Sharif Digital Repository

Similar to the classical Poincare-Hopf index formula for the Euler characteristic, Zhang gave a counting formula for the Kervaire semi-characteristic of a 4q+1 manifold. We first study Witten deformation techniques in the proof of the Poincare-Hopf formula. Then we will represent Zhang’s formula which uses similar analysis. Both these formulas establish a connection between topological and geometrical data on a manifold. Both proofs will be analytical. Index theory will play the ’bridge’ between the topology and analysis. We begin with an analytic interpretation of the topologically defined quantities as indices of differential operators. We deform the operators with respect to appropriate... 

In this thesis, the aim is to stating some of the noncommutative geometry(NCG) applications in formulating and describing the gravity. So, in the first chapter, we will work on some of metric aspects of NCG. In this chapter, we will review elements of the spin geometry, specifically we will define the Dirac operator which is the most important object in this thesis. Then, we will try to find counterparts of some of Riemannian geometric notions like integral and distance in the NCG framework. We will define some notions such as noncommutative infinitesimals, Dixmier trace, Wodzicki residue, noncommutative integral and spectral triples. Then, in the second chapter, we will work on some of the... 

In this thesis, ionic liquids and polymeric ionic liquids were investigated as solvent and support for immobilization of molybdenum and palladium catalysts. Three newly synthesized room temperature ionic liquids containing molybdate anion, [DMIm][MoO2(NCS)4], [RPy][MoO2(NCS)4] (R = butyl or decyl), and previously reported [BMIm][MoO2(NCS)4] were used as catalysts for the reduction of sulfoxides. For facilitating the recyclability of the catalysts, the ionic liquid solvents, [RMIm][PF6] and [RPy][PF6] (RMIm=1-n-alkyl-3-methylimidazolium, RPy= 1-n-alkylpyridinium), were applied to immobilize molybdenum catalysts. These catalysts showed high catalytic activity for sulfoxide reduction in this... 

Zirconia toughened alumina (ZTA) Nanocomposites were prepared using nano sized Zirconia (ZrO2) powders doped with 3% mol of yttria (Y2O3) nanopowders and the sintering behavior at different temperature (1450 °C, 1550 °C and 1650 °C) were studied. The ZTA composite with different amount of partially stabilized Zirconia (PSZ)(5, 10, 15 and 20% mol) were prepared via axial pressing and then sintered to achieve maximum densification. After that phase changes of the samples were monitored. SEM was used for microstructural study and hardness and fracture toughness were determined by means of Vickers indentation. X-ray diffraction pattern showed that at constant composition, tetragonal zirconia... 

In this thesis, we first define the pseudo-distance p on the group of Hamiltonian diffeomorphisms.Using the concept of displacement energy, we show that the pseudo-distance p is degenerate and if the manifold is closed, p will be zero for each p = 1; 2; 3; : : : Then, we introduce Lagrangian submanifolds and prove that if L R2n is a rational Lagrangian submanifold, we have the following inequality e(L) ≥ 1γ(L). : Finally, using the above inequality and the concept of displacement energy, for M = R2n we prove that 1 is non-degenerate. Therefore, the hypothesis for 1 to be a metric, are satisfied. This metric is called Hofer’s metric  

Knot theory is the study of ambient isotopy classes of compact 1–manifolds in a 3-manifold. In classical knot theory this 3-manifold is R3 or S3. This field has experienced a great transformative advances in recent years because of its strong connections with and a number of other mathematical disciplines including topology of 3-manifolds and 4-manifolds, gauge theory, representation theory, categorification, morse theory, symplectic geometry and the theory of pseudo-holomorphic curves. In this thesis we start with classical knot theory, introducing some of its (classical) invariants like unknotting number, Seifert genus and slice genus of a knot, knot group and finally Alexander Polynomial... 

Composite quantum systems are generally correlated and these correlations may have classical or quantum nature. Entanglement is only a special type of quantum correlations and separable states may be quantum correlated. Quantum discord, local quantum uncertainty and the rank of the correlation matrix are the most important measures of quantum correlations beyond entanglement. Regarding the various applications of discordant separable states in the field of quantum information, the important problem is how to produce discordant separable states and what is the resource which should be used for this preparation. In this thesis we present a method of preparation for such states in two qubit... 

In this thesis we are going to explore a new formalism in micro domain which describes quantum phenomena in a realistic casual fashion by introducing an unified concept of matter, energy, and Information. In this theory, a micro-entity, e.g. an electron, is a combination of a particle and its associated field integrated to a new entity called particle-field. The dynamics of such system will be analyzed. Then, some quantum examples which have controversial aspects will be discussed within the new theory. In a generalized form of formalism, the non-linear Schrödinger Equation is introduced, which enables us to predict some experimental data for common Quantum Mechanical stationary systems.... 

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, . . .This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution  

Inlet air cooling is a simple and economical method to increase the power output of gas turbines. High-pressure fogging systems and mechanical chillers are two common methods. High water consumption, damage to compressor blades by water droplets, and inefficiency in humid climates are disadvantages of high-pressure fogging systems. Mechanical chillers have high electricity consumption and initial costs. In this research, an earth-to-air heat exchanger (EAHE) is introduced as a new method for inlet air cooling of gas turbines and is technically and economically compared with the two common methods in the long term in the climate of Tehran city. Temperature distribution in the ground is... 

Natural tissues of body consist of Extra Cellular Matrix (ECM) and cells. Scaffold produces a temporary matrix for cells and facilitates oxygen and nutrients transport which enhances tissue regeneration. Therefore, attempts in regeneration of tissues and organs by scaffolds attracted great interest in today’s researchs. Choosing scaffold fabrication method and its polymer type, play a key role in scaffold specifications as they determine scaffold properties. In this project electrospinning was chosen as the scaffold fabrication method which is because of the unique properties of scaffolds fabricated by this method and also its ability in producing micro and nano fibers. At first set of... 

In recent years, many studies have conducted research about stem cells due to their prominent features such as proliferation and differentiation. By changing the specific parameters of the cellular micro-environment, it is possible to determine the stem cells fate and thereby use them in medical affairs. For this purpose, various devices and methods have been designeds such as microfluidic devices and scaffolds. The microfluidic devices has been especially focuced in the researchs due to their unique features, like the possibility of testing with small amounts of samples, the creation and control of low cost cellular micro-environment and low practical time. Two-dimensional scaffolds made up... 

Asphaltene deposition, considered as the heaviest and the most polarizable fraction of crude oil, can cause severe problems in oil production and extraction systems. Oil production companies annually bear huge reduction or even cessation in production and, in turn, costs due to asphaltene precipitation and deposition in wellbore or production tubings. To gain more and better insight into asphaltene formation in production systems, the conceptual investigation on the mechanisms of asphaltene adsorption and deposition on a solid surface is indispensable. In this study Asphaltene's particle adsorption and deposition onto the metal surface under the effect of flow is investigated by experimental... 

Torsional misalignment of lower extremities is a bone deformity of femur, tibia, knee twist or a complex of all these factors. These deformities affect the patient's gait kinematics. These patients are usually treated with osteotomy surgery with the aim of correction of anatomy. But it doesn't necessarily lead to the modification of gait. Therefor development and application of subject-specific musculoskeletal models to analyze patient's specific condition and predict corrective surgery results are considered. Accordingly, the aim of this project is to create a subject-specific musculoskeletal model for a patient with femoral anteversion in order to predict result of anatomical correction... 

Measurement of human movement during work, sport as daily activities has important effects for rehabilitation and biomechanics experts.
Recently, several researches are concentrated on this technology significantly because of new progress in sensors and fusion sensors. In the near future, wearable and ambulatory devices will be used considerably in biomedical applications. In this study, we reviewed some methods about wearable measuring system then introduced and designed innovative wearable clothing for this purpose. Some specifications and advantages of our system in comparison with relevant researches are; using textile sensors that are manufactured through nano electro active polymer... 

Carbon dioxide is one of the main geenhouse gases emitted from factories as well as transportation vehicles that adversely affect the atmosphere and cause global warming. Among the proposed solutions to reduce carbon dioxide in the atmosphere, carbon dioxide separation would be the most viable medium-term approach. However, the high cost of carbon dioxide separation prevents the development of carbon dioxide absorption technologies. Therefore, it seems that integrating separation and production processes is the most efficient way to save energy and reduce carbon emissions. This method decrease a high proportion of the energy consumption in upstream operations (carbon dioxide removal,... 

Fatigue life prediction of a mechanical part is one of issues which a group of engineers are engaged with it and always they try to design the parts with the maximum of lifetime. Although many researches have been done in this field but yet we can see that predicted life are different from that happens in the reality because there are some uncertainties in the phenomena. Our effort in this project is creating an algorithm design so that the parts are designed by it, have the maximum fatigue life and the minimum uncertainty in prediction. In this project we have considered geometrical, material and random loading uncertainties as error resources. Older methods those are presented in this... 

The purpose of this research is the aerodynamic design of a 100 kW transonic ducted fan. Today, the aviation industry is moving towards the design of electric driven aircraft propulsion. Transonic ducted fans are one of the viable options that have been used in medium and heavy aircrafts due to their high specific power. In this research, the meanline model has been used for the initial design. By applying the design constraints, design limitations, design and functional parameters, the initial design point is found and then a sensitivity analysis is performed with respect to the effective design parameters to obtain the optimal design point. For the initial design of the transonic ducted... 

Recently, many investigations are done in the field of the modeling of the cardiovascular system. For the purpose of understanding of this system, mainly the location of formation and development of atherosclerosis, these investigations are so vital. The multi-scale modeling is an appropriate method to reduce the cost of calculation and also, this method simplifies the complicated model of cardiovascular system. This research presents a multi-scale 1D-3D modeling of cardiovascular system. In this model, the three dimensional geometry of carotid bifurcation is coupled with a one dimensional full model of cardiovascular system. We used some user defined function in the Fluent software for... 

Recently, conductive nanocomposites have found great deals of attentions due to their vast applications in different fields. According to the definition of nanocomposite, the filler component should be in the range of 10-100 nm. In this study, silver nanoparticles was used as filler with 4 nm size and synthesized by microemulsion method that is known as the best approach for fabricating silver nanoparticles with small sizes, narrow size distribution and high stability.
Copoly (ortho-phenylenediamine/dopamine) was used as matrix component. Ortho-phenylenediamine is one of the conductive polymers that was used less than other conductive polymers such as polyaniline in this research area....