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

Study on hybrid combustion of aero-suspensions of boron-aluminum powders in a quiescent reaction medium

© 2017. The present research deals with a hybrid combustion of aluminum/boron dust particles in a heterogeneous quiescent reaction medium with spatially discrete heat sources. A developed thermal model is employed to estimate flame propagation speed in a reaction medium. The burning velocity and minimum ignition energy are studied parametrically as a function of dust concentration and particle diameter for different percentages of boron powder in a hybrid mixture of aluminum/boron dust cloud. The model shows that the addition of boron powder as a component of the mixture decreases the burning rate and causes a higher amount of minimum ignition energy needed for ignition, owing to the role of boron as a heat sink. Comparison of the simulation results with the available experimental data shows that the model captures the flame propagation speed as a function of particle concentration, except at very low concentrations

Fluctuations and like-torque clusters at the onset of the discontinuous shear thickening transition in granular materials

The main mechanism driving rheological transitions is usually mechanical perturbation by shear — an unjamming mechanism. Investigating discontinuous shear thickening is challenging because the shear counterintuitively acts as a jamming mechanism. Moreover, at the brink of this transition, a thickening material exhibits fluctuations that extend both spatially and temporally. Despite recent extensive research, the origins of such spatiotemporal fluctuations remain unidentified. Here, we numerically investigate the fluctuations in injected power in discontinuous shear thickening in granular materials. We show that a simple fluctuation relation governs the statistics of power fluctuations. Furthermore, we reveal the formation of like-torque clusters near thickening and identify an unexpected relation between the spatiotemporal fluctuations and the collective behavior due to the formation of like-torque clusters. We expect that our general approach should pave the way to unmasking the origin of spatiotemporal fluctuations in discontinuous shear thickening