相关论文: Crossover from directed percolation to compact dir…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…

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.…

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…

We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…

We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…

Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…

We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…

A detailed study of critical spreading in the one-dimensional pair contact process is performed using a recently devised reweighting method. The results confirm the validity of a generalized hyperscaling relation among the (nonuniversal)…

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…

We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging…

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…

We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…

In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…

Recently, the number of non-standard percolation models has proliferated. In all these models, there exists a phase transition at which long range connectivity is established, if local connectedness increases through a threshold $p_c$. In…