相关论文: Crossover from Self--Similar to Self--Affine Struc…
In bootstrap percolation it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
Many real-world infrastructures, from sensor and road networks to power grids, are spatially embedded and anisotropic, with constraints on the maximum number of links each node can establish. Such systems can be represented as anisotropic…
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly…
Using molecular dynamics simulations we investigate the translational dynamics of particles with dipolar interactions in homogenous external fields. For a broad range of concentrations, we find that the anisotropic, yet normal diffusive…
Scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is still lacking, which is of our interest in this…
We show that smoothing of multiaffine surfaces that are generated by simulating a crosslinked polymer gel by a frustrated, triangular network of springs of random equilibrium lengths [G.M. Buend{\'\i}a, S.J. Mitchell, P.A. Rikvold, Phys.…
We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We consider numerically the crossover scaling behavior from the directed percolation universality class to the compact directed percolation universality class within the one-dimensional Domany-Kinzel cellular automaton. Our results are…
A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of…
Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show…