Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2012-03-21
Nonlinear Sciences
Chaotic Dynamics
Short talk presented at The 13th Small Triangle Meeting on Theoretical Physics, November 13-16, 2010, Star\'a Lesn\'a, Slovaki
Scientific paper
Using perturbative renormalization group we study the influence of random velocity field on the critical behaviour of directed bond percolation process near its second-order phase transition between absorbing and active phase. We consider Kraichnan model with finite correlation time for modelling advecting velocity field. Using functional integral representation we are able to apply field-theoretic renormalization group to determine possible universality classes. The model is analyzed near its critical dimension by means of three-parameter expansion in $\epsilon,\delta,\eta$, where $\epsilon$ is the deviation from the Kolmogorov scaling, $\delta$ the deviation from the critical space dimension $d_c$ and $\eta$ is the deviation from the parabolic dispersion law for the velocity correlator. Fixed points with corresponding regions of stability are evaluated to the leading order in the perturbation scheme.
Hnatic Michal
Lucivjansky Tomas
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