Related papers: Scaling in a simple model for surface growth in a …
Recently anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nano-porous medium, were reported: the mean height and the width of the propagating front increase with time $t$ both…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into…
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…
In this article we study a one dimensional model for a polymer in a poor solvent: the random walk on $\mathbb{Z}$ penalized by its range. More precisely, we consider a Gibbs transformation of the law of the simple symmmetric random walk by…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…
On the integer lattice we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane…
We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
In this study we have carried out computer simulations of random walks on Watts-Strogatz-type small world networks and measured the mean number of visited sites and the return probabilities. These quantities were found to obey scaling…
In this paper we study the scaling behavior of the fluctuations in the steady state $W_S$ with the system size $N$ for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD)…
We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The…
The dynamics of particle transport under the influence of localised high energy anomalies (explosions) is a complicated phenomena dependent on many physical parameters of both the particle and the medium it resides in. Here we present a…
We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Self-similar dynamical processes are characterized by a growing length scale $\xi$ which increases with time as $\xi \sim t^{1/z}$, where z is the dynamical exponent. The best known example is a simple random walk with z=2. Usually such…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
We present results of numerical simulations of kinetic roughening for a growth model with surface diffusion (the Wolf-Villain model) in 3+1 and 4+1~dimensions using lattices of a linear size up to $L=64$ in 3+1~D and $L=32$ in 4+1~D. The…