Sharif Digital Repository

In the present paper we investigate the problem of water propagation in 2 dimensional (2D) petroleum reservoir in which each site has the probability p of being occupied. We first analyze this propagation pattern described by Darcy equations by focusing on its geometrical features. We find that the domain-walls of this model at p=pc ≃ 0.59 are Schramm-Loewner evolution (SLE) curves with κ=3.05 ∓ 0.1 consistent with the Ising universality class. We also numerically show that the fractal dimension of these domain-walls at p=pc is Df ≃ 1.38 consistent with SLEκ=3. Along with this analysis, we introduce a self-organized critical (SOC) model in which the water movement is modeled by a chain of... 

In this paper we define some stochastic perturbations of the BTW model which make it into Manna model. These models have a continuous parameter p, where p = 0 and 1 correspond to the BTW and Manna models respectively. We have investigated the properties of the statistical observables of the waves of avalanches for various values of p. Our data supports the expectation of a crossover in such systems; at large scales Manna model is dominant. Therefore we find strong evidence in favor of the universality classes being distinct. Also it is observed that the BTW fixed point is unstable when Manna-type perturbation is added to the model  

We investigate the statistics of isoheight lines of (2+1) -dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged. The statistics of the winding angle confirms the previous observation that these contour lines are in the same universality class as self-avoiding random walks. © 2009 The American Physical Society  

Statistical behavior and scaling properties of isoheight lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLEκ). We present some evidence that the isoheight lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently SLE8/3. This leads to the conclusion that all these discrete growth models fall into the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in two dimensions  

In this paper, we consider several known growth processes with height-dependent noise. This type of noise is interesting from a theoretical standpoint, for example, it paves the way to the derivation of the exact height distribution of the KPZ equation through the Hopf–Cole transformation. In addition, it may have implications for experimental growth processes. Using numerical methods, we observe that adding such a noise to different growth processes, can change their universality class or ruin the scaling laws. In the case of Mullins–Herring equation, a two-fold cross-over is observed. © 2020 Elsevier B.V  

Supercoiled DNA, crumpled interphase chromosomes, and topologically constrained ring polymers often adopt treelike, double-folded, randomly branching configurations. Here we study an elastic lattice model for tightly double-folded ring polymers, which allows for the spontaneous creation and deletion of side branches coupled to a diffusive mass transport, which is local both in space and on the connectivity graph of the tree. We use Monte Carlo simulations to study systems falling into three different universality classes: ideal double-folded rings without excluded volume interactions, self-avoiding double-folded rings, and double-folded rings in the melt state. The observed static properties...