Related papers: Scale Dependent Dimension in the Forest Fire Model
In this article we present an example of a random oriented tree model on d-dimensional lattice, that is a forest in d=3 with positive probability. This is in contrast with the other random tree models in the literature which are a forest…
We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are…
Straightforward physical arguments are used to derive the properties of Lyman-alpha forest absorbers. It is shown that many aspects of the current physical picture of the forest, in particular the fact that the absorption arises in extended…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…
The non-equilibrium dynamics of three paradigmatic models for two-dimensional systems with quenched disorder is studied with a focus on the existence and analysis of a growing length scale during aging at low temperatures: 1) The random…
We consider a deterministic discrete-time model of fire spread introduced by Hartnell [1995] and the problem of minimizing the number of burnt vertices when deploying a limited number of firefighters per timestep. We consider the process…
We investigate the GOY shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an ``effective dimension'' between $d=2$ and $d=3$. We identify a…
To the naked eye, turbulent flows exhibit whirls of many different sizes. To each size, or scale, corresponds a fraction of the total energy resulting from a cascade in five dimensions: scale, time and three-dimensional space. Understanding…
According to Richardson's cascade description of turbulence, large vortices break up to form smaller ones, thereby transferring kinetic energy towards smaller scales. Energy dissipation occurs at the smallest scales due to viscosity. We…
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed…
Atmospheric flows exhibit scale-free fractal fluctuations. A general systems theory based on classical statistical physical concepts visualizes the fractal fluctuations to result from the coexistence of eddy fluctuations in an eddy…
We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
We investigate the properties of the Lyman alpha forest as predicted by numerical simulations for a range of currently viable cosmological models. This is done in order to understand the dependencies of the forest on cosmological…
We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random…