Related papers: Scale Dependent Dimension in the Forest Fire Model
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical…
We explore the fractal nature of particle showers using Monte-Carlo simulation. We define the fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
We investigate the cosmological evolution of an interacting phantom energy model in which the phantom field has interaction with the dark matter. We discuss the existence and stability of scaling solutions for two types of specific…
In dense molecular clouds collisions between dust grains alter the ISM-dust size distribution. We study this process by inserting the results from detailed numerical simulations of two colliding dust aggregates into a coagulation model that…
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…
The Drossel-Schwabl Forest Fire Model is one of the best studied models of non-conservative self-organised criticality. However, using a new algorithm, which allows us to study the model on large statistical and spatial scales, it has been…
We consider random dynamics on a uniform random recursive tree with $n$ vertices. Successively, in a uniform random order, each edge is either set on fire with some probability $p_n$ or fireproof with probability $1-p_n$. Fires propagate in…
Rugged (or, rough) energy landscape (REL) with spatially distributed maxima and minima are often employed in applications of physics, chemistry and biology (enzyme kinetics, protein folding, diffusion in disordered solids, transport in…
We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential…
A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is…
We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…
We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
Armed conflict data display scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching, armed-conflict model that relates multiple properties to one another…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal…
A holographic dark energy model characterized by the conformal-age-like length scale $L= \frac{1}{a^4(t)}\int_0^tdt' a^3(t') $ is motivated from the four dimensional spacetime volume at cosmic time $t$ in the flat Friedmann-Robertson-Walker…