PhD

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Study of Cosmic Acceleration and Thermodynamic Consequences in Alternative Theories of Gravity
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Ayesha Iqbal; FA14-PMATH-002; LHR TP 7450; Dr. Abdul Jawad
In this thesis, we discuss two interesting issues: the accelerated expansion of the universe and thermodynamics. We consider flat Friedmann-Robertson-Walker universe model in alternative theories of gravity like loop quantum cosmology, Dvali- Gabadaze-Porrati brane world and fractal universe. We use different models of dark energy like Ricci Gauss-Bonnet dark energy and some latest holographic dark energy models namely Tsallis, Renyi and Sharma-Mittal holographic dark energy models for the analysis of both issues. For accelerated expansion of the universe, we examine the cosmological parameters like effective equation of state parameter, deceleration parameter, statefinder parameters, Om-diagnostic, plane of effective equation of state parameter with its evolutionary parameter and squared speed of sound parameter. We investigate the validity of the generalized second law of thermodynamics and thermodynamical equilibrium for the case of thermodynamic analysis. Firstly, we consider loop quantum cosmology and fractal universe in flat FRW universe with an interacting scenario between a non-canonical scalar field model of dark energy and dark matter. We make the analysis by using constant and variable (CPL parametrization) forms of equation of state parameters. We discuss the deceleration parameter for expansion rate along with squared speed of sound for stability analysis. Taking Bekenstein, logarithmic and power law entropies as the horizon entropy, we examine generalized second law of thermodynamics and thermal equilibrium. Secondly, we study the cosmological implications using Tsallis, Renyi and Sharma- Mittal holographic dark energy models in the interacting framework. We take into account two theories, fractal and Dvali-Gabadaze-Porrati brane world. We discuss the cosmological parameters and planes in both theories for the evolving universe. Finally, we examine the validity of generalized second law of thermodynamics of a physical system enveloped by apparent as well as event horizons. The system is comprised of Ricci Gauss-Bonnet dark energy and dark matter. We use various forms of entropy namely Bekenstein, Renyi, logarithmic and power law entropy corrections. We also examine the thermodynamic equilibrium in case of each entropy.
Algebraic Characteristics of Graphs
(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Muhammad Asim Razzaq; FA13-PMATH-004; LHR TP 7454; Dr. Kashif Ali
Graph theory is a vital and special branch of discrete mathematics. It deals with geometric computational study of various objects. The main component and object of the theory is graph and its generalization approach. Therefore, it has vast application to other mathematical and provides computational assistance to non-mathematical sciences. The most prominent use of graph theory as a significant tool in chemistry, this branch is named as chemical graph theory. It provides helpful assistance for obtaining molecular descriptor to develop essential relationship between molecular graphs and chemical compounds. Graph theory also serves its specialization in algebraic graph theory specifically labellings. In this dissertation, we formulate and discuss all these types of indices. We develop a new approach to calculate the eccentricities of vertices of any graph by using computer aid softwares. This approach help us to find the exact expression of the ECI and ABC5 for the butterfly, bene and torodial grid graphs. We also express a new type of counting polynomial associated with the previous counting polynomials. Moreover, we work some topological indices relative to degree dependent on generalized subdivision of line graphs. We also determine the general results about subdivision of line graphs for neighborhood valency-based indices. We also discuss the stability of line graph of chemical molecules.”Line0graphs furnish0a tool for0studying the0topological properties of0alpha-systems.”In addition to this, we study four important counting polynomials called omega, theta, PI and Sadhana for V-Phenylenic. We also introduced a new polynomial Upsilon on the basis of ”co” relation and find new results relative to new counting polynomial.”We also determine that inertia indices for V-phenylenic nanotube and these indices are not0equal for the line0graph of V-phenylenic0nanotube. We also find that the0nullity for this0nanotube and of line0graph of these0nanotube.”Lastly, we also discuss H-group magic labellings of some graphs. We mainly study about the H-groupmagic0total graph0labelings G(v; e) over finite0abelian0group Zt Zv, where H =K2; Ct and e = (t 􀀀1)v:
A Computational Investigation of Fluid and Air Bubble Dynamics in Two-Phase Flow
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Shamsul Jahan Shamsa (FA23-RMT-038); Dr. Mohsan Hassan; LHR TP 9783
This work investigates heat transfer in two–phase flow of Newtonian fluid (water bubbles) and power-law non-Newtonian fluid (carboxymethylcellulose) in a L-shaped pipe geometry. The problem is simulated using Computational Fluid Dynamics (CFD) techniques, specifically the Level Set interface tracking method. Focusing on pressure, velocity and temperature distributions under different flow conditions, the research addresses challenges related to computing efficiency, numerical stability, and interface dynamics. These findings lay a foundation for optimizing fluid system by illustrating how flow parameters affect phase interactions and pressure gradients.

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