Critical behaviour of a tumor growth model: Directed Percolation with a mean-field flavour
A. Lipowski1 , A.L. Ferreira2 , J. Wandykier3
1 Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland
2 Departamento de Fisica and I3N, Universidade de Aveiro, 3810-193 Aveiro, Portugal
3 Institute of Physics, Opole University, 45-052 Opole, Poland
Phys. Rev. E, 86, 041138 (2012)
We examine the critical behaviour of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report (Ferreira et al., Phys. Rev. E 85, 010901 (2012)), which suggested that the critical behaviour of the model differs from the expected Directed Percolation (DP) universality class. Surprisingly, only some of the critical exponents (beta, alpha, nu_perp, and z) take non-DP values while some others (beta', nu_||, and spreading-dynamics exponents Theta, delta, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations beta=alpha*nu_||, beta'=delta*nu_||, and the generalized hyperscaling relation Theta+alpha+delta=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent beta most likely takes the mean-field value beta=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient.