M.Phil / MS

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This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.

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    Stellar Solutions in Rastall Modified Gravity by Embedding Technique
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Farooq Jamal; CIIT/FA18-RMT-011/LHR
    In this thesis, we discuss the compact stars models with the anisotropic mat- ter distribution in the context of Rastall theory of gravity. We solve the Rastall field equations by taking into account spherically symmetric line element. We construct the stellar models with the help of embedding technique. In order to achieve the purpose, first we choose the Karmarker condition with grr compo- nent of metric space as eλ(r) = 1 + cr2(1+ar2) n (1+br2)2 . We find the solutions for different values of Rastall parameter. We analyze the properties of stellar model by taking into account observational data of a compact star, named Vela X-1. We take into account different positive values of n and observe the scenario regarding the physical acceptability of the solution by presenting graphical analysis of ther- modynamical quantities, i.e., ρ, pr and pt. Next, we choose Karmarker condition with another radial component, i.e., eλ = (A − Br2) 2 and analyze the viability of model considering observational data of compact stars, namely CenX − 3, PSRJ1614 − 2230 and, LMCX − 4. In order to check the physical viability of the solution, we discuss energy condition, TOV equilibrium condition, causal- ity condition and stability condition through graphical analysis. We have also presented variation of gradients, EoS, red-shift function and mass function. We find our solutions physical well-behaved for different values of n in the case of first model, while the graphical description of second stellar model guarantees its physical acceptability.
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    On Metric Dimension - Edge Metric Dimension
    (Library Information Services, COMSATS University, Lahore Campus, 2020) Muhammad Rafiullah,; FA18-PMAth-001; Dr. Hafiz Muhammad Afzal Siddiqui, Assistant Profesor
    On Metric Dimension - Edge Metric Dimension and Topological Properties of Connected Graphs The distance between any two vertices of a connected graph is the length of a shortest path between them. Any two vertices/edges are said to be resolved by a vertex if they have different distances w.r.t. that vertex. A set is a resolving set/edge resolving set if every vertex/edge of is resolved by some vertices of , respectively. A topological index is a real number associated to a graph that describes its topological properties. The main objective of this thesis is to study edge metric dimension of certain families of wheel related graphs and generalized Petersen graphs . It has been proved that the gear graph, the fan graph, the friendship graph, the sunflower graph and certain convex polytopes have unbounded edge metric dimension whereas the generalized Petersen graph has a constant edge metric dimension. An explicit Matlab program has also been given to generate the edge resolving set and edge coding for generalized Petersen graphs A comparative study between the metric dimension and the edge metric dimension of the aforementioned families of graphs has also been conducted. The second part of the thesis studies the Zagreb and co-Zagreb indices of iterated strong double graphs and some eccentricity-based indices of Sierpinski graphs and their regularizations. Moreover, some explicit algorithms have also been given to verify the validity of the results. x
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    Laminar Flow in Porous Channels Through Transverse Magnetic Field by Using Optimal Homotopy Analysis Method
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Farooq Abid; FA18-RMT-063; LHR TP 6462; Dr. Muhammad Yousaf Bhatti
    In this work, we have investigated the laminar flow in porous channels applying transverse magnetic field on it. We have reviewed the work of Suryaparkasarao et al.\cite{surya} in detailed. Suryaparkasarao et al. did this by reducing the order of the main equation to third order nonlinear differential equation which was derived after the simplification of Navier stokes equation and continuity equation. They have calculated the velocity components, pressure distribution and skin friction coefficients. Noreena et al. have solved same problem in two different ways. In the first part, they solved the forth order non-linear differential equation in a simplified way without reducing its order. In second part, they have employed Homotopy Perturbation method which is better approximation then regular perturbation method. We discuss the same problem with a different technique is known as Optimal Homotopy analysis method (OHAM). Finally, we compute the velocity components and compare these results .
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    Non-Linear Interaction of Dark Energy Models in Fractal Cosmology
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ayesha Sadiq; FA18-RMT-076; LHR TP 6037; Dr. Shamaila Rani
    We investigate the cosmological aspects of various dark energy models in fractal universe by assuming non-linear interaction term between the dark energy and dark matter components. We work with three well-known models named as generalized ghost dark energy, power law corrected entropy and holographic dark energy. We investigate the cosmological parameters such as (deceleration parameter q, equation of state ωΛ, squared speed of sound, Om-diagnostic) and cosmological planes (ωΛ−ω´Λ, state-finder parameter). We explore these parameters graphically for the analysis of evolution of the universe. It is observed that by using different observational schemes the equation of state parameter gives consistent ranges. We check the model’s stability using the squared sound speed. In the present scenario, the squared speed of sound is stable for these three models. We also find the consistent results of the ωΛ − ω´Λ and statefinder planes with observational schemes.
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    Zagreb Connection Numbers of Different Chemical Graphs
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) ASAD ZUBAIR; FA18-RMT-051; LHR TP 6029; Dr. Muhammad Hussain
    Topological indices are real numerical parameters of a molecular structural networks 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 connectivity(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 connection based topological indices the so-called first Zagreb connection index, second Zagreb connection index and first modified Zagreb connection index of Honeycomb Network, Linegraph of Honeycomb Network, Line graph of subdivision of Honeycomb Network Triangular Benezenoid Network,line graph of sub-division of Triangular Benezenoid Network and Hourglass system. This study will give us a very interesting and different results by using new topological index that is first Zagreb, second Zagreb, first modified Zagreb connection index.
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    Thermodynamic Quantities and Quasinormal Modes of Specific Black Holes
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Yasir; FA18-RMT-049; LHR TP 6027; Dr. Abdul Jawad
    It is not for the sun to exceed the moon, nor does the night leave behind the day. They all float/travel, each in an orbit. (Quran 36:40) The Joule-Thomson effect and quasinormal modes (QNMs) onto regular non-minimal magnetic black hole (BH) with a cosmological constant are being investigated. For this purpose, we extract some thermodynamical parameters such as pressure P and mass M in the presence of magnetic Qm as well as electric q charge. These parameters lead to inversion tem perature Ti, pressure Pi and corresponding isenthalpic curves. Introducing the tortoise coordinate, however, the Klein-Gordon wave equation leads to the second-order ordinary Schr¨odinger equation. For this BH, computing complex frequencies of QNMs under the scalar field perturbation satisfied their boundary conditions by using the Wentzel-Kramers-Brillouin (WKB) technique. Moreover, we consider the Lorentz symmetry violating Ba˜nados, Teitelboim and Zanelli (BTZ) BH and Hairy BH of dimensionally contin ued gravity. These solutions are obtained in massive gravity and power Yang-Mills magnetic field. We utilize the general form of first law of BH thermodynamics and compute different thermodynamical quantities. The cosmological constant Λ (either positive or negative) plays an important role in BH thermodynamics when treated as a positive thermodynamical pressure. We derive corresponding equations of state and discuss the phase transitions which is comparable with chemical Van der Waals fluid. We also find out the critical points and observe that system exhibits first order small as well as large BHs phase transition
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