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Observation of SLE$(\kappa,\rho)$ on the Critical Statistical Models
Schramm-Loewner Evolution (SLE) is a stochastic process that helps classify critical statistical models using one real parameter $\kappa$. Numerical study of SLE often involves curves that start andExpand
Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point.
The carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage is characterized and the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Expand
Water propagation in two-dimensional petroleum reservoirs
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 thisExpand
Geometrical clusters of Darcy's reservoir model and Ising universality class
In this paper the geometrical features of the fluid propagation in two-dimensional petroleum reservoir described by Darcy equations are studied. The porous media are considered to be tuned by theExpand
Avalanche frontiers in the dissipative Abelian sandpile model and off-critical Schramm-Loewner evolution.
This paper considers the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation, finding that the avalanche frontiers tend to self-avoiding walk and the corresponding driving function is proportional to the Brownian motion. Expand
Statistical investigation of the cross sections of wave clusters in the three-dimensional Bak-Tang-Wiesenfeld model.
The analysis of the critical loops that are interfaces of the 2D-induced model is of special importance and it is shown that their fractal dimension is D(f)=1.387±0.005, which is compatible with the Fractal dimension of the external perimeter of geometrical spin clusters of 2D critical Ising model. Expand
Bak–Tang–Wiesenfeld model on the square site-percolation lattice
The Bak–Tang–Wiesenfeld (BTW) model is considered on the site-diluted square lattice, tuned by the occupancy probability p. Various statistical observables of the avalanches are analyzed in terms ofExpand
Monte Carlo study of the Ising ferromagnet on the site-diluted triangular lattice
Abstract In this paper we consider the Ising model on the triangular percolation lattice and analyze its geometrical interfaces and spin clusters. The (site) percolation lattice is tuned by theExpand
Observation of Schramm-Loewner evolution on the geometrical clusters of the Ising model
Schramm–Loewner Evolution (SLE) is a stochastic process that, by focusing on the geometrical features of the two-dimensional (2D) conformal invariant models, classifies them using one real parameterExpand
Condensation of nonextensive ideal Bose gas and critical exponents
Abstract We investigate the condensation of a three dimensional nonextensive ideal Bose gas. We use the distribution function of nonextensive Bose statistics and define the q -generalizedExpand