Branching Process in a Stochastic Extremal Model

We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the the number $M$ of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions $d$ =1 and 2. However on the scale-free graphs the critical fitness value is non-zero even in the thermodynamic limit but the critical behavior is mean-field like. Finally $$ has been made even smaller than two by probabilistically updating the mutation zone which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.Comment: 6 pages, 7 figure

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

A quasi-random spanning tree model for the early river network

We consider a model for the formation of a river network in which erosion process plays a role only at the initial stage. Once a global connectivity is achieved, no further evolution takes place. In spite of this, the network reproduces approximately most of the empirical statistical results of natural river network. It is observed that the resulting network is a spanning tree graph and therefore this process could be looked upon as a new algorithm for the generation of spanning tree graphs in which different configurations occur quasi-randomly. A new loop-less percolation model is also defined at an intermediate stage of evolution of the river network.Comment: 10 pages, RevTex, 4 postscript figures, accepted in PR

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