Water droplet avalanches

Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

In many situations we are interested in the propagation of energy in some portions of a three-dimensional system with dilute long-range links. In this paper, a sandpile model is defined on the three-dimensional small-world network with real dissipative boundaries and the energy propagation is studied in three dimensions as well as the two-dimensional cross-sections. Two types of cross-sections are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross-section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long-range links (α) increases. This trend is numerically shown to be a power law in a manner described in the paper. Two regimes of α are considered in this work. For sufficiently small αs the dominant behavior of the system is just like that of the regular BTW, whereas for the intermediate values the behavior is nontrivial with some exponents that are reported in the paper. It is shown that the spatial extent up to which the statistics is similar to the regular BTW model scales with α just like the dissipative BTW model with the dissipation factor (mass in the corresponding ghost model) m^{2}∼α for the three-dimensional system as well as its two-dimensional cross-sections.

Dissipative stochastic sandpile model on small-world networks: Properties of nondissipative and dissipative avalanches

A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities ϕ, where ϕ=0 represents regular lattice and ϕ=1 represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at ϕ=0 and mean-field scaling at ϕ=1, the dissipative avalanches display nontrivial critical properties at ϕ=0 and 1 in both one and two dimensions. In the small-world regime (2^{-12}≤ϕ≤0.1), the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size s_{c}. Stochastic scaling is found to occur for s<s_{c} and the mean-field scaling is found to occur for s>s_{c}. As different scaling forms are found to coexist in a single probability distribution, a coexistence scaling theory on small world network is developed and numerically verified.

Memristive Sisyphus circuit for clock signal generation

Frequency generators are widely used in electronics. Here, we report the design and experimental realization of a memristive frequency generator employing a unique combination of only digital logic gates, a single-supply voltage and a realistic thresholdtype memristive device. In our circuit, the oscillator frequency and duty cycle are defined by the switching characteristics of the memristive device and external resistors. We demonstrate the circuit operation both experimentally, using a memristor emulator, and theoretically, using a model memristive device with threshold. Importantly, nanoscale realizations of memristive devices offer small-size alternatives to conventional quartz-based oscillators. In addition, the suggested approach can be used for mimicking some cyclic (Sisyphus) processes in nature, such as "dripping ants" or drops from leaky faucets.

Marginally subcritical dynamics explain enhanced stimulus discriminability under attention

Recent experimental and theoretical work has established the hypothesis that cortical neurons operate close to a critical state which describes a phase transition from chaotic to ordered dynamics. Critical dynamics are suggested to optimize several aspects of neuronal information processing. However, although critical dynamics have been demonstrated in recordings of spontaneously active cortical neurons, little is known about how these dynamics are affected by task-dependent changes in neuronal activity when the cortex is engaged in stimulus processing. Here we explore this question in the context of cortical information processing modulated by selective visual attention. In particular, we focus on recent findings that local field potentials (LFPs) in macaque area V4 demonstrate an increase in γ-band synchrony and a simultaneous enhancement of object representation with attention. We reproduce these results using a model of integrate-and-fire neurons where attention increases synchrony by enhancing the efficacy of recurrent interactions. In the phase space spanned by excitatory and inhibitory coupling strengths, we identify critical points and regions of enhanced discriminability. Furthermore, we quantify encoding capacity using information entropy. We find a rapid enhancement of stimulus discriminability with the emergence of synchrony in the network. Strikingly, only a narrow region in the phase space, at the transition from subcritical to supercritical dynamics, supports the experimentally observed discriminability increase. At the supercritical border of this transition region, information entropy decreases drastically as synchrony sets in. At the subcritical border, entropy is maximized under the assumption of a coarse observation scale. Our results suggest that cortical networks operate at such near-critical states, allowing minimal attentional modulations of network excitability to substantially augment stimulus representation in the LFPs.

Critical properties of a dissipative sandpile model on small-world networks

A dissipative sandpile model is constructed and studied on small-world networks (SWNs). SWNs are generated by adding extra links between two arbitrary sites of a two-dimensional square lattice with different shortcut densities ϕ. Three regimes are identified: regular lattice (RL) for ϕ≲2(-12), SWN for 2(-12)<ϕ<0.1, and random network (RN) for ϕ≥0.1. In the RL regime, the sandpile dynamics is characterized by the usual Bak, Tang, and Weisenfeld (BTW)-type correlated scaling, whereas in the RN regime it is characterized by mean-field scaling. On SWNs, both scaling behaviors are found to coexist. Small compact avalanches below a certain characteristic size s(c) are found to belong to the BTW universality class, whereas large, sparse avalanches above s(c) are found to belong to the mean-field universality class. A scaling theory for the coexistence of two scaling forms on a SWN is developed and numerically verified. Though finite-size scaling is not valid for the dissipative sandpile model on RLs or on SWNs, it is found to be valid on RNs for the same model. Finite-size scaling on RNs appears to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

Rain: relaxations in the sky

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power of 1.4. This is the rain equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterized by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal H=0.76>0.5. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organized criticality, which refers to the tendency of slowly driven nonequilibrium systems towards a state of scale-free behavior.

Self-organized criticality in a sheared granular stick-slip system

We present an analysis of results obtained from a mechanical apparatus consisting of an annular plate shearing over a granular bed. The size, energy dissipation, and duration of slips in the system exhibit power-law distributions and a 1/f(2) power spectrum, in accordance with self-organized criticality. We draw similarities with earthquakes.