Related papers: A survey on dynamical percolation
Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…
We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in micro-fluidic micro-models of porous media.…
The Social Percolation model recently proposed by Solomon et al. is studied on the Ising correlated inhomogeneous network. The dynamics in this is studied so as to understand the role of correlations in the social structure. Thus the…
In the colour string model the impact of string percolation on multiplicities, their long-range correlations and average transverse momentum is studied. The multiplicities are shown to be damped by a simple factor which follows from the…
Seals are extremely useful devices to prevent fluid leakage. However, the exact mechanism of roughness induced leakage is not well understood. We present a theory of the leak-rate of seals, which is based on percolation theory and a…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
We study a simple model of the stochastic information filtering, in a randomly organized information system. For simplest versions of the model it appears to be possible to describe the filtering dynamics in terms of the master equations.…
We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be…
Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
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…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…