Related papers: Percolation of hard disks
We investigate the effect of excluded volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean…
Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
An adapted, right-continuous, non-decreasing, integer-valued process with unit jumps and starting at zero has a minimal predictable intensity if and only if it is a standard Poisson process under an absolutely continuous transformation of…
A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
This paper analyses the impact of collisions in a system of $N$ identical hard-core particles driven according to a velocity jump process. The physical space is essentially a channel in $\mathbb{R}$ with a probability of occupants being…
The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by…
Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching…
We expect that the experimental study of percolation cluster formation and appearance of the critical transparency of the strongly interacting matter can give the information about the onset state of deconfinement.
In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered…
Let $X$ be either $Z^d$ or the points of a Poisson process in $R^d$ of intensity 1. Given parameters $r$ and $p$, join each pair of points of $X$ within distance $r$ independently with probability $p$. This is the simplest case of a…
We turn the long time puzzle of the free volume, known for its highly irregular form, into exact analytical formulae and develop statistical mechanics of the hard disk model. The free volume is exactly expressed in terms of the intersection…
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
Some of the centrality experiments indicate regime change and saturation in the behavior of characteristics of the secondary particles. It is observed as a critical phenomenon for hadron-nuclear, nuclear-nuclear interactions and…
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system…
The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…
I consider a one dimensional system of particles which interact through a hard core of diameter $\si$ and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$…