Related papers: A survey on dynamical percolation
Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
A discussion on the viscoelastic properties of weakly attractive colloids and the relation to a newly developed percolation theory is presented. The need for taking into account the particle-particle bond lifetime in order to compare…
Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
We describe the percolation model and some of the principal results and open problems in percolation theory. We also discuss briefly the spectacular recent progress by Lawler, Schramm, Smirnov and Werner towards understanding the phase…
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…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…