Fractal Dimension of Backbone of Eden Trees

We relate the fractal dimension of the backbone, and the spectral dimension of Eden trees to the dynamical exponent z. In two dimensions, it gives fractal dimension of backbone equal to 4/3 and spectral dimension of trees equal to 5/4. In three dimensions, it provides us a new way to estimate z numerically. We get z=1.617 +/- 0.004.Comment: 6 pages, Latex, and 4 postscript figures, uuencoded. Minor typographical errors, and problems with postscript files fixe

Internal Avalanches in a Granular Medium

Avalanches of grain displacements can be generated by creating local voids within the interior of a granular material at rest in a bin. Modeling such a two-dimensional granular system by a collection of mono-disperse discs, the system on repeated perturbations, shows all signatures of Self-Organized Criticality. During the propagation of avalanches the competition among grains creates arches and in the critical state a distribution of arches of different sizes is obtained. Using a cellular automata model we demonstrate that the existence of arches determines the universal behaviour of the model system.Comment: 4 pages (Revtex), Four ps figures (included

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.Comment: 5 pages, 6 figure