dimension two. For intermediate \alpha, the 3D clusters have quasi-2D structure with a fractal dimension very close to that of the ordinary 2D-DLA. This allows one to control morphology of a growing cluster by tuning a single external parameter \alpha.Comment: 6 pages, 6 figures, to appear in Phys. Rev. E (2012

A response function perspective on yielding of wet granular matter

When dry ganular matter is tilted beyond a critical angle $\theta _{c}$, grains start to flow until a state is reached where the slope of the surface is smaller than $\theta _{c}$. In dry granulates this relaxation preferentially involves surface fluxes. In contrast wet granulates yield in the bulk. We uncover the origin of this behaviour by focusing on the structure of the balance equations of the forces, rather than applying a continuum model. The predictive power of the approach is demonstrated by a parameter-free prediction of the yielding of 2D packings with thermal motion and mass disorder

zu Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen

In this thesis, the stability and the dynamics of wet granular materials under shear are explored. Inspired by the Green’s function approach, a theoretical model for yielding of a wet pile on an inclined plane is presented. It enables one to predict the critical inclination angle at which the pile fluidizes. The theory is based on the balance of forces acting on each particle at the vicinity of the fluidization and has two major consequences. First, the theory shows that yielding of a wet pile does depend on the gravitational acceleration, whereas a dry pile fluidizes for any arbitrary small non-zero gravitational acceleration when the inclination angle exceeds a certain value depending on the geometry. Second, the theory shows that a wet pile yields in the bottom layer where the pile touches a non-slip boundary. There is excellent agreement between the theory and extensive MD-type simulations where one calculates forces between each individual pair of particles. The dynamics of driven wet particles is studied in two different ways. First, we explore dynamics of wet particles in a channel driven by gravity. Second, we apply a spatially sinusoidal driving force. In both cases we find discontinuous hysteretic solid-fluid transitions, i.e. solid-to-fluid and fluid-to-solid transitions and encountered at different forcing of the system. We calculate phase diagrams separating solid and fluid states and thresholds for the solid-to-fluid and the fluid-to-solid transitions. Beside that, we study the spatial and temporal distributions of drift velocity, granular temperature, area fraction, stress tensor, interparticle force etc. i Kurzzusammenfassung In dieser Arbeit wird die Stabilität und Dynamik feuchter granularer Medien unter der Einwirkung von Scherkräften untersucht. In Anlehung an den Greenschen Formalismums wir

Liste des centrales nucleaires dans le monde

SIGLEAvailable from CEN Saclay, Service de Documentation, 91191 Gif-sur-Yvette Cedex (France) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc