Sharif Digital Repository

Ethylene process is one of the most complex systems in petrochemical industries.The first section of the ethylene plant is the cracking furnace.The radiant section of predicted olefin furnaces is symmetrical with respect to a plane through the center line of the furnace and at an angle of 90° with the side walls. There are a total of 24 vertical radiant coils located centrally in the firebox wherein, bottom andside wall burners supply the heat necessary. Each four coils known as a ZONE so, as a result there are six zones, called zone A through F. Failures(rapture, creep, material degradation) rate on the coils decreases from zone A to zone F (A, B, C, D, E and F) respectively.From... 

For a Banach space E and a compact metric space (X, d), a function F : X → E is a Lipschitz function if there exists k > 0 such that ∥F (x) − F (y)∥ ≤ kd(x, y) for all x, y ∈ X.The smallest such k is called the Lipschitz constant L(F ) for F . The space Lip(X, E) of all Lipschitz functions from X to E is a Banach space under the norm defined by ∥F ∥ = max{L(F ), ∥F ∥∞}, where ∥F ∥∞ = sup{∥F (x)∥ : x ∈ X}.Recent results characterizing isometries on these vector-valued Lipschitz spaces require the Banach space E to be strictly convex. We inves- tigate the nature of the extreme points of the dual ball for Lip(X, E) and use the information to describe the surjective isometries on Lip(X, E) under... 

Experiments conducted in recent two decades indicated critical behavior in neural activity at different scales. Theoretically occurrences of these critical and power-law behavior can significantly facilitate brain activities correspondent to computation and memory tasks, but attaining the critical point essentially demands externally fine-tuning which has not been established yet. This fine-tuning often lies with placing system at transition point. Recent studies of group showed that a transition from synchronous to asynchronous phase could be achievable by a change in external parameters. At the very transition point, neuronal avalanches statistically demonstrate a power-law behavior which... 

In this thesis, we deal with the problem of direction of arrival (DOA) using single-snapshot samples taken from multiple source signals by an array of sensors. The array we are looking for in this work is a uniform linear array. There are many ways to solve this problem, including MUSIC and Prony. But one of the few methods that are able to estimate correctly with single-snapshot samples with incomplete uniform linear arrays in compressed sensing base algorithms. In the first step, we can estimate the data of a incomplete uniform linear array by arranging them in the form of low-rank Hankel matrices and using leverage scores and minimizing the weight nuclear norm. If the weight matrices are... 

The purpose of Direction-of-arrival(DOA) estimation in MIMO communication networks is to find the direction of signals that are mixed together and mixed with noise by using an array of multiple receiving antennas. DOA estimation is an important issue in array signal processing. The traditional methods for DOA estimation try to solve this problem with mathematical algorithms. For example, some of these methods are based on parameter estimation; such as DOA estimation methods using maximum likelihood estimation methods. Some of other traditional methods are based on subspace decomposition; Like the famous MUSIC method. The traditional methods of DOA estimation usually have a drawback, and that... 

The rapid development of scientific areas in this modern era makes the process of finding new field of research slow and laborious for prospective scholars. Thus, having a vision of the future could be helpful to pick a right path for doing researches and ensuring that it is worth to invest in. This thesis seeks to predict research trends by using link prediction approaches on keywords network and discusses about the performance of various algorithms in different situations. Moreover, for the last part of the experiments, novel link prediction algorithms are proposed by the author, enhances the accuracy of prediction results. The data set collected from Sciencedirect and Scopus by a strong... 

A complte set of characteristic parameters of the sandpile models is still unknown. We have studied the existence of ”weak chaos” critical exponent in different sandpile models and we have shown that it is a characteristic exponent of deterministic models. We have shown that BTW and Zhang models do not belong to the same universality class (contrary to Zhang’s previous conjecture and contrary to Ben-Hur & Biham’s results.) Also we have shown that directed models, specificly Ramaswamy-Dhar’s directed model form a different universality class. ”Weak chaos” exponent in also studied in massive models and we have shown that by increase of dissipation, the exponent decreases rapidly to an... 

We study the Abelian Sandpile Model and its relation with surface growth. ese two models are related through their field theories and equations of motion. It has been shown that the different features of different sandpile models can be expressed in terms of the noise term in the surface growth equation. A mapping between the simplest sandpile model, the BTW model, and a surface growth has already been introduced. is surface growth has not been studied in details so far. In this thesis we study different features of this surface growth corresponding to the BTW model, continuous sandpile model and also massive abelian sandpile model. We also consider different boundary conditions  

The four-page article by Bak, Tang and Wiesenfeld in 1987 was a beginning to a new wave of physicists’ efforts to explain and describe the concept of complexity; a not-so-well-defined concept that resists against the reductionist tools and methods of physics. The Self-organized Criticality theory presented in that article via a simple model, known as sandpile model, was first of all an effort to explain the numerous occurrence of power law distribution in nature. SOC was introduced to tell us why so many natural phenomena like Earthquakes, landslides, forest fires, extinction and other seemingly non-related catastrophic events, more or less obey the scale-less power law distribution; A... 

In this research, we want to address the question of universality classes in BTW and Manna sandpile models. So far, number of works has been devoted to this issue but the the answer remained unsolved. We will try another approach to study this question by perturbing the original models. To this end, we introduce three models that have evolution rules between BTW model and Manna model. By simulating this models, we observe that in the presence of perturbation, the probability dis- tribution has two regimes of behaviour which are separated by a new characteristic scale. The regime of small avalanches is described by the exponent of BTW model and the regime of large avalanches by the exponent... 

Edwards-Wilkinson’s equation can be achieved from a Hamiltonian. When we have the Hamiltonian for the system, there are common approaches that makes it out of critical. In other words,the ”mass” should be added to the system. In this study we have tried to simulate and solve analytically these models that are involved mass term. We try to onstruct these mass terms in a way that have a minimum impact on the system and we study the quantities that characterize the out of critical behaviors  

Percolation is a phenomenon that can be found in many physical problems. Additionally, as a statistical model, it has a very rich physics, since many fundamental concepts in the context of critical phenomena and complex systems-such as phase transition, scaling laws etc can be found in the model. Percolation phenomenon can be defined on different lattices. In this thesis we study percolation on small-world networks. In small-world networks, in addition to local bonds that connects the neighbouring sites, there exist some long-ranged bonds that connect cites far from each other. Social networks, some networks of internet or the gene networks are examples of such networks. Therefore, to study... 

Self-organized critical phenomena are interesting phenomena which are ubiquitous in nature. Examples include mountain ranges , coastlines and also activities in the hu-man's brain. In these processes, without fine-tuning of any external parameter such as the temperature, the system exhibits critical behavior. In other words, the dynamics of the system, drives it towards an state in which long range correlations in space and scaling behaviors can be seen.The first successful model which could characterize such systems was BTW model, introduced by Bak , Tang and Wiesenfeld in 1987. This model, later named Abelian sandpile model, was very simple and because of this simplicity, a large amount of... 

Since the concept of Self-Organized Criticality was introduced in terms of BTW Sandpiles model, its major features have been known as broad power law distributions without any tuning parameters. In some selforganized critical systems like brain and neural networks, some evidences and experiments show a periodic or non-power law distribution of avalanches in addition to the power-law distributions of avalanches. In this thesis we try to observe the same phenomenon in the well-known SOC models, namely the BTW and Manna sandpile models. We have considered small lattice sizes with periodic boundary conditions and a small amount of dissipation. Within such conditions we observe a periodic-like... 

Power law behavior of earthquakes has been a matter of interest for many scientists. One on these power laws known as Gutenberg-Richter law describes the magnitude distribution of earthquakes. The Burridge-Knopoff model of faults, produces the same power law distribution of events as the Gutenberg-Richter law for earthquakes. Olami, Feder and Christensen in 1992, introduced a 2-D, continues sand pile model Known as OFC that displays self-organized-criticality. They claimed that this model is equivalent to Burridge-Knopoff model. It means that criticality is the origin of power law behavior of the Burridge-Knopoff model. Nevertheless, there are some evidence against criticality in the... 

Surface growth have been one of the most interesting topics of research in non-equilibrium Statistical physics, due to their relevance in studying industrial growth processes. Many models such as Edwards-Wilkinson and KPZ have been proposed to study these systems where by incorporating renormalization group, numerical integration and computer simulations we can derive their critical exponents. In general, a thermal noise is implemented in these models, however, other types can be used as well. In particular for the case of Edwards-Wilkinson, it has been shown that a multiplicative noise changes the universality class of the model. In this thesis we want to investigate the effects of... 

In this thesis, the impact of both time offsets (TOs) and carrier frequency offsets (CFOs) on the average output signal-to-interference-plus-noise ratio (SINR) of OFDM systems is investigated with a novel and simple approach. First, TOs are partitioned into five cases based on how they occur. Then the mathematical models for different cases are derived. Considering CFOs and benefiting from the obtained models, closed-form expression for the SINR in each case is derived. It is proved that, SINR is independent of the observed subcarrier for the given TO and CFO. Besides, it is shown that the performance of the affected system deteriorates rapidly as the number of subcarriers increases. It is... 

Nowadays increasing demands of Bandwidth, higher data rate and efficiency cause a huge and novel challenges in communicational systems. One of the recent innovative idea to satisfy these increasing demands is Heterogeneous Networks. Compressive deployment of small cell in Heterogeneous Networks can fulfill a large number of satisfactory parameters in wireless networks. After first Presentation of Heterogeneous Networks idea, loads of structure based on them was proposed.In this Research we consider two outstanding and common structure for this technology and analyze the user association and resource allocation problem at their specific structure. The first one is equipped with simple...