Related papers: Scaling behavior of randomly alternating surface g…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its…
Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…
We present a random-matrix realization of a two-dimensional percolation model with the occupation probability $p$. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a…
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…
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
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…
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…
To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining…
The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our…
We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent…