Quantum Physics Division

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Critical behaviour of a tumor growth model: Directed Percolation with a mean-field flavour

A. Lipowski^{1}
,
A.L. Ferreira^{2}
,
J. Wandykier^{3}

^{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)**

**DOI:** 10.1103/PhysRevE.86.041138

Abstract:

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.

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