Tumor growth has long been a target of investigation within the context of mathematical and computer modeling. The objective of this study is to propose and analyze a two-dimensional stochastic cellular automata model to describe avascular solid tumor growth, taking into account both the...

A concept of higher order neighborhood in complex networks, introduced previously [Phys. Rev. E <Emphasis Type="Bold">73, 046101 (2006)], is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself,...</emphasis>

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance r<Superscript>α</Superscript>, 1α2, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and...</superscript>

Substitution sequences are used for modelling non-homogeneous interactions between elements (atoms, spins, etc.) that form up neither periodic nor disordered lattice models whose physical properties may be different from those of homogeneous systems. In this work, we present a classification of...

The power law sensitivity to initial conditions is investigated for self-organized critical (SOC) models within the damage spreading framework. A class of two-dimensional abelian directed models are analyzed. Results for the time evolution of the normalized squared euclidian distance indicate...

We analyze the ferromagnetic Ising model on non-Euclidean scale invariant lattices with aperiodic interactions (J <Subscript> A </Subscript>,J <Subscript> B </Subscript>,J <Subscript> C </Subscript>,J <Subscript> D </Subscript>) defined by Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR) and transfer matrix (TM) techniques. The analysis of the invariant sets...</subscript></subscript></subscript></subscript>

We report some numerical simulations to investigate the existence of a self-organized critical (SOC) state in a random-neighbor version of the OFC model for a range of parameters corresponding to a non-conservative case. In contrast to a recent work, we do not find any evidence of SOC. We use a...

We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal–Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the...