Sharif Digital Repository

We study linear and semilinear stochastic evolution partial differential equations driven by additive noise. We present a general and flexible framework for representing the infinite dimensional Wiener process, which drives the equation. The equation is discretized in space by a standard piecewise linear finite element method. We show how to obtain error estimates when the truncated expansion is used in the equation. We show that the orthogonal expansion of the finite-dimensional Wiener process, that appears in the discretized problem, can be truncated severely without losing theasymptotic order of the method, provided that the kernel of the covariance operator of the Wiener process is... 

Centrifuge is a method in which great gravitational-like forces are used. Gravitational forces which cause molecules to move and are relevant to molecular weight; can cause isotope separation. The separation of light isotope from heavy one is done with a centrifugal field which produces a pressure gradient for the gas mixture. Pressure gradient is different for each of the isotopes due to the dependence of pressure gradient to the mass of the materials. But the separation in this way is very limited. The capacity of separation can be brought up by producing an additional axial flow in the rotor. This rotational flow can be produced with internal or external incitement. Rotational flow with... 

A phase shifter is a microwave element that changes the phase of the input signal at a specific center frequency and bandwidth and, ideally, produces a signal with the same amplitude and a modified phase at the output. In practice, this phase change in the passive phase shifter is accompanied by a decrease in amplitude due to different factors. Various use cases can be described for phase shifters in telecommunication circuits, but its most important application is in regulating the relative phase of each antenna in a phased array system, which is the most common method of beam steering and forming. A phased array system is one of the leading solutions to achieve beamforming and high... 

High-quality online services demand reliable and fast packet delivery at the network layer. However, clear evidence documents the existence of compromised routers in the ISP and enterprise networks, threatening network availability and reliability. A compromised router can stealthily drop, modify, inject, or delay packets in the forwarding path to launch Denial-of-Service, surveillance, man-in-the-middle attacks, etc. So researches tried to create intrusion detection methods to identify adversarial routers and switches. To this end, data-plane fault localization (FL) aims to identify faulty links and is an effective means of achieving high network availability. FL protocols use... 

Confining nematic liquid crystal between two curved boundary conditions while the nematic molecules have a degenerate planar anchoring leads to complex and beautiful textures of molecular disparagement(defect) in the bulk and on the surfaces. Such the liquid crystal shells are made with double-emulsion techniques in microfluidic devices have provided applications for micro-scale colloidal linkers.In this work, we have numerically minimized the elastic energy in one-constant approximation in present of Fournier’s degenerate surface potential with finite element method. The nematic shell is confined between two spherical surfaces that we have studied the final energies and their related... 

Secure routing is a major key to service maintenance in wireless ad hoc networks. Ad hoc nature exposes the network to several types of node misbehavior or attacks. Wormhole attack is one of the most severe active attacks to mobile ad hoc networks. Noting the resource limitations in such networks, nodes may have a tendency to behave selfishly. Selfish behavior can have drastic impacts on network performance. We have proposed a Misbehavior-Tolerant Multipath Routing protocol (MTMR) which detects and punishes all types of misbehavior such as selfish behavior, wormhole, sinkhole and grey-hole attacks. The protocol utilizes a proactive approach to enforce cooperation. In addition, it uses a... 

Providing high bandwidth network infrastructures for ever increasing need of data transport is of great importance. The underling infrastructure for many communication services such as GSM/3G/4G mobile networks and Internet services is Synchronous Digital Hierarchy (SDH) optical transport systems. SDH are standardized protocols that multiplex multiple lower rate digital bit streams, such as E1 and Ethernet, and transfer them synchronously over optical fiber using lasers or LEDs. In addition to high data transfer rates, flexible network management and protection mechanisms have great importance, hence are part of SDH standards. In order to obtain flexible network architecture and protected... 

Development of Smart Grid and deployment of smart meters in large scale has raised a lot of concerns regarding customers’ privacy. Consequently, several schemes have been proposed to overcome the above mentioned issue. These schemes mainly rely on data aggregation as a method of protecting users’ privacy from the grid operators. However, the main problem with most of these schemes is the fact that they require a large amount of processing power at the meter side. This, together with the fact that smart meters don’t usually have a powerful processor, can cause the unavailability of smart meter data at the required time for operators of the grid, and at the same time disables smart meters from... 

A liquid crystal is a state of matter composed of highly anisotropic building blocks. When liquid crystals are exposed to surfaces with given shapes and anchoring conditions, the orientation of their molecules gets spatially disordered and topological defects may form in the system. The interplay between liquid crystals and the geometry and topology of the colloidal particles has motivated extensive recent studies.In this thesis, we present the numerical modeling results for two faceted colloidal particles in a thermotropic nematic liquid crystal. To obtain the equilibrium nematic field with a finiteelement method, we numerically minimize the free energy of the system that based on the... 

Today, in different industries,as the use of high voltage DC power supplies is increasing, the need of output voltage precision also is increasing. One way to make High DC voltage is to use a multi-output DC-DC converter and makethe output series.Existing problems in measuring high voltages, results in this idea That in these converters, we measure and regulate only one of the outputs and estimate the others by circuit elements. In this estimatin, differences between the transformer parasitic elements are very effectiveon transformer various output voltages. In this thesis after a comprehensive study on the pulse transformer parasitic elements and choose a suitable model for it, the... 

Applications of high voltage power supplies is increasing. Microwave power module is one of the applications. In microwave power module, the dimensions of the power supply are very important. On the other hand, the parasitic elements of the transformer of a high voltage power supply are significant because of high insulation distances and transformer high turn ratio. These elements including stray capacitance and leakage inductance change the converter behavior. In this thesis, a method for dimensional efficient design of high voltage power supply used in microwave power module is presented considering and analyzing the transformer parasitic elements. Beforehand, at first, the transformer... 

Dynamic spectrum access with the aid of cognitive radio (CR) technology is a viable solution to spectrum scarcity. There are many military and emergency applications that require the use of cognitive radio ad-hoc networks (CRAHNs). In these net- works, nodes must first find each other in a wide spectrum and then exchange their desired data. The process of finding each other in a multichannel environment is a challenging task and is usually known as rendezvous. Since rendezvous is the first step in communication, disrupting will disable the nodes from establishing proper communication sessions. That results in a drastic degrade in the performance of the network. Therefore, it is important to...