相关论文: Universal Scaling of Gap Dynamics in Percolation

The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…

We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…

In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…

Moving beyond simple associations, researchers need tools to quantify how variables influence each other in space and time. Correlation functions provide a mathematical framework for characterizing these essential dependencies, revealing…

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular…

Mitra et al. [Phys. Rev. E 99 (2019) 012117] proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But the conclusion is…

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the…

Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…

The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…

The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…

Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…

It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…

Marine stratocumulus clouds play a critical role in the Earth's climate system. They display an amazing array of complex behaviors at many different spatiotemporal scales. Precipitation in these clouds is in general very light, but it is…

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature…

We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…

Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…

We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of…