Final Year Projects (FYPs) - Undergraduates
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/53
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Coupled Parallel Fluid Flow in Porous Medium Adjacent to Free Flow Domain(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Ifrah Tehreem; CIIT/SP17-RMT-023/LHR; Dr. Mohsan Hassan; LHR TP 5746Fluid flow through a partially filled porous channel, in which porous layer is considered at center of the channel bounded by free flow regions. Fluid flow over a partially filled porous channel is directed by different types of mathematical model with various kinds of boundary conditions at interface. In chapter 2, we consider the fluid flow through fluid-porous channel in which the flow in free region is governed by Stokes equation and Darcy-Forchheimer model. At interface, we assume the velocity for the free fluid is proportional to the shear rate of the permeable region. In this chapter, we examined the effects of the Darcy number, interfacial velocity slip coefficient and Knudsen number on the velocity distribution. In chapter 3, we consider the same channel in which porous media, but here mathematical model is govern by Stokes equation for free region and Brinkman model for porous region. In addition, at the interface, we use the continuity condition of velocity and shear stress with jump effect to find the fluid flow behavior through the channel. In this case, the effect of different values of Darcy number on the velocity distribution is analyzed and compare with the results of Chapter 2.Item Structural Properties Of Certain Molecular Graphs(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Shahid Imran,; FA14-BSM-017; Dr. Muhammad Hussain, Assistant Profeso; LHR TP 5261Abstract Let G=(V,E)beasimple connected graph. The sets of ver tices and edges of GaredenotedbyV =V(G)andE =E(G) respectively. In such a simple molecular graph, vertices rep resent atoms and edges represent bonds. In chemical graph theory, we have many invariant polynomials and topological indices for molecular graph. In this thesis we focus on the structure of molecular graph of Bakelite network. Morever the vertices having degrees (2,2),(2,3) and (3,3) gives the generalized form of count of edges in terms of m and n. The m in chemical structure represent the number of rows and n represent the number of column in Bakelite structure. In this thesis we compute the different indices such as Atom bond conecctivity ABC,Geometric arithmatic G(A), Zagreb, Hyper Zagreb, Augmented Zagreb, Randic index and Har monic indices of Bakelite network. Topological indices are real numerical parameter of a chemical structural networks and structural networks. These networks are characterize its topology and graph invariant. The topological indices like Randic, ABC, G(A), are used to diagnose the bioactiv ity of chemical compounds. Actually these topological in dices is designed by transforming a chemical structure into a numeric number. iItem Rheological Modeling of Viscoelastic Materials through Different Methods(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Arooj Khizar; SP19-RMT-016; LHR TP 6473The present work is concerned with the rheological modeling of viscoelastic materials through different methods. The viscoelastic fluids have mechanical properties that are intermediate between ordinary liquid and solids. These properties are measured through the several kinds of expressions which are developed through different methods. In this thesis these methods are discussed in detail. The thesis contains five chapters, first chapter comprises of introduction of whole thesis, definitions and basic terminologies that are used throughout. In second chapter, we have discussed the differential form of Maxwell model, Kelvin-Voigt model, Burgers model and Standard linear model for viscoelastic fluids. In third chapter, the Creep and Recovery form of all the models along with different loading conditions are investigated. In fourth chapter, the small amplitude oscillatory form of the models is modeled and used to investigate the behavior of elasticity and viscosity against angular frequencyItem Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to a Tansportation Problem(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Mudasir Nazar, Umer Farooq; CIIT/FA22-BSM-031/LHR, CIIT/FA22-BSM-59/LHR; Dr. Madiha Khalid; LHR TP 9924This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli- cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever- aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini- mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac- terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant roleItem Deviation of Rotating Black Hole in Loop Quantum Gravity from Kerr Black Hole(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) MADIHA KANWAL; CIIT/FA20-BSM-041/LHR; Dr. Muhammad Zubair; LHR TP 9916First and foremost, I would like to thank ALLAH Almighty (the most beneficent and most merciful) for giving me the strength, knowledge, ability and opportunity to undertake this research study and to preserve and complete it satisfactorily. My heartiest gratitude to Hazrat Muhammad (S.A.W) for His guidance to humanity and for material and spiritual uplift. I would like to express my deepest gratitude to my supervisor Dr. Muhammad Zubair, for his excellent guidance, interest, patience, and for providing me a decent atmo- sphere for the research. It was not an easy task but his extraordinary support made it so. I am also thankful to my senior research fellow Muhammad Ali Raza (PhD student) who always taught me with his humble attitude and with whom I collaborated and learned many things. Lastly, I would like to thank my parents and siblings, who always supported me and prayed for my success. Without their support, love and efforts, I would have not achieved all this. They gave me wings to fly.Item Dynamics of a Vector-Host SIR-SI Model in Dengue Transmission(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Rayan Zahid; CIIT/SP21-BSM-001/LHR; Dr. Syed Tahir Raza Rizvi; LHR TP 9877Dengue fever is a major health problem, especially in tropical and subtropical areas, affect- ing around 50 countries. The disease is mainly spread by Aedes mosquitoes, with Aedes aegypti being the most important carrier. Urbanization, climate change, and population movement make it spread more easily. Dengue symptoms can range from mild fever to se- vere hemorrhagic fever, which can be fatal. To control the disease, effective strategies are needed, and epidemiological models are crucial for understanding disease spread, testing interventions, and predicting outbreaks. In this project, we will create a model that describes the relationship between humans and mosquitoes using a susceptible-infected-recovered (SIR) model for people and a susceptible- infected (SI) model for mosquitoes. The goal is to understand how these two groups in- teract and use this information to improve control measures. We will calculate the basic reproduction number (Ro) using the Next Generation Matrix method to determine whether the disease will spread (Ro > 1) or fade out (Ro < 1). We will also use stability analysis with the Lyapunov function to check these results. Furthermore, we will run simulations in MATLAB to test the model and explore the effects of control measures like mosquito population control, vaccination, and quarantine. By doing sensitivity analysis, we will identify the most important factors affecting disease spread and help prioritize the best in- terventions. The project aims to provide useful insights into how dengue spreads and guide effective ways to control it.Item Discussions on Solutions of Fredholm Integral Equations(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Muhammad Adeel Khan; CIIT/SP21-BSM-022/LHR; Dr. Kashif Nazar; LHR TP 9888This thesis investigates the analytical and numerical solutions of Fredholm integral equa- tions of the second kind, focusing on both homogeneous and non-homogeneous cases. In the analytical framework, we explore solutions with degenerate kernels and methods to ap- proximate complex kernels by degenerate forms, providing efficient pathways for problem simplification. The study covers both theoretical and applied aspects, emphasizing cases where the kernel exhibits specific structures that facilitate closed-form solutions. Numer- ical methods are also developed and analyzed for solving these integral equations in both homogeneous and non-homogeneous settings. The numerical approaches are evaluated for their accuracy and computational efficiency, providing insights into practical implemen- tations and approximations for real-world applications. Through comprehensive analysis and comparison of methods, this research contributes to the effective solution of Fredholm integral equations, offering new perspectives for both theoretical exploration and applied problem-solving.Item Metric Dimension of Wheel Based Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Muzammal Ashraf; CIIT/SP21-BSM-037/LHR; Dr. Hani Shaker; LHR TP 9894The concept of metric dimension is essential for solving a variety of structural and opti- mization issues. The smallest size of a set of vertices that allows the original vertex to be uniquely determined by the shortest distances from any vertex to these selected vertices is known as the graph’s metric dimension. This idea finds use in the construction of effective routing algorithms, network navigation, and locating issues. In this study, we investigate the metric dimension of different classes of graphs, such as trees, pathways, cycles, and more intricate structures like grids and hypercubes. We explore methods for computing the metric dimension and present novel approaches to obtain accurate values or constraints for particular graph families. The study sheds light on the behavior of the metric dimen- sion under various graph settings, emphasizing how it varies with respect to graph factors including degree, vertex connectivity, and diameter. Furthermore, we examine the compu- tational difficulty of figuring out the metric dimension and suggest effective strategies for real-world uses. In order to provide more efficient solutions for graph-based problems in practical settings, we seek to optimize the determination of metric dimensions by utilizing recent developments in computational techniques.Item Neutrosophic Fuzzy Number Optimized Path in a Network(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Shahzaib Sajid; CIIT/SP21-BSM-029/LHR; Dr. Madiha Khalid; LHR TP 9889Fuzzy and neutrosophic numbers are mathematical tools designed to handle un- certainty and imprecision in real-world problems. Fuzzy numbers, grounded in fuzzy set theory, represent values with gradual transitions between membership and non-membership, characterized by a membership function. These numbers effectively model uncertainty when precise values are unavailable, as seen in applications like decision-making, optimization, and engineering systems. Neutrosophic numbers extend this concept by incorporating indeterminacy into the model, a key feature of neutrosophic set theory. They consist of three components: truth (T), indeterminacy (I), and falsity (F), each of which is independently assessed. This structure enables a more nuanced representation of uncertainty, capturing scenarios where incomplete, contradictory, or vague information coexists. Both approaches play crucial roles in addressing the complexity of real-world problems where classical mathematics may fall short. While fuzzy numbers are suitable for problems with well-defined boundaries of uncertainty, neutro- sophic numbers offer superior flexibility in environments with higher levels of indeterminacy. Together, these tools have broadened the scope of uncertainty modeling across disciplines such as artificial intelligence, economics, and risk managementItem Properties of Total Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) BISMA ATIQ; CIIT/FA20-BSM-007/LHR; Dr. Imran Ahmed; LHR TP 9913With every graph G (finite and undirected with no loops or multiple lines) there is associated a graph L(G), called the line-graph of G, whose points correspond in a one-to-one manner with the lines of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of G are adjacent. Let G = (V, E) be a graph. The Gallai total graph ΓT (G) of G is the graph, where V (ΓT (G)) = V ∪ E and uv ∈ E(ΓT (G)) if and only if (i) u and v are adjacent vertices in G, or (ii) u is incident to v or v is incident to u in G, or (iii) u and v are adjacent edges in G which do not span a triangle in G. The anti-Gallai total graph ∆T (G) of G is the graph, where V (∆T (G)) = V ∪ E and uv ∈ E(∆T (G)) if and only if (i) u and v are adjacent vertices in G, or (ii) u is incident to v or v is incident to u in G, or (iii) u and v are adjacent edges in G and lie on a same triangle in G. The Gallai middle graph ΓM(G) of a graph G = (V, E) is the graph whose vertex set is V ∪E and two edges ei, ej ∈ E are adjacent in ΓM(G), if they are adjacent edges of G and do not lie on a same triangle in G, or if e = uv ∈ E then e is adjacent to u and v in ΓM(G). The anti-Gallai middle graph ∆M(G) of G is the graph whose vertex set is V ∪E and two edges ei, ej ∈ E are adjacent in ∆M(G) if they are adjacent in G and lie on a same triangle in G, or if e = uv ∈ E then e is adjacent to u and v in ∆M(G).In this paper, we present Eulerian and Hamiltonian properties of Gallai and anti-Gallai middle graphs. In this paper, we investigate Total Graph, Gallai and anti-Gallai Total Graphs and Middle graph.