Sharif Digital Repository

We introduce a scheme for perfect state transfer in regular two- and three-dimensional structures. The interactions on the lattices are of the XX spin type with uniform couplings. In two dimensions, the structure is a hexagonal lattice, and in three dimensions, it consists of hexagonal planes joined to each other at arbitrary points. We will show that compared to other schemes, much less control is needed for routing, the algebra of global control is quite simple, and the same kind of control can upload and download qubit states to or from built-in read-write heads  

We study the first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time of the fractional Brownian motion and subordinated walk on the different fractal curves (loop-erased random walk, harmonic explorer, and percolation front) are derived. We also define natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean-square displacement and mean first passage time for NS-SLE are obtained by numerical means  

In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot (WM) function as the drift of the Loewner equation we introduce a large class of fractal curves with discrete scale invariance (DSI). We show that the fractal dimension of the curves can be extracted from the diffusion coefficient of the trend of the variance of the WM function. We argue that, up to the fractal dimension calculations, all the WM functions follow the behavior of the corresponding Brownian motion. Our study opens a way to classify all the... 

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  

The authors' research work on pressure drop along gas transmission pipelines raised questions regarding the development length of the corresponding compressible flow and the effect of heat transfer in the entrance region on the pressure drop along the whole length of the pipe. In this paper, laminar, viscous, compressible flow in the entrance region of a pipe is investigated numerically in two dimensions. The numerical procedure is a finite-volume based finite-element method applied on unstructured grids. This combination together with a new method applied for boundary conditions allows accurate computation of the variables in the entrance region. The method is applied to some incompressible... 

In poorly developed fractured rocks, the contribution of individual fracture on rock conductivity should be considered. However, due to the lack of data, a deterministic approach cannot be used. The conventional way to model discrete fractures is to use a Poisson process, with prescribed distribution, for fracture size and orientation. Recently, a stochastic approach, based on the idea that the elastic energy due to fractures follows a Boltzmann distribution, has been used to generate realizations of correlated fractures in two dimensions. The elastic energy function has been derived by applying the appropriate physical laws in an elastic medium. The resulting energy function has been used... 

Oil reservoirs are very complex with geological heterogeneities that appear on all scales. Proper modeling of the spatial distribution of these heterogeneities is crucial, affecting all aspects of flow and, consequently, the reservoir performance. Reservoir connectivity and conductivity evaluation is of great importance for decision-making on various possible development scenarios including infill drilling projects. This can be addressed by using the percolation theory approach. This statistical approach considers a hypothesis that the reservoir can be split into either permeable (good sands) or impermeable flow units (poor sands) and assumes that the continuity of permeability contrasts...