Avalanche Statistics of Driven Granular Slides in a Miniature Mound

We examine avalanche statistics of rain- and vibration-driven granular slides in miniature sand mounds. A crossover from power-law to non power-law avalanche-size statistics is demonstrated as a generic driving rate $\nu$ is increased. For slowly-driven mounds, the tail of the avalanche-size distribution is a power-law with exponent $-1.97\pm 0.31$, reasonably close to the value previously reported for landslide volumes. The interevent occurrence times are also analyzed for slowly-driven mounds; its distribution exhibits a power-law with exponent $-2.670\pm 0.001$.Comment: 4 pages, 3 figures, 1 tabl

Self-organization without conservation: true or just apparent scale-invariance?

The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description - (i) a simple mean field, (ii) a more detailed mean-field description in terms of a (self-organized) branching processes, and (iii) a full stochastic representation in terms of a Langevin equation-, it is shown on general grounds that non-conserving dynamics does not lead to bona fide criticality. Contrarily to conserving systems, a parameter, which we term "re-charging" rate (e.g. the tree-growth rate in forest-fire models), needs to be fine-tuned in non-conserving systems to obtain criticality. In the infinite size limit, such a fine-tuning of the loading rate is easy to achieve, as it emerges by imposing a second separation of time-scales but, for any finite size, a precise tuning is required to achieve criticality and a coherent finite-size scaling picture. Using the approaches above, we shed light on the common mechanisms by which "apparent criticality" is observed in non-conserving systems, and explain in detail (both qualitatively and quantitatively) the difference with respect to true criticality obtained in conserving systems. We propose to call this self-organized quasi-criticality (SOqC). Some of the reported results are already known and some of them are new. We hope the unified framework presented here helps to elucidate the confusing and contradictory literature in this field. In a second accompanying paper, we shall discuss the implications of the general results obtained here for models of neural avalanches in Neuroscience for which self-organized scale-invariance in the absence of conservation has been claimed.Comment: 40 pages, 7 figures

A laboratory-numerical approach for modelling scale effects in dry granular slides

Granular slides are omnipresent in both natural and industrial contexts. Scale effects are changes in physical behaviour of a phenomenon at different geometric scales, such as between a laboratory experiment and a corresponding larger event observed in nature. These scale effects can be significant and can render models of small size inaccurate by underpredicting key characteristics such as ow velocity or runout distance. Although scale effects are highly relevant to granular slides due to the multiplicity of length and time scales in the flow, they are currently not well understood. A laboratory setup under Froude similarity has been developed, allowing dry granular slides to be investigated at a variety of scales, with a channel width configurable between 0.25-1.00 m. Maximum estimated grain Reynolds numbers, which quantify whether the drag force between a particle and the surrounding air act in a turbulent or viscous manner, are found in the range 102-103. A discrete element method (DEM) simulation has also been developed, validated against an axisymmetric column collapse and a granular slide experiment of Hutter and Koch (1995), before being used to model the present laboratory experiments and to examine a granular slide of significantly larger scale. This article discusses the details of this laboratory-numerical approach, with the main aim of examining scale effects related to the grain Reynolds number. Increasing dust formation with increasing scale may also exert influence on laboratory experiments. Overall, significant scale effects have been identified for characteristics such as ow velocity and runout distance in the physical experiments. While the numerical modelling shows good general agreement at the medium scale, it does not capture differences in behaviour seen at the smaller scale, highlighting the importance of physical models in capturing these scale effects

Self-organized pattern formation in a diverse attractive-repulsive swarm

A diverse, asynchronous swarm consisting of N mobile, attractive-repulsive particles evolves inside a two-dimensional confinement. Each particle k is characterized by a preferred neighboring distance $\rho _{k}$ determined from a truncated normal distribution of mean $\overline{\rho}$ and standard deviation $\sigma _{\rho}$, for $0\leqslant \rho \sigma _{\rho c}$ stellate patterns are formed. This work explores the role of diversity in self-organized pattern formation in an attractive-repulsive swarm system