相关论文: Avalanches and the Directed Percolation Depinning …

The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry.…

We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…

Hyperuniformity is an emergent property, whereby the structure factor of the density $n$ scales as $S(q) \sim q^\alpha$, with $\alpha>0$. We show that for the conserved directed percolation (CDP) class, to which the Manna model belongs,…

In this study, we investigate the suitability of dissipative particle dynamics (DPD) simulations to predict the dynamics of polymer chains in dilute polymer solutions, where the chain is represented by a set of beads connected by almost…

In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…

We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete ``forest fire'' lattice models through Monte Carlo simulations in two and…

Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law…

The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…

There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…

The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented…

We uncover a nontrivial signature of the hierarchical structure of quasi-degenerate random directed polymers (RDPs) at zero temperature in 1+1 dimensional lattices. Using a cylindrical geometry with circumference $8 \leq W \leq 512$, we…

Study of the KPZ universality class has seen the emergence of universal objects over the past decade which arise as the scaling limit of the member models. One such object is the directed landscape, and it is known that exactly solvable…

We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…

In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena…

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…

In this article we discuss an exactly solvable, one-dimensional, periodic toy charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103}, 46002 (2013)]. In particular, driving the system with a uniform force, we show…

Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically…

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species…