%0 Journal Article %1 Lipowski2012Critical %A Lipowski, Adam %A Ferreira, António L. %A Wendykier, Jacek %D 2012 %J Physical Review E %K cancer, directed\_percolation, lattice\_model %N 4 %R 10.1103/PhysRevE.86.041138 %T Critical behavior of a tumor growth model: Directed percolation with a mean-field flavor %U http://dx.doi.org/10.1103/PhysRevE.86.041138 %V 86 %X 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.

@article{Lipowski2012Critical, 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.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Lipowski, Adam and Ferreira, Ant\'{o}nio L. and Wendykier, Jacek}, biburl = {https://www.bibsonomy.org/bibtex/216b547a52ee61dea916a56a3f133dfd7/nonancourt}, citeulike-article-id = {10786582}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.86.041138}, citeulike-linkout-1 = {http://arxiv.org/abs/1206.2392}, citeulike-linkout-2 = {http://arxiv.org/pdf/1206.2392}, day = 11, doi = {10.1103/PhysRevE.86.041138}, eprint = {1206.2392}, interhash = {3432cd8f43b230a433ca4fa3710b5b7c}, intrahash = {16b547a52ee61dea916a56a3f133dfd7}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {cancer, directed\_percolation, lattice\_model}, month = oct, number = 4, posted-at = {2012-06-13 14:55:54}, priority = {2}, timestamp = {2019-06-10T14:53:09.000+0200}, title = {{Critical behavior of a tumor growth model: Directed percolation with a mean-field flavor}}, url = {http://dx.doi.org/10.1103/PhysRevE.86.041138}, volume = 86, year = 2012 }