Sharif Digital Repository

After the discovery of integer and fractional quantum Hall effects, a comprehensive effort started to understand the physics behind these findings thoroughly. At the end, these efforts resulted in the introduction of topological phases of matter and the notion of topological phase transition. With the recent developments in this field, as the introduction and synthesis of 3D topological insulators, many researchers began inspecting the effects of disorders and impurities in the lattice structure on the topological phases, As these imperfections are inevitable in the lab-created instances. Since, in the previous works only on-site disorders was studied, the concentration of this thesis is on... 

During times, reinforced concrete sturctures might need to be strengthened due to environmental factors, material properties, design errors or changes indesign guidelines.Fibre-reinforced-polymer (FRP)composites are prominentmaterialsfor this purpose. Externally full bonding systemhas been widely used for flexural strengthening of reinforced concrete sturctures with FRP. However, the drawback of using this strengthening system is the high reduction of structure's deformability.In this research, partially bonding system used in finite element modeling of a bridge’s deck to increase deformability compared to full bonding system. Results showed that not only deformability but also load... 

Vibration of a stationary structure excited by another structure moving on the surface of the stationary Structure is very common in engineering, such as vibration of bridges or railway track under travelling vehicles. In the simplest case, the moving structure maybe modeled as a constant load or a mass or an oscillator, in this case the moving mass is attached to the structure either by a spring or by a mass-spring assembly.The model of a moving mass brings some improvements to the model of the moving load where there is no inertia effect. However, the relative displacement between the moving structures and the beam cannot be considered in the moving mass model. A more appropriate model in... 

Performance based design was first introduced in order to evaluate seismic vulnerability of structures in retrofitting topic and was rapidly implemented in new design codes. The main cause conducting widely developing of performance based design methods, has been accurate estimation of seismic demand parameters. Since seismic structural members displacement during earthquake has a direct effect on the amount of sustained damages, displacement index has always been a key concept in performance based design. The main goal followed by this research is comparing the results obtained from the standard pushover method (with two theorems of distributed plasticity and plastic hinges) and the... 

Through the recent years application of FRP material in structural engineering has been developed significantly. According to possible changes of a building function during its lifetime or alteration of the building codes, building structures usually need to be strengthened. Referring to merits of FRP material, its application seems to be a convenient idea toward the cited requirement. Curved beam and slab are known as highly used elements in building structures. Bridges composed of horizontal or vertical arches could be noted as common examples which need to be reinforced by FRP. However curved concrete surfaces, reinforced by FRP plates, seem to be studied than it is really required; For,... 

The Hubbard model is one of the simplest interacting models in theoretical physics, especially condensed matter physics which despite its simplicity, its solutions are highly nontrivial and intractable. After 5 decades since its introduction, its phase diagram is not fully understood and whether or not, it has a high-temperature superconducting phase. In this thesis, we aim to employ the recent advances in machine learning and GPU programming to accelerate the QMC method. By accelerated QMC methods, we can explore the Hubbard model's phase diagram more efficiently. Using massive parallelization of the GPUs can speed up the measuring process by several times. The self-learning quantum... 

In this study the dynamic responses of finite Euler-Bernoulli beams and homogeneous isotropic 2D half-spaces, as one and two dimensional structures, under a moving object are investigated. First, the dynamic responses of finite beams with various boundary conditions were investigated. The results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC’s. Dynamic response of a half-space under an inertial foundation subjected to a time-harmonic loading was investigated in the next... 

Finding suitable locations for installing conventional concentric bracings such as X and V, without interfering with building architecture and its openings, is a routine challenge in building design. One of the less known forms of concentric bracings which can be used to solve this issue, is the y-shaped bracing composed of three braces. In the current thesis, results of analytical studies, computer modeling and experimental tests are presented to extend the knowledge of structural behavior of y-bracings. As the first step, effective buckling lengths of braces with rigid connections were found from equilibrium equations incorporating the effect of axial force on rotational stiffness of... 

The Hamiltonian of the Hubbard model was introduced by Hubbard in 1963 to model electron correlations in narrow energy bands and it provided an approximate description of electrons in solids.This model provides a simple description of materials, but its exact solution is possible only in one dimension.In the physical examining of this model in quasi two-dimensional systems, the Density Matrix Renormalization Group(DMRG) is used, which is one of the most powerful numerical methods in studying quantum systems. The quantity that is important to solve the systems is the density matrix, which by knowing, many of the observable quantities of the systems can be obtained. Calculating the density... 

This thesis investigates superconductivity generated by the Kohn–Luttinger mechanism in a model defined on a two-dimensional square lattice. The model allows for several band dispersions and includes onsite Hubbard and nearest-neighbor density–density interactions. We analyze the system using a perturbative renormalization-group approach. We begin by summarizing the basic features of conventional and unconventional superconductors. We then examine the Cooper instability, the generic weak-coupling instability of a Fermi liquid and the basis of BCS theory for conventional superconductivity. Next, we present the renormalization-group framework as a general tool for describing phase... 

Recent advances in numerical computations in the field of strongly correlated systems have provided us to calculate the entanglement spectrum and the entanglement entropy for interacting systems. Calculating the explicit form of the entanglement Hamiltonian (a.k.a. the modular Hamiltonian) is considered as a difficult problem.In this dissertation, we intend to introduce a method and by means of the d ensity-matrix-renormalization-group algorithm to obtain for the first time the second quantization form of the entanglement Hamiltonian of interacting systems at zero temperature. We implement our method for one-dimensional Heisenberg spin chain and also Heisenberg model on a square lattice... 

After the introduction of the framework of quantum mechanics and its experimental success, it was assumed that any physical phenomenon could be analyzed and understood accurately using quantum mechanics. But very soon we found out that in most cases, it is too hard or sometimes impossible to solve the Schrödinger equation exactly even for few-body systems. The reason is that the dimension of the Hilbert space increases exponentially with the number of particles, in a way that for a spin chain(spin-1/2), which has only two single-particle states, even using modern classical computers we are barely able to find an exact solution of a 30-40 particles system which is far smaller than the... 

This thesis investigates the time evolution of one-dimensional quantum systems following sudden parameter quenches in their Hamiltonians. Such quenches drive the system out of its initial equilibrium and lead to rich non-equilibrium dynamics. To explore these phenomena, two powerful numerical methods are employed: Exact Diagonalization (ED) and Matrix Product States (MPS) using TEBD and DMRG algorithms. The main focus is on the growth and propagation of entanglement entropy, the evolution of local and non-local spin correlations, and the structure of the Schmidt spectrum after the quench. Furthermore, the entanglement Hamiltonian and its spectral properties are analyzed to probe the... 

Steel shear wall system has been used in recent years as the lateral-load resisting system in the design and retrofit of high-rise buildings. This system consists of infill shear panel is framed by surrounding steel frames. Infill shear panel can be applied in two types: stiffened or unstiffened. Considering to the previous studies, the stiffened type is more convenient in the seismic performance and utility condition. However, in the stiffened system, the construction cost is considerably higher because of the complicated construction details. This dissertation concentrates on the experimental and analytical studies of trapezoidally corrugated steel shear walls as an option for removing the... 

The present parametric study discusses the effective factors on seismic performance of spherical RC domes. For this perpose, a series of domes with different spans, a variety of contact angles (the angle between the bottom of the sphere and the center of the sphere), openings with different areas and various support condition are studied. Then the value of response modification factor and it's components is determined to take into account the effect of each component. The results obtained indicated that the response modification factor increases as the contact angle enhances. However, the span of domes insignificantly affects the value of response modification factor.also analysis on domes... 

Base plate is one of the crucial elements in steel structures which transfer force from column to foundation and also prevent stress concentration in jointing area between them. For investigating the behavior of base plate under different caseloads such as axial, transverse and earthquake loads, it is necessary to consider all the involved elements including column, base plate, foundation, anchor rods and also interaction between these elements. In this study the connection between column and base plate, base plate and foundation are analyzed thoroughly. The behavior of base plate with a box type column with and without stiffener under the static loads is analyzed using finite element... 

Solid foams are novel materials with outstanding characteristics that have found numerous applications in the construction of light, stiff structures during the past two decades. At the micro-level, solid foams benefit from a cellular structure, which is composed of either closed or open cells. Open-cell foams, which were the concern of this study, are described as a network of inter-connected struts (or ligaments) with beam-like action. The mechanical design of foams requires their mechanical properties to meet certain criteria. These criteria can be satisfied by careful selection of the base material and the microstructural morphology (geometry). However, the selected material has to be... 

Reinforced concrete shells are widely used to cover the small to large area with more aesthetics at minimum cost. Shell structures carries load through their shape rather than material strength. Funicular shells are special type of shells that their shape is obtained so that stresses be compressive under a special load (for shell, this load is its dead weight). This study deals with forced vibration of funicular shells on a rectangular ground plan under impulse loads using shallow shells theory. Two boundary conditions, simply supported and clamped, are considered. Displacement components are product of position and time functions. The analysis is based on the expansion of displacement... 

In the past few years, topological insulators (TIs), topological superconductors and their experimental observation have been in the center of condensed maer physicists’ aention. Kane and Mele proposed the simplest and the first model exhibiting TI phase for non-interacting electrons on the two dimensional honeycomb laice. On the other hand, in the Hubbard model for nonzero doping and near the half filling, the high temperature superconductivity is predicted theoretically. In this thesis, we fist investigate the interacting topological insulators by adding the Hubbard interaction to the Kane-Mele model. en, in the strong correlation limit we find an effective spin model -the so called... 

In recent decades, most of the codes have placed a high value on Performance Based Design of structures; however, these methods are computationally complex and time-consuming, and caused researchers to seek new and efficient methods to investigate performance of structures under different intensities of seismic loading. The Usage of Endurance Time method (ET) and thus reducing the size of analysis can be a useful tool for excuting Performance Based Design of structures. Endurance Time analysis is based on time history analysis, but in this method structure subjected to an intensifying acceleration function and different damage indices of the structure are evaluated through analysis time. The...