PhD

Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/50

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

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Now showing 1 - 9 of 9

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.
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:
Degree and Distance Based Parameters of Certain Graph Structures Zeshan Saleem Mufti
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Zeshan Saleem Mufti; FA12-PMATH-006; LHR TP 5950; Dr. M. Faisal Nadeem
Topological indices are a rapidly developing area of research in graph theory. There are various topological indices such as degree-based topological indices, spectrum based topological indices and distance related topological indices. These topological indices correlate certain physico-chemical properties such as boiling point, stability of chemical compounds and many more. In this dissertation, we focus on degree based and spectrum based topological indices. Under the degree based topological indices, we study topological indices such Randic index, general Randic index, Zagreb index, general sum connectivity index, first and second multiple Zagreb indices, geometric index, atom bond connectivity index for para-line graphs of some chemical structures such as Phenylene, Anthracene, Benzenoid, Pentacene. Similarly, we study the spectrum based topological indices such as Estrada index for certain chemical graph structures such as Phenylene, Anthracene, Bi-smuth Tri-iodide, benzene ring embedded in P-type-surface in 2D network (BRE). Also we find the energy of above mentioned structures. We also discuss the notion of distance related parameters such as metric dimension and edge metric dimension. We compute the edge metric dimension for the barcycentric Subdivision of Cayley Graphs. Also we have studied the M-polynomial and entropy of generalized Sierpinski graphs.
Dynamical Properties of Specific Black Holes
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Umair Shahzad; FA13-PMATH-005; LHR TP 5606; Dr. Abdul Jawad
The present thesis comprises the study of three dynamical phenomenon such as thermal fluctuations, accretion and tidal forces of black holes/regular black holes. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations. We examine the effects of thermal fluctuations on a regular black hole of the non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal regular black hole. Furthermore, we discuss the thermal fluctuation problem by utilizing the higher order corrected entropy. We examine the thermodynamical behavior of two well-known black holes such as Reissner-Nordström Anti de Sitter black hole with global monopole and f(R) black hole in the presence of higher order corrected entropy. We also discuss the accretion problem in two phases. In first phase, we analyze the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, non-linear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. In second phase, we develop the Hamiltonian dynamical system to tackle the accretion problem. We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sftesos black hole and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. Finally, we investigate the tidal forces occurring in a Kiselev black hole surrounded by radiation and dust fluids. We also solve the geodesic deviation equation for radially free-falling bodies toward Kiselev black hole. We explain the geodesic deviation vector graphically and point out the location of the event and Cauchy horizons for specific values of the radiation and dust parameters.
FACE ANTI-MAGIC LABELINGS AND DEFICIENCY OF GRAPHS
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Ali Tabraiz; FA12-PMATH-001; LHR TP 4824; Dr. Muhammad Hussain
Labeling of graph is a beautiful and rich technique of Mathematics. It has extensive usage in applications such as data transmission, x-ray, circuit design, astronomy, communication links and coding theory. A labeling of a graph is a mapping that carries some set of graph elements into (usually positive integers). An ) , ( d a face anti-magic total labeling of a graph, with p vertices, q edges and f faces, is a one-to-one mapping that takes the vertices, edges and faces into }, , , 2 , 1 { f q p such that the sums of the label on the edges, vertices and faces form an arithmetic progression starting at a and having difference . d An edge magic total labeling of a graph G is a one-to-one mapping from ) ( ) ( G E G V onto the integers }, , , 2 , 1 { q p with the property that there is an integer constant k such that k y xy x ) ( ) ( ) ( for any ). (G E y x Furthermore, the edge-magic deficiency of a graph , G ) (G is defined as the minimum non-negative integer n such that 1 K n G is edge-magic.
Generalizations of Cyclic Refinements of Jensen’s Inequalities
(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Nasir Mehmood; FA14-PMATH-005; LHR TP 7451; Dr. Saad Ihsan Butt
In recent years, the concept of convex functions has been generalized extensively. Applications of convex functions are widely seen in many areas of modern analysis. Convex functions also have significant relation with the theory of inequalities and many useful inequalities are the result of the applications of convex functions. The Jensen's inequality has tremendous implications in many fields of modern analysis. It helps computing useful upper bounds for several entropic measures used in information theory. We consider discrete and continuous cyclic refinements of Jensen's inequality and extend them from convex to higher order convex function by using new Green functions introduced by us and employing different interpolating polynomials and identities. We formulate monotonicity of the linear functionals for nconvex functions at a point. We calculate some new Grüss and Ostrowski type bounds. As an application of our obtained results we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.
Koszul Loops Algebraic And Topological Description
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Muhammad Nadeem; SP13-PMATH-003; LHR TP 6346; Dr. Sarfraz Ahmad
In this thesis we explore interactions between three well established fields namely Algebra, Combinatorics and Chemistry. Main idea is to solve complicated problems in one field by using comparatively easy approaches of the second. We work it out in three different ways. In the first part, we explore chemical properties of some compounds using combinatorial techniques. In recent days atomic properties of chemical structures are intensively explored using results of graph theory depending upon degrees and distances of the associated graphs. In particular, we work on one of the interesting classes of degree based indices, namely, the Zagreb indices. These indices are very useful in QSPR and QSAR studies. We compute Zagreb index, its co index and multiple index for the topological descriptors of 2-dimensional silicon carbons 𝑆𝑖2𝐶3 − 𝐼𝐼𝐼, � �𝑖𝐶3 − 𝐼𝐼𝐼. On the other hand it is of great importance to explore the irregularity of a graph in Chemistry, Pharmacy and Bio technology. We compute irregularity, total irregularity, variance and irregularity index of some networks including (𝐻𝐻𝐶 − 1), (𝐻𝐻𝐶 −2),(BSN−1),(BSN−2) and nanocone 𝑁𝐶𝑘[𝑛]. In the second part we focus on connections between Algebra and Combinatorics. We construct a family of Wilson loops of different orders with the help of additive and multiplicative groups. We associate these newly obtained algebraic structures to the graphs through link labeling. As a main result of this session we prove that the Latin square of the Wilson loop is connected with a bipartite graph. Similarly its normal sub loop of the Wilson loop is associated with the class of star graphs. Let 𝑅 = 𝑘[𝑥1,…,𝑥𝑛] be a polynomial ring in 𝑛 variables. There is one to one correspondence between set of all square free monomial ideals in 𝑅 and set of all simplicial complexes over 𝑛 vertices. The 𝑓- and ℎ-vectors of the simplicial complex ∆ play an important role to describe algebraic properties of the associated square free monomial ideal 𝐼∆. Let ∆𝑠𝑢𝑏 be subdivided simplicial complex obtained from ∆. In the last part of this thesis, we discuss the transformation maps sending the ℎ-vectors of the simplicial complex ∆ to the ℎ-vectors of the subdivided simplical complex ∆𝑠𝑢𝑏. In the end we give algebraic applications describing the primary decomposition of an ideal 𝐼𝑃 associated to the partially ordered set = 𝐶𝑖 × 𝐶𝑗 , where 𝐶𝑖 is the chain 1 < ...<
Some Studies of Two-Population Neural Field Model
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Zeeshan Afzal; CIIT/FA13-PMATH-009/LHR; Dr. Muhammad Yousaf Bhatti; LHR TP 5949
We investigate the appearance and disappearance of localized activity states, so called bumps in Wilson-Cowan type two population neural ﬁeld model under the inﬂuence of transient spatio-temporal external input with smooth α-type and piecewise-type temporal functions. This two-population model is composed of two coupled nonlinear differential equations derived for the dynamics of spatially localized populations of both excitatory and inhibitory model neurons. The model with no external input corresponds to atmost two bump pair solutions. Such a system can be interpreted as a minimal cortical model for short term working memory, that is the ability of the brain to actively hold stimulus-related information for some seconds in short term memory and discards once it becomes irrele- vant Initially, if there is no activity in the system, persistent activity state can be evoked by switching on a suitable transient excitatory external input. This activity remains stable even though external input is switched off. The effect of external input on appearance and disappearance of bumps for different spatial, smooth α-type and piecewise-type temporal functions of external input is investigated and found that certain parameters play a key role in the generation of persistent activity states in the network e.g. relative inhibition time constant, total duration and the amplitude of external input. It is found that the minimum values of the amplitude and active time to evoke the activity in the network is smaller than those observed in showing that the present choice of temporal functions in the external in- put is more effective and more close to natural behavior.
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.