Tracer Dispersion in a Self-Organized Critical System

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.Comment: 4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available upon request, Submitted to Phys. Rev. Let

Stretched exponentials and power laws in granular avalanching

We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion. Comment: 8 pages, more concise and some points clarified

Analysis of Ozone (O3) and Erythemal UV (EUV) measured by TOMS in the equatorial African belt

We presented time series of total ozone column amounts (TOCAs) and erythemal UV (EUV) doses derived from measurements by TOMS (Total Ozone Mapping Spectrometer) instruments on board the Nimbus-7 (N7) and the Earth Probe (EP) satellites for three locations within the equatorial African belt for the period 1979 to 2000. The locations were Dar-es-Salaam (6.8° S, 39.26° E) in Tanzania, Kampala (0.19° N, 32.34° E) in Uganda, and Serrekunda (13.28° N, 16.34° W) in Gambia. Equatorial Africa has high levels of UV radiation, and because ozone shields UV radiation from reaching the Earth’s surface, there is a need to monitor TOCAs and EUV doses. In this paper we investigated the trend of TOCAs and EUV doses, the effects of annual and solar cycles on TOCAs, as well as the link between lightning and ozone production in the equatorial African belt. We also compared clear-sky simulated EUV doses with the corresponding EUV doses derived from TOMS measurements. The TOCAs were found to vary in the ranges 243 DU − 289 DU, 231 DU − 286 DU, and 236 DU − 296 DU, with mean values of 266.9 DU, 260.9 DU, and 267.8 DU for Dar-es-Salaam, Kampala and Serrekunda, respectively. Daily TOCA time series indicated that Kampala had the lowest TOCA values, which we attributed to the altitude effect. There were two annual ozone peaks in Dar-es-Salaam and Kampala, and one annual ozone peak in Serrekunda. The yearly TOCA averages showed an oscillation within a five-year period. We also found that the EUV doses were stable at all three locations for the period 1979−2000, and that Kampala and Dar-es-Salaam were mostly cloudy throughout the year, whereas Serrekunda was mostly free from clouds. It was also found that clouds were among the major factors determining the level of EUV reaching the Earth´s surface. Finally, we noted that during rainy seasons, horizontal advection effects augmented by lightning activity may be responsible for enhanced ozone production in the tropics.publishedVersio

Self-organized criticality in a rice-pile model

We present a new model for relaxations in piles of granular material. The relaxations are determined by a stochastic rule which models the effect of friction between the grains. We find power-law distributions for avalanche sizes and lifetimes characterized by the exponents $\tau = 1.53 \pm 0.05$ and $y = 1.84 \pm 0.05$, respectively. For the discharge events, we find a characteristic size that scales with the system size as $L^\mu$, with $\mu = 1.20 \pm 0.05$. We also find that the frequency of the discharge events decrease with the system size as $L^{-\mu'}$ with $\mu' = 1.20 \pm 0.05$.Comment: 4 pages, RevTex, multicol, epsf, rotate (sty files provided). To appear Phys. Rev. E Rapid Communication (Nov or Dec 96

Avalanche statistics of sand heaps

Large scale computer simulations are presented to investigate the avalanche statistics of sand piles using molecular dynamics. We could show that different methods of measurement lead to contradicting conclusions, presumably due to avalanches not reaching the end of the experimental table.Comment: 6 pages, 4 figure

Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).Comment: Explanations added; relation to other model

Universality classes for rice-pile models

We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states that belong to three different universality classes. The models with local relaxation rules belong to a known universality class that is characterized by an avalanche exponent $\tau \approx 1.55$, whereas the models with nonlocal relaxation rules belong to new universality classes characterized by exponents $\tau \approx 1.35$ and $\tau \approx 1.63$. We discuss the values of the exponents in terms of scaling relations and a mapping of the sandpile models to interface models.Comment: 4 pages, including 3 figure

Excitation of Rydberg wave packets with chirped laser pulses

We study Rydberg wave packets produced by pairs of time separated femtosecond laser pulses. The time separation ranges from femtosecond to picosecond time scales. The wave packets consist predominantly of f states of principal quantum numbers n = 22-32 in Li. With a direct analysis of the field ionization spectra the n-level-resolved classical orbit times are displayed. By chirping the second excitation pulse we demonstrate controlled amplitude oscillations of n-level amplitudes on femtosecond time scales.Fil: Preclíková, J.. University of Bergen; NoruegaFil: Kozák, M.. Karlova Univerzita; República ChecaFil: Fregenal, Daniel Eduardo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Frette, Ø.. University of Bergen; NoruegaFil: Hamre, B.. University of Bergen; NoruegaFil: Hjertaker, B. T.. University of Bergen; NoruegaFil: Hansen, J. P.. University of Bergen; NoruegaFil: Kocbach, L.. University of Bergen; Norueg

Slowly driven sandpile formation with granular mixtures

We introduce a one-dimensional sandpile model with $N$ different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial when N=1, but for N=2 we observe four broad classes of sandpile structure in different regions of the parameter space. We describe and explain the behaviour of each of these classes, giving quantitative analysis wherever possible. The behaviour of sandpiles with N>2 essentially consists of combinations of these four classes. We investigate the model's robustness and highlight the key areas that any experiment designed to reproduce these results should focus on

Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of L\'evy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.Comment: 4 pages, RevTex, includes 3 PostScript figures, submitted to Phys. Rev. Let