The self-organized critical forest-fire model on large scales

We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively different types of fires that superimpose to give the effective exponents typically measured in simulations. We show that this explains not only why the exponent characterizing the fire-size distribution changes with increasing correlation length, but allows also to predict its asymptotic value. We support our arguments by computer simulations of a coarse-grained model, by scaling arguments and by analyzing states that are created artificially by superimposing the two types of fires.Comment: 26 pages, 7 figure

Phase Transitions in a Forest-Fire Model

We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only one side and hysteresis. The critical behavior is found to be that of the self-organized critical forest-fire model [B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992)], whereas in the adjacent phase one finds the spiral waves of the Bak et al. forest-fire model [P. Bak, K. Chen and C. Tang, Phys. Lett. A 147, 297 (1990)]. In the third phase one observes clustering of trees with the fire burning at the edges of the clusters. The relation between the density distribution in the spiral state and the percolation threshold is explained and the implications for stationary states with spiral waves in arbitrary excitable systems are discussed. Furthermore, we comment on the possibility of mapping self-organized critical systems onto 'ordinary' critical systems.Comment: 30 pages RevTeX, 9 PostScript figures (Figs. 1,2,4 are of reduced quality), to appear in Phys. Rev.

Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models

The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability $p$ and the other with probability $1-p$. The $p-$dependance produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in $p$ (or $1-p$). We show that the origin of such dependance is the existence of two different average time rates. Thus, the quadratic $p-$dependance is an universal behavior of all the CGM. We derive analytically the continuous equations for two CGM, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic CGM presented here and with the proposed scalings.Comment: 9 pages, 3 figure

Synchronization and Coarsening (without SOC) in a Forest-Fire Model

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.Comment: 23 pages, 13 figure

Forest fires and other examples of self-organized criticality

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.Comment: 37 pages RevTeX, 13 PostScript figures (Figs 1, 4, 13 are of reduced quality to keep download times small

Renormalization group approach to the critical behavior of the forest fire model

We introduce a Renormalization scheme for the one and two dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain $\nu=1.0$, $\tau=1.0$ and $\nu=0.65$, $\tau=1.16$ respectively for the one and two dimensional case, in very good agreement with numerical simulations.Comment: 4 pages, 3 uuencoded Postcript figure

Crossover from Percolation to Self-Organized Criticality

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As long as the immunity is below its critical value, the asymptotic critical exponents are those of the original self-organized critical model, i.e. the system performs a crossover from percolation to self-organized criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR

The impact of demographic developments on flood risk management systems in rural regions in the Alpine Arc

Demographic trends across Europe indicate that many regions face sustained population decline due to aging and out-migration. Rural regions are often prone to flood hazards and have repeatedly been affected by damaging events in the past. However, we lack in-depth knowledge about how demographic trends challenge their capacities, abilities, and plans to manage flood risks. In this paper, we aim to close this gap. We employed a mixed-methods approach in the Gailtal-region in Carinthia (Austria), which combines the assessment of exposure to flood risk, social vulnerability, coping ability and adaptation capacity, as well as a discourse analysis. This comprehensive approach was designed to assess how demographic change impacts flood risk management. The findings do not support the hypothesis that population decline increases communities’ social vulnerability and reduces their coping ability and adaptation capacity. Additionally, the selected municipalities showed a strong increase in exposure. This is an example of the exposure paradox, which describes the phenomenon that settlement and population dynamics are not interconnected at all, especially in regions with a limited share of suitable land. Finally, our results show that current flood risk management and the corresponding social and political discourse mainly neglect the challenge of population decline. Overall, this study indicates that public administrations need to address the challenges of weak communities in flood risk management and consider how they might empower local authorities and citizens to adapt to future events – in full consideration of the demographic trends they have to expect