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 Thermodynamics of Specific Black Holes(Library Information Services, COMSATS University, Lahore Campus, 2020) Amna Khawer; , FA16-RMT-024; Dr. Abdul Jawad, Assistant Profesor; LHR TP 5190In this thesis, we modify the first law of thermodynamics for regular black hole of non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a regular black hole, which is associated with cosmological constant by the surface tensions. The corresponding Smarr relations are also satisfied for them. The cosmological constant is taken as constant as well as variable (which is correlated with pressure). We calculate the Gibbs free energy to discuss the global stability of the above mentioned regular black holes in general relativity. At first, the cosmological constant is adopted as fixed and then as a variable, which is correlated with the pressure. The first law of thermodynamics is modified for both regular black holes, mentioned above, when the cosmological constant is treated as fixed and as a variable. Also, we investigate the thermodynamical properties and consider the logarithmic correction to entropy in order to analyze thermal fluctuations of two another regular black hole: 1) The AdS black hole in Born-Infeld massive gravity with a non-abelian hair. 2) The charged AdS black hole with a global monopole. We develop the many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, the Gibbs free energy and the Helmholtz free energy for both black holes. We observe the critical behavior and phase transition and check the validity of the first law of thermodynamics. We observe the local stability and the global stability of the black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter η and massive parameter m. ixItem Topological Indices Related to Graph Operations(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2020) Urooj Akram,; FA16-RMT-005; Dr. Syed Tahir Raza Rizvi, Assistant Profesor; lhr tp 5179Topological Indices Related to Graph Operations In this thesis we find out the atomic bond connectivity index, Randic index, augmented Zegreb index, geometric arithmetic index and product connectivity index for sum and corona of any two connected graphs. By using neighborhood degree we formulate fourth version of atomic bond connectivity index ABC4 and fifth version of geometric arithmetic index GA5 of sum of two graphs. We also formulate atomic bond connec tivity index for product of any two regular graphs . Furthermore, we formulate new atomic bond connectivity index of F-sum of cycle (Cm) and path (Pn) graphs. At the end we calculate new atomic bond connectivity index ABC5 depending on graphs kC8 where k are the stages ofC8 depends on straight chain and pairwise zigzag chainItem New Solitary Wave Solution for Nonlinear Schrodinger Equation(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2020) Urooj Akram,; FA16-RMT-005; Dr. Syed Tahir Raza Rizvi, Assistant Profesor; lhr tp 5179A nonsingular and localized wave which propagates without change of velocity and shape is called a solitary wave. A soliton is a solution of NLPDE which has a per manent form and is localized. A solitary traveling wave does not obey superposition principle; it does not disperse. Solitary waves retain its permanent structure even when it collides with other soliton [25]. Soliton has many applications in other fields like engineering and biology. Soliton solutions can be calculated with the help of differ ent nonlinearities. These nonlinearities are Kerr law, power law, parabolic law, dual power law, exponential law etc. In this thesis we will study, the soliton solutions of Lakshmanan-Porsezian-Danial (LPD) model. In order to obtain exact soliton solutions several powerful methods have been proposed. We will use modified trail equation method with Kerr and parabolic law to obtain some hyperbolic and rational function solutions to LPD model. We also find new and more general exact traveling wave solution by using improved G′/G-expansion method with Kerr and parabolic laws of nonlinearitiesItem Cosmological Evolution in the Background of Non-Minimally Coupled Gravity(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2020) Muhammad Zeeshan,; FA16-RMT-010; DR. MUHAMMAD ZUBAIR, Assistant Profesor [Supervisor]; lhr tp 5182In current cosmic scenario, an accelerated expansion era is being reported by various observations. The reasoning of such scenario is still unknown, the pres ence of an unknown energy component is seen which is named as DE. There are various approaches to discuss the existence of DE and present acceleration of universe. One of such attempts is the modification of Einstein’s gravity, here we attempt to explore this problem within the modified gravity based on non minimal matter-geometry coupling. We examine f(R,T,Q) theory (where R is the Ricci Scalar, T is the trace of EMT Tuv and Q = RuvTuv is interaction of EMT Tµν and Ricci Tensor Ruv). We formulate the dynamical equations in the back ground of FLRW model and find the result of non-conserved EMT using the divergence of the field equations. In this scenario test particles deviates from geodesic motion and an extra force is there due to non-minimal coupling. We appliedthis result to findanexpressionforenergydensityρforparticularchoice of Lagrangian. Furthermore, we discuss the energy bound on the modelparam eters and discuss the late time cosmic acceleration for best suitable parameters in accordance with recent observations.Item Fractional Integral Inequalities For (α-m) Convex Functions(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Muhammad Irshad,; SP14-BSM-007; Dr. Saad Ihsan Butt, Assistant Profesor [Supervisor]; LHR TP 5263The aim of this project is to establish the Hermite Hadamard’s inequality involving frac tional integral for m-convex function. The obtained results have some relationship with [S.S Dragomire, R.P. Agrawal, two inequality for differentiable mapping and application to special means of real numbers and to trapezoidal formula, Appl.Math.Lett.,11(5)(199Item Topological Indices Of Chemical Graphs(COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2018) Sahar Dilber,; SP14-BSM-002; Dr. Muhammad Hussain, Assistant Profesor; LHR TP 5262Topological indices are real numerical parameters of a molecular structural net works and structural networks. These networks are characterize its topology and graph invariant. The molecular networks plays a vital role in QSAR \QSPR study, phisco-chemical properties and topological indices like Randic, atom-bond connec tivity(ABC) and geometric-arithmetic(GA) are used to diagnose the bioactivity of chemical compounds. Actually these topological indices is designed by transforming a chemical structure into a numeric number. In the area of research graph theory has been found to be very useful. In this thesis, we will compute the degree based topological indices the so-called general Randic index Rγ(G) for γ = {1, 12−1,−12 },atom bond connectivity(ABC), geometric-arithmetic(GA), first Zagreb, second Zagreb, second modified Zagreb, third zagreb, hyper Zagreb and augmented zagreb topological indices for subdivision of dif ferent kinds of networks like sierpinksi s(n,k) networks as well as molecular structural networks. This study will give us a very interesting and different results by using new topological index that is first Zagreb, second Zagreb, second modified Zagreb, third zagreb, hyper Zagreb and augmented zagreb topological indicesItem 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 Solution of Differential Equations by New Homotopy Perturbation Method(Library Information Services, COMSATS University, Lahore Campus, 2018) By: Muhammad Azeem,; FA14-BSM-009; Dr. Mohsan Hassan, Assistant Profesor [Supervisor]; LHR TP 5256In this project, a new modification of Homotopy perturbation method (HPM), called New Homotopy Perturbation Method (NHPM), has been applied for solving systems of non-linear partial differential equations. In chapter 2 we solved differential equations by HPM and in chapter 3 we solved same differential equations by NHPM. HPM and NHPM methods have been applied to three examples successfully and achieved approximate solutions. The basic idea described in this project is strong enough to be employed to solve other differential equations. The computations associated with the examples were performed using Mathematica 9.Item Discrete Mathematical Analysis Of Vascular Tumor(Library Information Services, COMSATS University, Lahore Campus, 2020) Muhammad Awais,; FA16-RMT-007; Dr. Ayesha Sohail, Assistant Profesor [Supervisor]; LHR TP 5181In this thesis, the growing field of mathematical oncology is discussed in a discrete manner. The discrete mathematical modeling of cancer has remained a topic of debate during the past decade. In the proposed research, we aim to discuss the effects of chemotherapy, on angiogenesis and on the associated tumour microenvironment with the help of a computational tool. Different combination of drug applications will be analyzed in order to predict the best dose candidate to eliminate the tumour. During this research, we will demonstrate, with the help of mathematical tools, the importance discrete agent based approach to model cancer invasion.