Related papers: Two-dimensional forest fires with boundary ignitio…
Wildfires are uncontrolled fires in the environment that can be caused by humans or nature. In 2020 alone, wildfires in California have burned 4.2 million acres, damaged 10,500 buildings or structures, and killed more than 31 people,…
We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the…
Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed $v>1$. How large must $v$ be to ensure that the fire can be contained, and how should the fire fighter proceed? We…
Forest fires are among the most dangerous and unpredictable natural disasters worldwide. Forest fire can be instigated by natural causes or by humans. They are devastating overall, and thus, many research efforts have been carried out to…
Inspired by Stufler's recent probabilistic proof of Otter's asymptotic number of unlabeled trees, we revisit work of Palmer and Schwenk, and study unlabeled forests from a probabilistic point of view. We show that the number of trees in a…
We study a model for the destruction of a random network by fire. Suppose that we are given a multigraph of minimum degree at least 2 having real-valued edge-lengths. We pick a uniform point from along the length and set it alight; the…
We present a simple, efficient model for learning boundary detection based on a random forest classifier. Our approach combines (1) efficient clustering of training examples based on simple partitioning of the space of local edge…
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…
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…
The paper aims at assessing a hypothesis that resolution required to evaluate fuel consumption and heat release rates by directly (i.e., without a subgrid model of unresolved influence of small-scale turbulent eddies on the local flame)…
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically,…
A recent rotational flamelet model is developed and tested with an improved framework of detailed chemistry and transport. The rotational flamelet model incorporates the effects of shear strain and vorticity on local flame behavior and is…
In this paper we study the potential theory of Dirichlet forms on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-\alpha}\mathcal{B}(x,y)$ and the killing potential $\kappa x_d^{-\alpha}$, where $\alpha\in (0,…
The research deals with a study of local fractality in spatial distribution of forest fires in Portugal using the sandbox method. The general procedure is the following: (a) define a circle centred in each and all events with increasing…
We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary.…
Consider percolation on $T\times \mathbb{Z}^d$, the product of a regular tree of degree $k\geq 3$ with the hypercubic lattice $\mathbb{Z}^d$. It is known that this graph has $0<p_c<p_u<1$, so that there are non-trivial regimes in which…
The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…
Let C_n be the origin-containing cluster in subcritical percolation on the lattice (1/n) Z^d, viewed as a random variable in the space Omega of compact, connected, origin-containing subsets of R^d, endowed with the Hausdorff metric delta.…
Wildfires pose a significant natural disaster risk to populations and contribute to accelerated climate change. As wildfires are also affected by climate change, extreme wildfires are becoming increasingly frequent. Although they occur less…