6,139 research outputs found
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 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 =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
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