Sharif Digital Repository

Recently, a new tool in the study of two-dimensional continuous phase transition was provided by Schramm-Loewner evolution. The main part of SLE is a conformal map which relates growth process of a two-dimensional simple curve to one-dimensional motion on the real axis (so-called Loewner driving function). Time evolution of this map and Loewner driving function is connected via the Loewner differential equation. It turns out that for a certain class of stochastic and conformally invariant curves in two dimensions, the driving function shows Brownian motion in one dimension. Strength point of SLE comes from this fact that all the geometrical properties of such curves is described through a... 

Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... 

Brown and Henneaux showed that asymptotic symmetries of asymptotically form a conformal group in two dimensions [1]. Also they could derive classical central charge of theory. Fourteen years later, Maldacena, conjectured that this Holographic correspondence could be true for a specific theory a simplified chromodynamics in the boundary of ), this holographic theory attracted physicist communitee's attention. Many physicists tried to make this conjecture more precise. It is worth to say that, no example of holographic correspondence has been completely proven, till now, Because of the difficulty of the calculation. However these days we consider Madacena conjectrure in any arbitrary... 

Kardar-Parisi-Zhang (KPZ) equation was first proposed as a model to explain surface growth. This equation is very similar to Edwards-Wilkinson (EW) equation that is used to study scaling phenomena in non-equilibrium systems and phase transition. Although EW’s universality classes have been known well, it still remains a problem for KPZ. In the present thesis, in addition to a general review on surface growth models and a study on properties of rough surfaces, we study the physics of the KPZ model and the other related physical models. Also, using numerical results (like SLE method), renormalization group results and simulation, we study the dynamic and roughness exponents (α, z), and the... 

In the last two decades, Convolutional Neural Networks (CNN) have shown significant capabilities in artificial intelligence. These networks are able to provide comprehensive conclusions about the overall behavior a system by analyzing the relationship between the components of that system; Clearly, these networks have been successful in performing categorization tasks. However, there are no coherent theories as to why they work, and how to optimize them. On the other hand, according to recent research on the relationship between deep networks (in computer science) and Renormalization Group (in physics), convolutional networks seem to use a method similar to the Density Matrix Renormalization... 

XY Model due to topological defects (or vortex) has topological phase transition. According Kosterlitz-Thouless (KT) theory, phase transition is from low-temperature bounded vortices to high-temperature free vortices. XY model is appropriate choice for description of superfluidity in 2d thin films of . KT theory predicts universal jump in mass density of 2d superfluid in phase transition point. It is confirmed experimentally by Bishop and Reppy. All critical behavior of XY model is described with 2d coulomb gas, vortices are topological charges of the gas. KT predict variance of topological charge should obey of the “surface law vs perimeter law”, similar to behavior of Wilson loop in ... 

We propose a model for friction between two rough surfaces based on extreme value statistics (EVS). Different models for single-asperity contact, including adhesive and elasto-plastic contacts, were combined with EVS. The Hertzian model for contacts and Gumbel distribution for summit heights show the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson (GW) model. In comparison with other EVS distribution, Gumbel distribution seems the proper choice for summit‘ s height. Interestingly, here again, elasto-plastic contact and Gumbel distribution for summits achieve the best conformity with Amontons... 

In this study, we investigate opinion formation in society using the Blume–Capel model. The Blume–Capel model is a physical spin model in which each site can adopt one of three spin states; we use these spins to represent individuals’ opinions. Each spin corresponds to a distinct opinion (for example, positive, negative, or neutral), and the interactions among spins drive the dynamics of opinion formation in a community. In this research, we examine the Blume–Capel model and its ability to explain social phenomena such as societal bipolarization or multipolarization, as well as other related effects. We employ the model to simulate opinion–formation processes across various communities and... 

Statistical mechanics offers an important outlook for studying rough surfaces. Loop model is one of the effective statistical methods for study of surfaces. We present and analyze this method for characterization of the morphology of rough surfaces. By statistics of contour loops which could be obtained from an ensemble of a surface such as the SOS model, one can calculate fractal dimension, loops’ length and the probability of connection of two points by a certain loop, etc. Armed with these results, critical exponents in two dimensions are exactly obtainable. In this thesis, after reviewing the properties of different rough surfaces, we shall pursue some results on statistical analysis of... 

The effectiveness of activated bentonite, known as Clay, is studied in the process of removal of olefins from aromatics. The study on this subject can be divided in two categories: catalysis and process section. The catalyst activities is evaluated with the production of clay samples that are activated by sulfuric acid and hydrochloric acid. The performance and life time of the acid treated are characterized by XRD, XRF, BET, Pyridine FTIR analysis, SEM images and pilot test of the samples. In the process section, factors that are affecting the life time and performance of the catalytic activity of Clay are investigated and the effect of each known parameter on the operating time of this... 

The dimer model studies random dimer covers of a graph. A dimer cover is a subset of the edges of the graph such that each vertex is the endpoint of exactly one edge.The double-dimer model is a natural generalization of the dimer model, whose configuration is a union of two dimer covers, which ends up a set of even-length simple loops and doubled edges.The goal of this thesis is the study of statistical properties of very long doubledimer loops in very large lattices. To this end, we use the Grassmannian representation of the dimer model to compute some loop-related observables in rectangular domains of the square lattice, i.e. 1) the probability distribution of the number of nontrivial... 

Classical quench is the act of sudden change in the temperature of a system. This process is not new and has been used in some branches of science, like the smithing industry to produce a hard and stiff metal objects. Quantum Quench is the deformation of system's Hamiltonian in short time interval. This quantum version of quench is around for a few years and has attracted a lot of attention after its experimental realization in Ultracold Atoms setup. Suppose we have hamiltonian which depends on the constant g_0 which is the dynamical parameter of the system. It could be interaction strength between elements in the system or the external electric field amplitude on the system. At an arbitrary...