Department of Mathematics

Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21

Browse

Subject: search.filters.subject.department of Mathematics

Search Results

Now showing 1 - 5 of 5
  • No Thumbnail Available
    Item
    Phase Space Analysis and Cosmic Parameters of Dynamical Dark Energy Model
    (Library Information Services COMSATS University Lahore Campus, 2024-03-18) Ruqia Arif; SP23-RMT-027; Dr. Abdul Jawad; LHR TP 9581
    This thesis explores the stability analysis of Friedmann-like spacetimes using dynamical system methods. For this purpose, we begin by considering a modified cosmological sce nario based on Tsallis entropy corrections. These entropic formulations modify the cosmo logical field equations that govern the universe’s dynamics. We incorporate these modified Friedmann equations and convert them into a first-order autonomous system of differential equations. To identify the system’s equilibrium points, we consider the interaction between cosmological fluids. Various linear and non-linear forms of interaction models are exam ined. For each model, we calculate the critical points and discuss their behavior associated with eigenvalues. We investigate the different stages in the universe’s evolution including dust and radiation dominated era of the universe as well as quintessence, ΛCDM and phan tom regimes. In addition, we develop the phase space portraits of all the interaction models revealing the stable, unstable and saddle behavior of critical points. In most of the cases, the system supports stable critical points.
  • No Thumbnail Available
    Item
    Analysis of the Formulations and Continuities of Kernels of Integral Equations for Ahlfors Map
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Muhammad Amin Khan; FA22-RMT-017; Dr. Kashif Nazar; LHR TP 9380
    This study aims to examine and analyze the boundary integral equations of the Ahlfors map specifically for multiply connected regions. The Ahlfors map, known for mapping the boundary of a domain to the unit circle, helps in understanding the domain’s structure. Our goal is to rederive boundary integral equations that are more effective in determining the Ahlfors map and its unknown zeros. Identifying these zeros is crucial as they provide important information about the map’s behavior and the domain’s geometry. By develop ing these new equations, we hope to address existing challenges and solve long-standing problems in the field, ultimately advancing mathematical understanding and applications of the Ahlfors map in complex analysis and related disciplines.
  • No Thumbnail Available
    Item
    Modified Entropy Inspired Scalar Field Cosmic Inflation with Well-known Potentials
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Hafiza Iqra Nadeem; FA22-RMT-022; Dr. Abdul Jawad; LHR TP 9377
    This thesis is dedicated to discuss the inflationary setup with the help of modified Barrow entropy with f(R) gravity framework. We derive the Friedmann equations by using the first law of thermodynamics. With the help of these equations, we reconstruct f(R) gravity model to establish the relationships governing scalar and tensor perturbation power spectra and interestingly this model mimics thermodynamically under the slow-roll approximation. Two different types of potentials like the β potential and the exponential potential are used to explore the insights of inflationary parameters in the underlying scenario. Thus, the inflation-related quantities like scalar spectral index and tensor-to-scalar ratio are discussed graphically in our scenario by developing contour plots. It is worthwhile mention here that our results are consistent with Planck 2018 data.
  • No Thumbnail Available
    Item
    Atom Bond Sum Connectivity Index of Some Connected Graphs
    (Library Information Services COMSATS University Lahore Campus, 2023-03-13) Ayesha Rasool; SP22-RMT-022; Ayesha Rasool; LHR TP 8728
    In this thesis, our aim is to study a newly introduced topological index named Atom Bond Sum Connectivity (ABS) index for some wheel related graphs like Sunflower graph SFn, Jahangir graph J2n, Helm graph Hn and Friendship graph Fn. We obtained their ABS index and categorized these graphs based on this specific topological descriptor. ABS index is recently introduced by Akbar Ali et al. They combined the idea of three previous topo logical indices, namely the Randic index R(G), Sum-Connectivity index SC(G) and Atom Bond Connectivity index ABC(G). ABS index get the quick attention of researchers in a short period of time. The main goal of this project is to study the nature of ABS index by applying it on some wheel related graphs. We also observed the applications and uses of the ABS index as it can help check the chemical and physical properties of a chemical graph or network.
  • No Thumbnail Available
    Item
    Shadow of Charged Rotating Wormholes
    (Library Information Services COMSATS University Lahore Campus, 2023-03-13) Shokaib Shahid; SP22-RMT-032; Dr. Rabia Saleem; LHR TP 8733
    In this work, we investigate the optical appearance of qualitatively new observational fea tures of accretion disk images around the charged rotating traversable wormhole (TWH) space-time for different spin, throat, and charge values. To accomplish this, we first con sider the Hamilton-Jacobi method to derive the geodesic equations for the motion of pho tons and study the effects of parameters on the photon orbit in the observer’s sky. We found that each parameter affects the size and shape of the wormhole (WH) shadow and flatness is observed in the shadow because of spin and other parameters. To produce shadow im ages of sufficient visual quality but within manageable computational times, we adopt the ray-trace procedure and characterize the significant features of light trajectories on the ob server’s screen, depending on the interaction between the space-time structure and the ac cretion disk. In addition, we consider the static spherically symmetric accretion flow model to observe the specific intensity around the TWH space-time geometry. It is found that the intensity and positions of the photon ring vary with respect to the involved parameters. In future observation, this type of study may provide a fertile playground to test the nature of compact objects, specifically the WH in the strong-field regime.