http://103.99.128.19:8080/xmlui/handle/123456789/5 Mathematics 2026-09-13T04:02:06Z http://103.99.128.19:8080/xmlui/handle/123456789/589 Title: DESIGNING CONTROL SCHEMS FOR CHAOTIC SYSTEMS VIA SLIDING MODE CONTROL Authors: AFROJA, AFSANA; ID:, 21MMATH002P Abstract: Among various robust control methods, Sliding Mode Control (SMC) has attracted considerable interest in theoretical research due to its unique features. SMC is well known for its robustness to matched and bounded uncertainties, reduction in the order of the system during the sliding phase, simplified decoupling of system dynamics, and its ability to achieve zero steady-state error. These characteristics make SMC a powerful tool in designing control systems for uncertain and nonlinear environments. This thesis presents a comprehensive study on the control and synchronization of chaotic systems, focusing on the Modified Lorenz System (MLS) and the Liu financial dynamical system. Chaotic behavior, with its sensitivity to initial conditions, presents major challenges in nonlinear control. Sliding Mode Control (SMC) is applied to coupled MLS to ensure robust synchronization through a designed sliding surface and control law, with convergence proven via Lyapunov stability and validated through numerical simulations. In the Liu financial system, both SMC and Passive Control (PC) are implemented and compared. While SMC provides rapid synchronization (within 𝑡 ≥ 1, error reduced from 5.67 to 0.02), PC achieves synchronization more gradually (within 𝑡 ≤ 13, error reduced from 6.21 to 0.03) using a simpler, single-controller strategy. The results highlight key trade-offs between speed, robustness, and implementation complexity, offering valuable insights into managing chaos in nonlinear and financial systems. These limitations have motivated ongoing research aimed at improving SMC design. The core challenge remains how to develop a simple yet effective sliding mode control technique that retains its robustness and zero-error tracking while minimizing chattering and relaxing the need for precise uncertainty bounds. Description: A Master of Philosophy (M.Phil.) Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-07-07T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/567 Title: ISOTROPIC SOLUTION OF EINSTEIN’S EQUATIONS ONTHE FLUIDSPHERE Authors: HOSSAIN, MD.IMRAN; ID:, 21MMATH005 Abstract: This thesis investigates the theoretical framework of spherically symmetric perfect fluid spheres within the realm of general relativity. Our work seeks exact solutions to the Einstein field equations thereby facilitating a better knowledge of minuscule objects. The thesis begins by examining the fundamental aspects of special relativity, including the Lorentz transformations and the structure of spacetime. We then explore general relativity, with an eye towards the Einstein field equations and the geometric justification of gravity. Examining matter dispersion in astrophysical systems depends on first looking at the behavior of ideal fluids. The thesis delves into the intricacies of the Einstein field equations and their application to spacetimes with spherical symmetry. The key achievement of the research is the formulation of new exact solutions for static spherically symmetric ideal fluid spheres. Implementing two techniques in the context of static spherically symmetric ideal fluid line elements, we develop two new approaches that validate their characteristics and ensure that they satisfy Buchdhal criteria. The physical characteristics and possible astrophysical implications of these solutions are thoroughly investigated. Combining the ideas of general relativity with the simplified model of perfect fluids helps this work provide new understanding on the interactions between compact objects and their gravitational interactions. Description: An M.Phil. Thesis in Mathematics Department at Chittagong University of Engineering and Technology (CUET). 2025-03-20T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/527 Title: Term paper on........ Authors: Test 2025-12-09T00:00:00Z http://103.99.128.19:8080/xmlui/handle/123456789/514 Title: The Effect of the Angle of Perforation on Inserts in a Pipe Flow for Heat Transfer Analysis Authors: Acherjee, Simul Abstract: A numerical simulation study of heat transfer analysis is considered with perforated inserts using a different angle of perforation in a circular pipe. In our simulation, we have used 0°, 5°, 10°, 15°, 16°, 17°, 20°, 30°, 40°, 50°, 60°, 65°, 68° and 70° angles of perforation respectively in a perforated axial insert considering the non-isothermal laminar flow. The inserts are used perpendicular to the fluid flow inside a pipe. A uniform heat-flux around the circular tube is assumed for our simulations. The temperature and pressure distribution are measured for a different angle of perforation. The relation between heat transfer rate and wall temperature is observed and found that the heat transfer rate increases inversely with the wall temperature. The effect of Nusselt number and friction factor are the diagnosis for all including angles and Reynolds numbers. The Thermal Performance Evaluation Criterion (PEC) is also analyzed in this study. Description: An M.Phil. Thesis from the Department of Mathematics. 2024-08-21T00:00:00Z