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 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 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.Item Computing Connection Number-Based Indices for Graphs Derived from Metal Organic(Library Information Services, CUI Lahore, 2023) Muhammad Adeel Arshad; CIIT/FA21-RMT-068/LHR; Dr. Hafiz Muhammad Afzal SiddiquiMetal-organic networks consist of metals and organic ligands, forming their two distinctive components. In the realm of Mathematical Chemistry, metals are elements that exhibit metallic bonding and possess a propensity to readily form positive ions. Ligands, on the other hand, encompass neutral molecules or ions that attach to the central atoms or ions of metals, forming bonds. The recent surge in the significance of distance-based topological indices has led to their widespread use in exploring the structure-property relationship among molecules. Given their importance, this thesis focuses specifically on distance-based topological indices. It delves into Metal-organic Networks, examining their characteristics and properties. The thesis also involves the computation of several connection-based Zagreb indices to gain insights into the Metal-organic Networks. By emphasizing the role of distance-based topological indices, this study aims to contribute to our understanding of Metal-organic Networks and their structural features. The examination of these indices offers valuable information regarding connectivity and complexity, facilitating further research and potential applications in fields such as materials science, catalysis, and drug discovery. .Item Constructing Numerical Scheme Using Python in Neural Field Model(Library Information Services, CUI Lahore, 2023) GHULAM QADIR; CIIT/FA21-RMT-060/LHR; Dr. Muhammad YousafWe analyze a two-population neuronal network model of the Wilson-Cowan type to inves- tigate the presence of localized stationary solutions called “bumps”. Specifically, we focus on a scenario where two distinct types of bump solutions exist: a narrow pair and a broad pair.To assess the stability of these bumps, we employ two different approaches: one that generalizes the Amari method and another based on a direct linearization procedure. These approaches yield consistent predictions, except for one significant difference. The narrow pair is generally unstable, while the broad pair remains stable for small and moderate values of the relative inhibition time.Interestingly, at a critical relative inhibition time, the broad pair typically undergoes a Hopf bifurcation, transitioning into stable breathers. Notably, in our numerical example, the broad pulse pair remains stable even when the inhibition time constant is three times longer than the excitation time constant. Consequently, our model findings contradict the assertion that slow excitation mediated by NMDA-receptors or similar mechanisms is nec- essary for the presence of stable bumps.Item Study of Thermal Stability and Thermodynamic Geometries of Well-Known Black Holes through Entropy Corrections(Library Information Services, CUI Lahorez v, 2023) Mazhar Hussain; FA20-RMT-017; Dr. Abdul JawadIn this thesis, we investigate the thermal stability and thermodynamic geometries of non-rotating/rotating charged black holes. For these black holes, we apply Barrow and power-law entropy to determine the physical quantities such as mass and temperature of the system and ¯nd their sta- bility through ¯rst and second phase transitions of the heat capacity. We analyze the e®ects of scalar charge Q and hair parameter ¸ on black holes properties by taking both positive and negative values of these parame- ters. It is noted that heat capacity provide the stable, unstable regions and phase transition points for both black holes. To investigate the thermody- namic geometry of these black holes, various techniques such as Ruppeiner, Weinhold, Quevedo and HPEM metrics are considered. It is observed that Weinhold, Quevedo and HPEM give attrative/repulsive behavior of parti- cles in stable/unstable regions of black holes.Item Study of Cosmic Expansion through Several Equation of States(Library Information Services, CUI Lahore, 2023) Abu Bakar; /FA21-RMT-059/; Dr. Shamaila RaniIn this thesis, we discuss the cosmic acceleration of expanding universe through various cosmic parameters in the framework of f (Q) gravity. This gravity is also termed as modi¯ed symmetric teleparallel gravity, where Q stands for "non-metricity". The FRW space-time with perfect °uid are taken as geometry and matter of the universe. We consider two models for cosmic scale factor a(t) as power law form and Dabrowski and Marosek form. In the presence of holographic dark energy density, we study the dif- ferent parameterizations of its model parameter c(z) where z represents the redshift function. These parameterizations help to study the cosmic expan- sion through the cosmological parameters. We plot the equation of state parameter for each model in order to illustrate the cosmic analysis associ- ated with this theory. We examine the squared speed of sound parameter for these models to assess their stability. With regard to the particular values of the model parameters, we achieve some positive outcomes. In addition, we look into how energy conditions can be used to distinguish between the various models and to analyze how matter and energy behave in f (Q) gravity models. For example, by employing energy conditions to test this, one can produce the observed accelerated expansion of the cosmos which is thought to be driven by dark energy.Item Graph Energies on Bridge Chain for Composition of Graphs(Library Information Services, CUI Lahorez v, 2023) Ambar Munir; FA20-RMT-008; Dr. Muhammad HussainThe graph𝐺 consists of some vertex 𝑉(𝐺) are connected by 𝐸(𝐺) wherethe position of vertices does not matter. The degree of a graph vertex is basically a number of incident edges 𝐸(𝐺) and vertex 𝑢 can be denoted by du. The upper and lower bound of graph energy with minimal and maximal energy is abroad field of Spectral Graph theory. The energy of Graph 𝐸(𝐺)in term of vertices and number of edges in graph 𝐺 is involvedin absolute value of eigenvalue adjacency matrix of G where λis thespectral radius. The Graph has energy equal |.Finally, we determine the energy, pattern and irregularities of chain like cyclic graph. Our exploring outputs will rely upon Size and Order of Graph, Degree of Graph, Irregular Graph, Multi Graph, Cyclic Graph, Wheel Graph, Bridge Graph, Prism Graph, Connected and Planarity Graph, and Concept of Distance and Degree in Graph.