Sharif Digital Repository

In the present study, the Ricci curvature is defined on the graphs by using two methods and the lower bounds are obtained. In the first method, which is related to Bakry and Emery, a definition for Ricci curvature and lower bounds would be obtained by using Curvature-Dimension inequalities.The second method which is related to Ollivier, is based on the fact that in Riemannian Geometry,the Ricci Curvature controls the velocity of convergence and divergence of emanated geodesics from a same source. Next, the more Curvature-Dimension inequalities for Ricci curvature would be obtained by using local clustering. Finally, the Bonnet-Myers theorem would be proved on the graphs.
 

In this thesis, a discrete exterior calculus is studied. Discrete exterior calculus is an attempt to create a discrete analogy of differential geometry and topology which is potentially applicable in computer science and physics. At first, simplicial complexes are presented as approximation of smooth manifolds. Then discrete forms and discrete exterior derivative are defined. We will observe that Stokes, theorem can be stated and proved in discrete analogy too. We will obtain Hodge operator by using dual complex and after that discrete Laplacian and Heat kernel will be calculated by using Hodge operator. In addition, we will define discrete vector field independent of discrete forms and then... 

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  

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... 

Tapering the beam along its length may lead to an increase in the voltage density of piezoelectric energy harvester. In this study, the energy harvester voltage with linear variable cross section is studied by developing an analytical method in both linear and nonlinear states. In linear mode, the results are compared with the experimental results. For the development of linear and nonlinear analytic relations, the Euler–Bernoulli beam and linear voltage variations in the thickness direction are used, and for the separation of variables, the mass normalized mode shapes has been used. The results of the linear analytical method are compared with the results of past research and experimental... 

In this study, through explaining a micromechanical model of progressive damage, failure in a composite conical structure under mechanical and thermal loads with 36 layers of carbon/phenolic material have been studied. To this end, first, mechanical behaviors of composite layers in micro and macro scale and their properties via fiber and matrix characterizations are discussed. In the following, selection of a proper RVE along with different types of boundary conditions on RVE are discussed. Then stress reinforcement coefficients in order to convert the mechanical and thermal stresses from macro to micro scale for carbon / phenolic material are extracted through defining appropriate RVE for... 

A sustainable supply chain requires constant sustainable changes in the design and performance of its steps. The main characteristic of sustainability is the consideration of social, environmental and economic criteria in strategic and operational decisions. Due to the great importance of the sustainability in transportation network, proper planning and careful design for this issue in recent years has been considered and welcomed by relevant researchers. In this research we want to provide an integrated frame work for transportation network design toward sustainability. In this regard, we also use 3D printing technology as our innovation in operations. Our main issue is the Inventory... 

Quantum memory which stores the coherent information of logical qubits, is an essential ingredient of quantum information processings. Each logical basis should be encoded on macroscopically distinct physical states since otherwise the indistinguishability of logical bases is easily destroyed by local errors.On the other hand, the memory must be able to have superposition of macroscopically distinct states of physical qubits. To maintain such superposition is very difficult. First, if the size of the memory is infinite, such macroscopic superposition is impossible since superposition of different phases is just a classical mixture of them in an infinite system. Second, even in finite... 

Topologically ordered phases are of great interest in the field of quantum information and quantum computation in order that their degenerate ground states provide a suitable space for coding and processing the quantum information. Such space is resistant to local errors intrinsically. A natural question to ask is to what degree these topological phases are resilient against perturbations and how the transition from topological order to another kind of order occurs.In this thesis, at first we introduce the concept of topological order. We explain the Kitaev model, which is the first introduced topological model on lattice, and study the common properties between topologically ordered systems... 

In recent studies, it has been shown that entanglement is not the only kind of genuinely quantum correlation. There exist models of quantum computation that provide exponential speed up over the best known classical algorithms and don’t have any quantum entanglement. These models show that in some cases separable state can be very useful in quantum computing models. Look for a property that causes the performance of these scenarios, quantum correlation being one of the most important concepts, including but not limited to entanglement. Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical... 

Systems which have local ordered parameters are fragile and sensitive to local errors.Among these systems, quantum systems with local order face errors due to interaction with the environment, which eventuates in destruction of information. It goes without saying that quantum error-correction is a very difficult task to do. This happens in the grounds that not only is the observation of qubits impossible, but also based on no-cloning theory in quantum mechanics, there is no way to have copies of these qubits. Therefore, the interaction of quantum systems with the environment should be controlled in the way that in which we can correct errors using error-correction condition.However, there is... 

Banks are not only money brokers but also money creators. The ability of a bank to create money is due to its unique feature in issuing debts (deposits) that are accepted as a medium of exchange by economic agents. Although this bank function has been discussed under the "liquidity transformation" heading under the micro-banking literature, it has been less discussed in macro literature. In this study, we want to examine the consequences of the bank's liquidity transformation function by developing a New-Keynesian model in which banks can finance the economy by voluntarily expanding their balance sheet. To identify the mechanisms that the money creator bank creates in the model, we have... 

Entanglement is one of the most important concepts in quantum information science. Aer playing a significant role in the foundations of quantum mechanics, it has been discovered as a new physical resource with potential commercial applications such as teleportation, dense coding and so on. Perhaps one of the most important problems in studying the properties of entangled states is the quantification of entanglement. There are many measure of entanglement that all of them has to satis some conditions. The structure of entanglement in multipartite systems is much richer than that in the case of bipartite systems and is an open problem in quantum information theory. Graph states are special... 

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