407 research outputs found
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 and the other with
probability . The dependance produce crossovers between two different
regimes. We demonstrate that the coefficients of the continuous equation,
describing their universality classes, are quadratic in (or ). We show
that the origin of such dependance is the existence of two different average
time rates. Thus, the quadratic 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 , and ,
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
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