Sharif Digital Repository

Standard model of cosmology successfully describes the properties of the universe on large scales. General relativistic perturbation theory accurately describes how the initial fluctuations created in the inflation era grew larger and became the seeds of structure formation later in the radiation and matter dominated era. However, linear perturbation theory breaks at the scales of approximately 10Mpc. In such scales, the gravitational effects are non-linear and we should use standard pertubation theory to find the corrections to the linear power spectrum. In this thesis, I calculated these non-linear contributions analytically and proved the stability of the linear point which is believed to... 

The main goal of this thesis is to study the Teichmüller space and its geometric properties. The Teichmüller space of a surface can be studied from complex geometric or hyperbolic geometric points of view, and in this thesis we refer to both of these viewpoints where needed. Another goal of this thesis is to review a method of compactification of the Teichmüller space. Therefore, we introduce the compactification method proposed by Thurston. To this end, we first briefly review hyperbolic geometry. Then we extend some tools, and use some techniques in hyperbolic geometry, to describe Thurston’s construction and pave the way for it. In the second phase of this study, we introduce... 

The focus of this thesis is the computation of the discrepancy for any given distribution of points on S2. The problem of the distribution of points on the sphere has a long history and Thomson’s Problem, inspired by early atomic theory dating back to 1904, was a landmark. While Thomson’s Problem is based on the Coulomb potential, the discrepancy measures the deviation of the number of points in a set from the expected one. The Polar Coordinates method was introduced in the context of Thomson’s problem. In this thesis the order of the growth of the discrepancy for this method is investigated and a modification of it is shown to lead to the best known results. In addition a new algorithm is... 

Grothendieck’s theory of dessin d’enfant makes a connection between piecewise flat metrics and conformal structures on a compact surface R on one hand, and the defining equation for R whose coefficients lie in an algebraic number field on the other. This connection is realized by a combinatorial structure (a dessin) on a given surface R.In this thesis we begin by briefly reviewing Grothendieck’s theory of dessin d’enfant and Belyi’s theorem and also the approximation of a Belyi map via Thurston’s theory of circle packings.We then introduce a method for computing the explicit equation of the Riemann surface and Belyi map associated to a dessin. Also we explain how the absolute Galois group... 

The main goal of this thesis is the design and development of a rehabilitation device for helping patients “to improve blood circulation” & retain and recover their abilities if possible that were lost during the stroke or a accident like that (my research in karaj/iran shows that it is possible by just movement of the specific body part). The focus is on hand in this thesis because Injuries to the hand are common and can be very debilitating since our hands are our primary means for interacting with our world. For rehabilitation in case of human hand there are several practices that should be done for patients either in home or in a rehabilitation center, time and money that is supposed to... 

In the past few decades, shaking tables are widely used to evaluate system response of structures under seismic excitations. These devices are used without any fundamental research performed on a shaking table system as an entity model. In most of these studies for simplicity, it is assumed that there exist no considerable vibration and displacement around the shaking tables, and no attention is paid to the peripheral substances such as soil settled under the foundation.
In this thesis, result of ambient vibration test on shaking table system (solid deck, concrete foundation and soil layer) has been presented. Precise sensors known as low frequency and high accuracy accelerometers have... 

Out of several ground improvement techniques available, stone columns have been widely used. This technique has been successfully applied to increase the bearing capacity and to reduce the settlement for foundation of structures like liquid storage tanks, earthen embankments, raft foundations, etc., where a relatively large settlement is permissible. This technique has, generally, been proven successful in increasing the stiffness of weak soils, upgrading their safe bearing capacity, and reducing their total and differential settlements, as well as speeding up their consolidation process. The beneficial effects of stone column installation in weak deposits is manifested in the form of... 

Laminar forced convection flow through a channel partially filled with a porous material was numerically studied in this thesis. The Navier-Stokes and Brinkman-Forchheimer equations were used to model the fluid flow in the free and porous regions, respectively. Coupling of the pressure and velocity fields was resolved using the SIMPLEC algorithm. The local thermal equilibrium was adopted in the energy equation. The effects of the thermal conductivity ratio, Darcy number, porosity, Reynolds number and height of the porous insert on velocity and temperature field were investigated. The results show that the flow behavior and its associated heat transfer are susceptible to the variation of the... 

In the present study, a new version of haptic devices is presented in which user’s hand is in contact with the device just while collision with virtual surface. In this system, the position of user’s finger can be traced by using a camera and the haptic device follows user’s finger at the distance of about two centimeters. While the haptic device approaches to the virtual surface, gradually reduces its speed and stops about two centimeters distant of virtual plane. Then user’s hand collides with the haptic device which is static. Greater fidelity, transparency, more stability and also no need to large actuators are of the advantages of this system. In this project, first we present a new... 

In this thesis we try to find optimized parameters for imaging and manipulation of a biosample with AFM. For this we have prepared a numerous Molecular Dynamics simulation and find some reliable result. So, first we have focused on imaging process in Non contact mode (the less harmful mode). Then we headed into the manipulation process. The main problem about manipulating a biosample is the environment. In imaging section, the process of imaging a biomolecule by AFM is modeled using molecular dynamics simulations. Since the large normal force exerted by the tip on the biosample in contact and tapping modes may damage the sample structure and produce irreversible deformation, the non-contact... 

Results of previous studies on silt and clay indicated that variations in the small strain shear modulus, Gmax, during drying had a non-linear increasing trend with matric suction with greater values upon wetting. However, due to different material properties and inter-particle forces, different behaviour in Gmax is expected for sand. Although considerable research has been devoted in recent years to characterize the behaviour of Gmax of sand during drying, rather less attention has been paid to the effect of hydraulic hysteresis on Gmax and its variations during wetting. In the study presented herein, an effort was made to characterize the variation of Gmax for specimens of sand during... 

Abstract The problem of competetive facility location can be defined as follows: There are a number of customers in the form of points in space, and two players arrange a number of facilities in the form of points in space, given some limitations, respectively. Each customer’s connection to each facility has a cost for the customer and an advantage for the facility, and each customer wants to be connected to at most one of the facilities which has the lowest cost for him. The goal is to find the strategy of placing the facilities and determining the cost which the facility receives from the customer, in such a way that the player’s profit is maximised.In this thesis, we first sought to... 

Zero knowledge proofs allow a person (prover) to convince another person (verifier) that he has performed a specific computation on a secret data correctly, and has obtained a true answer, without having to disclose the secret data. QAP (Quadratic Arithmetic Program) based zkSNARKs (zero knowledge Succinct Non-interactive Argument of Knowledge) are a type of zero knowledge proof. They have several properties that make them attractive in practice, e.g. verifier's work is very easy. So they are used in many areas such as Blockchain and cloud computing. But yet prover's work in QAP based zkSNARKs is heavy, therefore, it may not be possible for a prover with limited processing resource to run...