Related papers: Fluid leakage near the percolation threshold
Wireless multi-hop ad hoc communication networks represent an infrastructure-less and self-organized generalization of todays wireless cellular networks. Connectivity within such a network is an important issue. Continuum percolation and…
Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
We study how much water can be retained without leaking through boundaries when each unit square of a two-dimensional lattice is randomly assigned a block of unit bottom area but with different heights from zero to $n-1$. As more blocks are…
Online experimentation platforms abstract away many of the details of experimental design, ensuring experimenters do not have to worry about sampling, randomisation, subject tracking, data collection, metric definition and interpretation of…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully…
We have developed a theory of air leakage at interfaces between two elastic solids with application to suction cups in contact with randomly rough surfaces. We present an equation for the airflow in narrow constrictions which interpolate…
The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin…
Many new products fail, despite preliminary market surveys having determined considerable potential market share. This effect is too systematic to be attributed to bad luck. We suggest an explanation by presenting a new percolation theory…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
Pipelines for water supply are susceptible to burst-leakage due to fluid pressures of various nature. High pressure heads resulting in circumferential and (or) axial stresses larger than the material yield stress could cause pipe failure.…
Dispersal is essential to the plethora of motile microorganisms living in porous environments, yet how it relates to movement patterns and pore space structure remains largely unknown. Here we investigate numerically the long-time dispersal…
An analysis of water clustering is used to study the quasi-2D percolation transition of water adsorbed at planar hydrophilic surfaces. Above the critical temperature of the layering transition (quasi-2D liquid-vapor phase transition of…
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have…
This paper discusses first passage percolation and flooding on large weighted sparse random graphs with two types of nodes: active and passive nodes. In mathematical physics passive nodes can be interpreted as closed gates where fluid flow…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…