Related papers: Percolation fractal exponents without fractal geom…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical…
We investigate site percolation on a weighted planar stochastic lattice (WPSL) which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by percolation threshold $p_c$ and by a set of critical…
The well-known problem of gradient percolation has been revisited to study the probability distribution of island sizes. It is observed that as the ordinary percolation, this distribution is also described by a power-law decaying function…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
One of the most well-known classical results for site percolation on the square lattice is the equation p_c + p_c^* = 1. In words, this equation means that for all values different from p_c of the parameter p the following holds: Either…
The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown…
We study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter p(N) vary with the size N of the box that one is considering, three possibilities arise in…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
The model of the universe is considered in which background of the universe is not defined by the matter but is a priori specified as a homogenous and isotropic flat space. The scale factor of the universe follows the linear law. The scale…
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…
We analyse the scaling of the weights added by invasion percolation on a branching process tree. This process is a paradigm model of self-organised criticality, where criticality is approach without a prespecified parameter. In this paper,…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
We revisit a known model in which (conducting) blocks are hierarchically and randomly deposited on a $d$-dimensional substrate according to a hyperbolic size law with the block size decreasing by a factor $\lambda \, > 1$ in each subsequent…
In this note we study some properties of infinite percolation clusters on non-amenable graphs. In particular, we study the percolative properties of the complement of infinite percolation clusters. An approach based on mass-transport is…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in…