Sharif Digital Repository

Describing the motion of a mass point in a domain with elastic reflections from the boundary has different dimensions and angles where various methods and approaches are tested and honed to it. Usually the dynamic of this motion is studied easily but in many cases this leads to some open problems where obtaining partial solutions of them requires advanced and complicated technics. The connection of this kind of problems with geometry and physics illustrate them very nice as an applied branch of mathematics. In this dissertation billiards problems and required tools for investigating them are gathered  

In this research, trade and transportation trends of Asia-Europe-Africa, in the both intercontinental and intracontinental levels have been analyzed. With analyses which are done in this research, determinant factors for modeling and investigating international bilateral trade in these three continents have been recognized. The relevant time-series data were extracted from centralized and international databases. The examined database consists of 11 variables grouped in four categories: bilateral trade data, transportation, geographical and socio-economic characteristics. Transportation data is based on three different networks. The first network consisted of highway, rail and marine modes... 

Wishart processes are popular models for stochastic correlation and volatility of financial assets due to their convenient analytical properties. However, they cannot reproduce the sudden and sustained surges in correlation and volatility observed during market crises. Moreover, the Wishart process (like the CIR model) does not impose a positive lower bound on variances, allowing them to approach zero. This thesis introduces a new stochastic process, called the Markov-Modulated Shifted Wishart (MMSW) process, to address these shortcomings. The MMSW process extends the Wishart model by adding a constant “shift” matrix to keep variances away from zero and by using a Markov chain to switch... 

A new experimental setup was fabricated; equipped with an adjustable chamber’s length, with air tangentially flowing through the wall of vortex engine. In a vortex combustion chamber, the tangential inlet fuel or oxidizer creates both inner and outer vortices which are rotating in the same angular direction. Indeed, inner vortex moves from head to the end of engine in the axial direction; however, outer vortex moves in the opposite direction. This setup was fabricated to see the effect of fuel nozzle characteristics on the wall temperature of the chamber. In a vortex engine, vortices affect spray droplets and force them to have a spiral path. Moreover, relative velocity of droplets and flow...