Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-02-13
Phys Rev E, 69, 065103(R), 2004
Physics
Condensed Matter
Disordered Systems and Neural Networks
9 pages, 3 figures
Scientific paper
10.1103/PhysRevE.69.065103
The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability $p$ and the other with probability $1-p$. The $p-$dependance produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in $p$ (or $1-p$). We show that the origin of such dependance is the existence of two different average time rates. Thus, the quadratic $p-$dependance is an universal behavior of all the CGM. We derive analytically the continuous equations for two CGM, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic CGM presented here and with the proposed scalings.
Braunstein Lidia A.
Buceta R. C.
Muraca D.
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