Related papers: Scaling in a simple model for surface growth in a …
We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…
The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
We consider a discrete-time stochastic growth model on the $d$-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation,…
We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption ($u_a$) and desorption($u_d$) rates…
The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $\phi$ where $\phi=0$ and $1$ represent a regular lattice and a random network respectively. In the…
We extend existing connections between random walks, branching processes, and spatial branching processes, and their respective scaling limits, to include processes in dependent random environments. More specifically, we prove new scaling…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…
Random deposition model with surface diffusion over several next nearest neighbours is studied. The results agree with the results obtained by Family for the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441, 1986].…