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Recent numerical studies have provided evidence that within the family of conservative, undirected sandpile models with short range dynamic rules, deterministic models such as the Bak-Tang-Wiesenfeld model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] and stochastic models such as the Manna model [S. S. Manna, J. Phys. A 24, L363 (1991)] belong to different universality classes. In this paper we examine the universality within each of the two classes in two dimensions by numerical simulations. To this end we consider additional deterministic and stochastic models and use an extended set of critical exponents, scaling functions, and geometrical features. Universal behavior is found within the class of deterministic Abelian models, as well as within the class of stochastic models (which includes both Abelian and non-Abelian models). In addition, it is observed that deterministic but non-Abelian models exhibit critical exponents that depend on a parameter, namely they are nonuniversal.
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Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. Recent empirical studies of stock market indices examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Lévy-stable distribution L(alpha)(r) with some index 0
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The study of the formation of molecular hydrogen on low-temperature surfaces is of interest both because it enables the exploration of elementary steps in the heterogeneous catalysis of a simple molecule and because of its applications in astrochemistry. Here, we report results of experiments of molecular hydrogen formation on amorphous silicate surfaces using temperature-programmed desorption (TPD). In these experiments, beams of H and D atoms are irradiated on the surface of an amorphous silicate sample. The desorption rate of HD molecules is monitored using a mass spectrometer during a subsequent TPD run. The results are analyzed using rate equations, and the energy barriers of the processes leading to molecular hydrogen formation are obtained from the TPD data. We show that a model based on a single isotope provides the correct results for the activation energies for diffusion and desorption of H atoms. These results are used in order to evaluate the formation rate of H2 on dust grains under the actual conditions present in interstellar clouds. It is found that, under typical conditions in diffuse interstellar clouds, amorphous silicate grains are efficient catalysts of H2 formation when the grain temperatures are between 9 and 14 K. This temperature window is within the typical range of grain temperatures in diffuse clouds. It is thus concluded that amorphous silicates are good candidates to be efficient catalysts of H2 formation in diffuse clouds.
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A generic model of stochastic autocatalytic dynamics with many degrees of freedom w(i,) i=1, em leader,N, is studied using computer simulations. The time evolution of the w(i)'s combines a random multiplicative dynamics w(i)(t+1)=lambdaw(i)(t) at the individual level with a global coupling through a constraint which does not allow the w(i)'s to fall below a lower cutoff given by cw, where w is their momentary average and 0
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A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method [Phys. Rev. Lett. 78, 4733 (1997)] is developed. This approach provides a classification of the set of transformations necessary for finding the orbits. Applications to the Ikeda and Henon map are performed, allowing a study of the distributions of Lyapunov exponents for high periods. In particular, the properties of the least unstable orbits up to period 36 are investigated and discussed.
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We present a model that describes adsorption and clustering of particles on a surface. A clustering transition is found that separates between a phase of weakly correlated particle distributions and a phase of strongly correlated distributions in which the particles form localized fractal clusters. The order parameter of the transition is identified and the fractal nature of both phases is examined. The model is relevant to a large class of clustering phenomena such as aggregation and growth on surfaces, population distribution in cities, and plant and bacterial colonies, as well as gravitational clustering.