pore network modeling uses a network of pores connected by throats to model the void space of a porous medium and tries to predict its various characteristics during multiphase flow of various fluids. in most cases, a non-realistic regular lattice of pores is used to model the characteristics of a porous medium. although some methodologies for extracting geologically realistic irregular network...

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time τ and the lattice spacing. The analytic solutions are the exact representation of these two flows without an...

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by 7 th-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.

The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali and I. V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional thermal model on the standard square lattice with nine velocities is developed and validated in the thermal Couette and Rayleigh-Bénard natural convection pr...

In 1980, Kesten showed the exponential decay of percolation probability in the subcritical phase for the two-dimensional percolation model. This result implies his celebrated computation that pc = 0.5 for bond percolation in the square lattice, and site percolation in the triangular lattice, respectively. In this paper, we present a simpler proof for Kesten’s theorem.

the quasi-periodic order is a type of geometrical order in universe which is observed in the structure of quasi-crystals. this order was first introduced in mathematics in 1973 by roger penrose and then discovered in quasi-crystals in 1984 while spreading in mathematics, chemistry and physics. the paper professor james lu et al published in science magazine in 2007 illustrated that iranians wer...

This paper introduces a novel feature extraction algorithm called FEUDOR. The features extracted by this method are octagonal homogeneous regions that have different mean square difference compared to their surrounding area. By using integral images we have implemented this algorithm efficiently. We have shown that the repeatability score of FEUDOR under various image transformations is compara...

Berezinskii-Kosterlitz Thouless (BKT) transition is a phase transition on spin vectors at 2 dimensional lattice from bound vortex anti vortex at low temperatures to unpaired vortices and anti-vortices above critical temperature. Those two phases di er in the way their long distance correlations decay, as a power law (at low temperatures) or exponentially above critical temperature. In disordere...

In 2003 Biskup [Commun. Math. Phys. 242, 137 (2003)] gave a rigorous proof for the behavior of equilibrium droplets in the two-dimensional (2D) spin-1/2 Ising model (or, equivalently, a lattice gas of particles) on a finite square lattice of volume V with a given excess delta M identical with M-M 0 of magnetization compared to the spontaneous magnetization M 0=m0V . By identifying a dimensionle...

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interaction J l , and a kth neighbor antiferromagnetic interaction J~. When Jk /J i = -1 /k , there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find tha...