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Homogenization of Hamilton - Jacobi Equations
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
The aim of homogenization theory is to establish the macroscopic behaviour of a system which is ‘microscopically’ heterogeneous, in order to describe some characteristics of the heterogeneous medium (for instance, its thermal or electrical conductivity). This means that the heterogeneous material is replaced by a homogeneous fictitious one (the ‘homogenized’ material), whose global (or overall) characteristics are a good approximation of the initial ones. From the mathematical point of view, this signifies mainly that the solutions of a boundary value problem, depending on a small parameter, converge to the solution of a limit boundary value problem which is explicitly described. In...
Generalized Young Measures and Calculus of Variations
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
In this thesis, issues related to the minimization of a class of energy functions defined over the space of vector valued functions, under a linear differential constraint are discussed. We collect a series of lower semi-continuity results with respect to the weak convergence obtained by using the tools of Young measures int the case of growth condition larger than one and using generalized Young measures in linear growth case.The general trend in these results is to obtain a good representation of the energy limit by a quantitative study of the oscillation and concentration effects in a weakly convergent sequence
Projection matrix by orthogonal vanishing points
, Article Multimedia Tools and Applications ; Volume 76, Issue 15 , 2017 , Pages 16189-16223 ; 13807501 (ISSN) ; Fouladi, S ; Kasaei, S ; Sharif University of Technology
Springer New York LLC
2017
Abstract
Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the...
Existence and Regularity of Renormalized Solutions for Boltzmann Equation
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
In 1989 DiPerna and Lions proved the stability of Boltzmann’s evolution equation using their theory of renormalized solutions. Their result , for the first time, proved the existence of solutions without extra assumptions on the initial condition and on arbitrary time intervals. While the wellknown Grad’s cut-off assumption is present in the original theory, there have been successful generalizations to account for the singular case. Also the renormalization theory has shed light on limiting regimes of the Boltzmann equation. Here we discuss the new techniques that are essential for such generalizations
Mathematical Frameworks for the Study of Oscillatory Networks in Neuroscience
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
In this thesis, we first introduce the required biological preparations and popular models for modeling single neuron, synapse and cable. Then by introduction of limit cycle oscillators and the necessary prerequisites, investigations are limited to systems involving weakly coupled oscillators. As two examples of such models, famous Kuramoto and Wilson- Cowan models are described. In the following, we introduce some methods for reduction dimension of weakly coupled oscillators and finally we apply one of the expressed methods on the dynamics of cortical network
Image Processing Using Calculus of Variations and PDEs Tools
, M.Sc. Thesis Sharif University of Technology ; Fotouhi, Morteza (Supervisor)
Abstract
The aim of this thesis is to investigate recent methods for Image Processing(Any signal process which it’s input is an image and it’s ouput is an image or a set of Image parameters) using Calculus of variation tools. Methods which are to be investigated has been divided into two well known parts of Image Processing : Image Restoration and Image Segmentation.Image Processing Chapter includes two sections: one calculus of variations methods(energy method), other methods based on PDEs(heat equation and Malik-Perona equation). In studing each of this methods, It has been tried to include experimental results and negative and positive points of them.In Image Segmentation Chapter, first...
Level Set Methods
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
Level set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the Eulerian approach). Also, the level set method makes it very easy to follow shapes that change topology, for example when a shape splits in two, develops holes, or the reverse of these operations. All these make the level set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water
Shape and Topology Optimization for Elliptic Boundery Value Problems using a Piecewise Constant Level Set Method
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
The aim of this thesis is describes the method a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy...
Development and Application of a Model for Assessing the Sustainability of Energy supply System
, M.Sc. Thesis Sharif University of Technology ; Saboohi, Yadollah (Supervisor)
Abstract
Depletion of fossil energy reserves and rapid growth of energy demand have been challenging issues in the energy sector. Proper solution of these issues requires development of an integrated and comprehensive approaches. Such conceptual framework could provide an appropriate means for studying energy problems and anlysing the development of efficient technologies which could improve the economic viability and reduce the impact of energy system on the environmental. Therefore, analytical tools need to be developed further and they could be applied for systematic analysis of impact of new energy technologies on the economical efficiency and environmental compatibility of energy...
Elliptic Problems in Nonsmooth Domains
,
M.Sc. Thesis
Sharif University of Technology
;
Fotouhi Firouzabad, Morteza
(Supervisor)
Abstract
The In this thesis, we focus are attention on elliptic boundry value problems in domain with nonsmooth boundaries and problems with mixed boundry conditions. Indeed most of the available mathematical theories about elliptic boundry value problems deal with domains with very smooth boundaries;few of them deal with mixed boundry conditions.However, the majority of the elliptic boundry value problems which arise in practice are naturally posed in domains whose geometry is simlpe but not smooth. These domains are very often three-dimensional polyhedra. For the purpose of solving them numerically these problems are usually reduced to two-dimensional domains. Thus the domains are plane polygons...
Homogenization Theory and its Applications in Periodic and Perforated Domains
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
Through this thesis the Homogenization Theory for composite materials is studied assuming that the distribution of heterogeneities is periodic. In this theory two scales characterize the problem: microscopic and macroscopic scale. The first method that is used to solve the problem is the classical Asymptotic Expansion method where an error estimate is presented for the solution. The second method which was introduced by Luc Tartar for the first time is Oscillating Test Functions method. In the next chapter after introducing the concept of two-scale convergence, the Two-Scale Convergence method has been introduced. At last the unfolding
periodic method, which is based on the concept of...
periodic method, which is based on the concept of...
Shape Optimization in Pipe
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
Shape optimization can be viewed as a part of the important branch of computational mechanics called structural optimization. In structural optimization problems one tries to set up some data of the mathematical model that describe the behavior of a structure in order to find a situation in which the structure exhibits a priori given properties. Nowadays shape optimization represents a vast scientific discipline involving all problems in which the geometry (in a broad sense) is subject to optimization. The problem has to be well posed from the mechanical point of view, requiring a good understanding of the physical background. Then one has to find an appropriate mathematical model that can...
Particle filter-based object tracking using adaptive histogram
, Article 2011 7th Iranian Conference on Machine Vision and Image Processing, MVIP 2011 - Proceedings ; 2011 ; 9781457715358 (ISBN) ; Gholami, A. R ; Kasaei, S ; Sharif University of Technology
2011
Abstract
Object tracking is a difficult and primary task in many video processing applications. Because of the diversity of various video processing tasks, there exists no optimum method that can perform properly for all applications. Histogram-based particle filtering is one of the most successfu1 object tracking methods. However, for dealing with visual tracking in real world conditions (such as changes in illumination and pose) is still a challenging task. In this paper, we have proposed a color-based adaptive histogram particle filtering method that can update the target model. We have used the Bhattacharyya coefficients to measure the likelihood between two color histograms. Our experimental...
Total Variation Regularization In Medical Imaging
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
In this thesis, we study image restoration problems, which can be modeled as inverse problems. Our main focus is on inverse problems with Poisson noise; which are useful in many problems like positron emission tomography, fluorescence microscopy, and astronomy imaging. As a popular method in the literature, we use statistic modeling of inverse problem with Poisson noise, in the MAP-estimation framework. Then we introduce a semi-implicit minimization method, FB-EM-TV, that involves two alternate steps, including an EM step and a weighted ROF problem. Then we study well-posedness, existence and stability of the solution. This method can be interpreted as a forward-backward splitting strategy,...
Regularity of the Free Boundary in Semilinear Problems
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
There are some situations where we would like to solve a partial differential equation (PDE) in a domain whose boundary is not known a priori; such a problem is called free boundary problem and the boundary is called free boundary. For this kind of problems, aside from standard boundary conditions, an extra condition is imposed at the free boundary and the goal would be finding the free boundary in addition to finding a solution for PDE. One of the classical examples of free boundary problems is the Stefan problem (melting of ice) in which ice and water temperatures are determined from the heat equation and we would be interested in finding the boundary between ice and water. Another famous...
A free boundary problem for an elliptic system
, Article Journal of Differential Equations ; Volume 284 , 2021 , Pages 126-155 ; 00220396 (ISSN) ; Shahgholian, H ; Weiss, G. S ; Sharif University of Technology
Academic Press Inc
2021
Abstract
We study solutions and the free boundary ∂{|u|>0} of the sublinear system Δu=λ+(x)|u+|q−1u+−λ−(x)|u−|q−1u−, from a regularity point of view. For λ±(x)>0 and Hölder, and 0
Adomian Decomposition Method for Solving Differential Equations and Its Convergence
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
In¬¬ this thesis we review adomian decomposition method in solving differential equations.First described the technique and then we will introduce two ways to obtain adomian polynomials.In the next section to ompare two methods of adomian decomposition and Taylor series with two examples, we will solve an example and compared decomposition method with the Picard method and finally using Cauchy-Kowalewski Theorm Convergence of answer Series shown and it will present a rate of convergence
Oscillators in Neural Networks
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract
In this Thesis, we investigate the Modeling of Oscillator Neural Networks. Let Oscillators are coupled to each other Weakly. agood way to use Phase Model to describe each Oscillator. Then provide specific Examples to see the nesseceryConditions forExsistence and Stability of Synchrony and desyncrony
Three-phase Model for a Fixed-bed Laboratory Scale Diesel Hydrotreating Reactor
, M.Sc. Thesis Sharif University of Technology ; Khorasheh, Fahad (Supervisor) ; Sadighi, Sepehr (Supervisor)
Abstract
The harmful environmental effects of gases resulting from the combustion of sulfur compounds in fuel, poisoning of catalysts, corrosion of equipment, as well as the intensification of environmental considerations and new standards adopted for the maximum amount of sulfur, have made the desulfurization of fuels important; Meanwhile, the desulfurization method using hydrogen has a high potential to remove sulfur compounds. For example, diesel fuel contains a variety of impurities such as sulfur, nitrogen (basic and Non-basic), and aromatic compounds, the sulfur in diesel fuel causes many problems related to environmental pollution and corrosion of engine components. Also, due to the high...
A Multiscale Moving Boundary Model For Cancer Invasion
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firoozabad, Morteza (Supervisor)
Abstract
Cancer invasion of tissue is a key aspect of the growth and spread of cancer and is crucial in the process of metastatic spread i.e. the growth of secondary cancers. Invasion consists in cancer cells secreting various matrix degrading enzymes (MDEs) which destroy the surronding tissue or extracellular matrix (ECM). Through a combination of proliferation and migration, the cancer cells then actively spread locally into the surrounding tissue. Thus processes occuring at the level of individual cells eventually give rise to processes occuring at the tissue level. In this thesis we introduce a new type of multiscale model describing the process of cancer invasion of tissue.Our multiscale model...