The complex scaling behavior of non--conserved self--organized critical systems

The Olami--Feder--Christensen earthquake model is often considered the prototype dissipative self--organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several different phenomena, including limited floating--point precision. Parallels between the dynamics of synchronized regions and those of a system with periodic boundary conditions are pointed out, and the asymptotic avalanche size distribution is conjectured to be dominated by avalanches of size one, with the weight of larger avalanches converging towards zero as the system size increases.Comment: 4 pages revtex4, 5 figure

Contrasting electricity demand with wind power supply: case study in Hungary

We compare the demand of a large electricity consumer with supply given by wind farms installed at two distant geographic locations. Obviously such situation is rather unrealistic, however our main goal is a quantitative characterization of the intermittency of wind electricity. The consumption pattern consists of marked daily and weekly cycles interrupted by periods of holidays. In contrast, wind electricity production has neither short-time nor seasonal periodicities. We show that wind power integration over a restricted area cannot provide a stable baseload supply, independently of the excess capacity. Further essential result is that the statistics are almost identical for a weekly periodic pattern of consumption and a constant load of the same average value. The length of both adequate supply and shortfall intervals exhibits a scale-free (power-law) frequency distribution, possible consequences are shortly discussed

Long-range correlations of extrapolar total ozone are determined by the global atmospheric circulation

International audienceTOMS (Version 8) ozone records are analysed between latitudes 60° S and 60° N, in order to extract autocorrelation properties with high spatial resolution. After the removal of semi-annual, annual, and quasi-biennial background oscillations, the residuals are evaluated by detrended fluctuation analysis. Long-range correlations are detected everywhere. Surprisingly, the latitude dependence of zonally averaged correlation exponents exhibits the same behaviour as the exponents for daily surface temperature records. This suggests that the correlation properties of total ozone column are dominated by the global atmospheric circulation patterns, and the effect of chemical processes seems to be subsidiary

Transitions in non-conserving models of Self-Organized Criticality

We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, $\alpha_c$, is approached, the cut--off of the avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The transition from non-SOC to SOC behaviour is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system. The relevance of the results are discussed in connection to the nearest-neighbours OFC model (in particular we analyse the relevance of synchronization in the latter).Comment: 8 pages in latex format; 5 figures available upon reques

Eruptive history of the Late Quaternary Ciomadul (Csomád) volcano, East Carpathians, part II: magma output rates

This study, which builds on high-precision unspiked Cassignol-Gillot K-Ar age determinations, presents an advanced DEMbased volumetrical analysis to infer long-term magma output rates for the Late Quaternary Ciomadul (Csomád) dacitic lava dome complex (East Carpathians, Romania). The volcanic field of Ciomadul developed on the erosional surface of Lower Cretaceous flysch and ~ 2 Ma old andesites and experienced an extended eruptive history from ~ 850 to < 30 ka. Predominantly effusive activity took place during the first stage (~ 850 to ~ 440 ka), producing volumetrically minor, isolated, peripheral domes. Subsequently, after a ~ 250 ky repose interval, a voluminous central dome cluster developed in the second stage (~ 200 to < 30 ka). During the youngest phase of evolution (~ 60 to < 30 ka), highly explosive eruptions also occurred, resulting in the formation of two craters (Mohos and St. Ana). The calculated ~ 8.00 ± 0.55 km3 total volume of the lava domes, which includes the related volcaniclastic (1.57 km3 ) as well as erosionally removed (0.18 km3 ) material, is in line with dimensions of other medium-sized dacitic lava domes worldwide. This volume was extruded at an average long-term magma output rate of 9.76 km3 / My (0.0098 km3 /ky). However, most of the domes (7.53 ± 0.51 km3 ) were formed in the 200 to < 30 ka period, implying a significantly increased magma output rate of 37.40 km3 /My (0.0374 km3 /ky), more than 30 times higher than in the first stage. Within these long-term trends, individual lava domes of Ciomadul (e.g. those with volumes between 0.02 and 0.40 km3 ) would have been emplaced at much higher rates over a period of years to tens of years. The active periods, lasting up to hundreds of years, would have been followed by repose periods ~ 30 times longer. The most recent eruption of Ciomadul has been dated here at 27.7 ± 1.4 ka. This age, which is in agreement with radiocarbon dates for the onset of lake sediment accumulation in St. Ana crater, dates fragmented lava blocks which are possibly related to a disrupted dome. This suggests that during the last, typically explosive, phase of Ciomadul, lava dome extrusion was still ongoing. In a global context, the analysis of the volumetric dynamism of Ciomadul’s activity gives insights into the temporal variations in magma output; at lava domes, short-term (dayor week-scale) eruption rates smooth out in long-term (millenia-scale) output rates which are tens of times lower

The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical exponent, and the dimension of the avalanches. Above the upper critical dimension D_u=4 the exponents equal the known mean field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.Comment: 7 pages, including 9 figures, accepted for publication in Physical Review

Crossover phenomenon in self-organized critical sandpile models

We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a crossover to the scaling behavior of a different sandpile model takes place where the sand-grains are equally transferred to the nearest neighbors. The crossover behavior is numerically analyzed in detail, especially we consider the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force $F_s$ on the surface of a glass rod immersed in dry sand. We observed that $F_s$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain-density yields to an exponentially increasing friction force. We also report on a novel periodicity of $F_s$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings.Comment: plain tex, 6 pages, to appear in Phys.Rev.

Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model

We derive the exact equations of motion for the random neighbor version of the Olami-Feder-Christensen earthquake model in the infinite-size limit. We solve them numerically, and compare with simulations of the model for large numbers of sites. We find perfect agreement. But we do not find any scaling or phase transitions, except in the conservative limit. This is in contradiction to claims by Lise & Jensen (Phys. Rev. Lett. 76, 2326 (1996)) based on approximate solutions of the same model. It indicates again that scaling in the Olami-Feder-Christensen model is only due to partial synchronization driven by spatial inhomogeneities. Finally, we point out that our method can be used also for other SOC models, and treat in detail the random neighbor version of the Feder-Feder model.Comment: 18 pages, 6 ps-figures included; minor correction in sec.

Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality

We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless we find that subsystems of linear dimension small compared to the overall system size obey finite (subsystem) size scaling, with universal critical coefficients, for the earthquake events localised within the subsystem. We provide evidence, moreover, that large earthquakes responsible for breaking finite size scaling are initiated predominantly near the boundary.Comment: 6 pages, 6 figures, to be published in Phys. Rev. E; references sorted correctl