Sharif Digital Repository

In the era of precision cosmology it is desirable to know if the collapse of an overdensity region within a FRW cosmological model leads to a black hole similar to that of Schwarzschild. Even the simple question of an event horizon within a dynamical universe is not a trivial one. This subject of studying collapsing over-densities within an expanding universe is called ”cosmological black holes”. Our aim is to construct such a black hole in the simplest possible scenario and study its similarities and differences to the familiar Schwarzschild one in vacuum. Therefore questions of rotating or charged black holes are not dealt with in our work. We insist, however, that the solution is dynamic... 

Sever plastic deformation can be used for decreasing the grain size and increasing the mechanical properties. In this method a square or circular cross section specimen is passed from two intersecting channel with equal cross section. Thereby, a large plastic strain without change of cross section is produced in the specimen. This large strain is the main reason for the interest of researchers in many fields. In the experimental research fields, researchers can study the response of material in the large plastic strain range, investigation of stage III of hardening and after it, change of microstructure to submicron and Nano, and increase of strength simultaneously with preserving of... 

When a crack is subjected to a compression field, it will close and its edges will get into contact with each other. Depending on the direction and magnitude of the loads and also the coefficient of friction, ‘stick’ or ‘slip’ situationsbetween the edges will occur. This type of crack is known as ‘frictional crack.’ In this project, first these cracks are studied analytically and the order of singularity is derived using asymptotic analysis and also the analytical fields are determined for both ‘isotropic’ and ‘orthotropic’ materials. Then, numerical simulations are carried out using extended finite element method which is considered as the most powerful means for analyzing the problems... 

The aim of this work is to study the optimal exponent p to have solvability of semilinear biharmonic problem with a singular term in a smooth and bounded domain such that contains origin in Euclidean space with dimension greater than 4. The singular term is related to the Hardy inequality. First of all, it is not difficult to show that any positive supersolution of problem is unbounded near the origin and then additional hypotheses on p are needed to ensure existence of solutions. We will say that problem blows up completely if the solutions to the truncated problems (with a bounded weight instead of the Hardy singularity) tend to infinity for every x in domain as n goes infinity. The main... 

In this thesis we first discuss the final fate of a spherical symmetric distribution of matter which has undergone a gravitational collapse, by reviewing some classical collapse models. Our emphasis will be on the visibility of singularity after it forms. Then we will mention some general aspects of quantum field theories in curved space-time and after that we investigate the quantum background effects on the evolution of a spherical symmetric and homogeneous distribution of dust. In fact by calculating the quantum corrections—due to massless scalar fields which are arbitrarily coupled to the background geometry— on the geometry of collapsing sphere, one can obtain the quantum corrected... 

In the present study, in order to investigate the nature of stress singularities in isotropic multimaterial wedges and junctions, determination of the singularity order and analytical asymptotic fields in the vicinity of singular points using the eigen-function expansion method are explained. Next, an efficient approach is proposed to model stress singularities within the X-FEM framework. In this approach, the Airy stress function coefficients are employed in conjunction with the standard singular enrichment functions to obtain modified singular enrichments. Performance and accuracy of the proposed method is shown via computation of the energy norm error and the convergence rates are... 

In this thesis by studying the extreme physical conditions near black hole horizons and singularity, we attack intriguing problems in the exciting era of quantum black holes and gravitational wave astronomy. We considered the backreaction of the energy due to quantum fluctuations of the background fields for a Schwarzschild black hole, in semi-classical gravity. We have shown that it results in modification of the horizon and also formation of an inner horizon. The process of the collapse of a thin shell stops before formation of the singularity. After the collapse stops the reverse process takes place. We also demonstrate the existence of a cold remnant for the black hole. We generalized... 

Black holes are a general set of solutions of Einstein’s general relativity. Their most important feature is the horizon, which is basically a region that separates the space-time into two causally disconnected regions. Studying the general features of black holes, classifying this family of solutions and studying the dynamics of particles and fields in the background of a given black hole are famous subjects in the field of classical black hole physics which are going to be covered in this thesis. By putting different conditions on the equations, we will get different solutions like Schwarzschild, Reissner-Nordstrom, Kerr, Kerr-Newman and etc, each of them having specific features. Then we... 

This thesis examines a new electromagnetic mode called line mode. This mode occurs when the boundaries have complementary surface impedances. It is possible to control the mode confinement by changing the surface impedance values. Impedance surfaces with non-complementary impedances guides the quasi-line mode, which is a mode between the line mode and the edge mode. Essential features of the line wave are its singularity over the line, its broad bandwidth, and its robustness to certain defects. Another significant characteristic of a line wave is that unlike surface waves in which it is not possible to change the spin orientation, in a line wave, the spin orientation can be altered by... 

Compliant mechanisms are generally used in quasi-static condition and therefore system dynamics do not have a significant effect on their performance; But if the inertia of the links is high, the dynamics of the mechanism will affect its performance altogether. By cleverly designing the mechanism, these effects can be used to create new movement patterns. In this research, a family of compliant mechanisms is introduced whose movement patterns are a function of input speeds. This means that at low speeds, the flexibility of the mechanism does not have a significant effect on its performance, but when the speed exceeds a certain limit, this flexibility changes the configuration of the... 

Morse 2-functions are higher-dimensional analogs to morse functions. A morse 2-function is a mapping to 2-dimensional disk with its critical points satisfying certain generality conditions. The goal of defining morse 2-functions and trisections is to generalize methods of 3-dimensional manifolds to dimension 4. A morse function on a 3-dimensional manifold leads to a decomposition of that manifold to two manifolds with boundary with common boundary. This decomposition is called Heegaard splitting. This decomposition is unique up to stabilization. Trisections are 4-dimensional analogs of Heegaard splittings and decompose manifold into three parts. The intersection of each pair is a solid genus... 

In recent years, nanoplasmonic quantum has been an active and developing field, resulting in several quanta and nonlinear qualities in the time-frequency interval, such as the creation of coherent single photons, nonlinear observation in nanometer dimensions, high-speed optical switch, etc. In the meantime, the controlled emission of surface polaritons resulted in the development of new devices such as nanolasers , subwavelength diodes, and high-speed phase and amplitude modulators , all of which have had a significant impact on the development of technology in very miniature dimensions. Numerous approaches have been proposed for the manufacturing of nanolasers, or reinforced plasmon...