514 research outputs found
Are Forest Fires Predictable?
Dynamic mean field theory is applied to the problem of forest fires. The
starting point is the Monte Carlo simulation in a lattice of million cells. The
statistics of the clusters is obtained by means of the Hoshen--Kopelman
algorithm. We get the map , where is the probability of
finding a tree in a cell, and is the discrete time. We demonstrate that the
time evolution of is chaotic. The arguments are provided by the calculation
of the bifurcation diagram and the Lyapunov exponent. The bifurcation diagram
reveals several windows of stability, including periodic orbits of length
three, five and seven. For smaller lattices, the results of the iteration are
in qualitative agreement with the statistics of the forest fires in Canada in
years 1970--2000.Comment: 13 pages, 13 figure
Language complexity of rotations and Sturmian sequences
AbstractGiven a rotation of the circle, we study the complexity of formal languages that are generated by the itineraries of interval covers. These languages are regular iff the rotation is rational. In the case of irrational rotations, our study reduces to that of the language complexity of the corresponding Sturmian sequences. We show that for a large class of irrationals, including e, all quadratic numbers and more generally all Hurwitz numbers, the corresponding languages can be recognized by a nondeterministic Turing machine in linear time (in other words, belongs to NLIN)
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