Capstone Projects

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Browsing Capstone Projects by Subject "Capstone Project"

Now showing 1 - 4 of 4
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    Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids
    (Nazarbayev University School of Science and Technology, 2015-04) Tazhimbetov, Nurbek Akhmetuly
    In this thesis, I present different discretization techniques for boundary integral method for Stokes flow in case of an incompressible Newtonian fluid. Boundary integral method (BIM) is one of many techniques that are used to solve Partial Differencial Equations (PDE) numerically. However, the basic advantage of the BIM is that it reduces the problem from n-dimensional domain to n - 1; for example, the two-dimensional square-box that contains viscous liquid can be solved by using the values of an unkown function at the boundary of square. Nevertheless, the BIM exhibits some challenges in finding the Green's function for a particular domain or differential operator, solving the integral equations and, especially, in computing the values of a complex domain. The latter one is quite diffcult because the flow diverges at corners (exhibits singularity). The goal of this work is to derive general analytical solution for Stokes equation (in integral equations form) and to compute the discretized integral equations using different quadrature rules for cavity problem.
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    Multiple Point Compression on Elliptic Curves
    (Nazarbayev University School of Science and Technology, 2015) Otemissov, Adilet
    The paper aims at developing new point compression algorithms which are useful in mobile communication systems where Elliptic Curve Cryptography is employed to achieve secure data storage and transmission. Compression algorithms allow elliptic curve points to be represented in the form that balances the usage of memory and computational power. The two- and three-point compression algorithms developed by Khabbazian, Gulliver and Bhargava [4] are reviewed and extended to generic cases of four and five points. The proposed methods use only basic operations (multiplication, division, etc.) and avoids square root finding. In addition, a new two-point compression method which is heavy in compression phase and light in decompression is developed.
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    Optimization of convex geometries: component quadratic and general
    (Nazarbayev University School of Science and Technology, 2016) Myrzakul, Zhanbota
    In this Capstone Project, we worked with a class of closure systems called convex geometries, which are closure systems with a closure operator that satisfies the anti-exchange property. We first looked at the result of optimization algorithm of component quadratic systems, which are discussed in [4], and reproved it for the case of convex geometries. We then investigated the following question: if a convex geometry is given by a set of implications, is it possible to find its optimum basis in polynomial time when the convex geometry does not have particular properties (for instance, not component quadratic)?
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    Stability Analysis of SEIS model with spatial variations
    (Nazarbayev University School of Science and Technology, 2016-05) Baki, Zhuldyzay
    In this report we present an SEIS model for infectious diseases with latent period and no immune response for spatially heterogeneous environment. Spatial heterogeneity is designed by several metapopulations. It was shown that global dynamics of an epidemics completely depends on basic reproduction number R0. By fxing the number of patches to two, we use next generation matrix method to obtain basic reproduction number and make further analysis on it. Migration rates of individuals are considered as one of the main factors that influence R0. Moreover, some numerical simulations for the dynamics of the system with different initial conditions is presented.