DSpace Collection: Thesis published in Dept. of MathematicsThesis published in Dept. of Mathematicshttp://103.99.128.19:8080/xmlui/handle/123456789/1242026-09-13T20:56:11Z2026-09-13T20:56:11ZDESIGNING CONTROL SCHEMS FOR CHAOTIC SYSTEMS VIA SLIDING MODE CONTROLAFROJA, AFSANAID:, 21MMATH002Phttp://103.99.128.19:8080/xmlui/handle/123456789/5892026-09-10T04:24:31Z2025-07-07T00:00:00ZTitle: 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).2025-07-07T00:00:00ZISOTROPIC SOLUTION OF EINSTEIN’S EQUATIONS ONTHE FLUIDSPHEREHOSSAIN, MD.IMRANID:, 21MMATH005http://103.99.128.19:8080/xmlui/handle/123456789/5672026-09-06T05:37:11Z2025-03-20T00:00:00ZTitle: 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).2025-03-20T00:00:00ZThe Effect of the Angle of Perforation on Inserts in a Pipe Flow for Heat Transfer AnalysisAcherjee, Simulhttp://103.99.128.19:8080/xmlui/handle/123456789/5142025-09-23T05:26:08Z2024-08-21T00:00:00ZTitle: 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.2024-08-21T00:00:00ZNumerical Investigation of Single and Double Differential Cross-Section for the Ionization of Metastable 2S State Hydrogen Atom by Electron ImpactChowdhury, Md. Thowhidul Hoquehttp://103.99.128.19:8080/xmlui/handle/123456789/4952025-09-14T10:47:22Z2023-12-19T00:00:00ZTitle: Numerical Investigation of Single and Double Differential Cross-Section for the Ionization of Metastable 2S State Hydrogen Atom by Electron Impact
Authors: Chowdhury, Md. Thowhidul Hoque
Abstract: This thesis focuses on the ionization of hydrogen atoms by electrons in an asymmetric coplanar geometry, which plays a crucial role in atomic ionization problems. The Double Differential Cross Sections (DDCS) from the ionization of hydrogen atoms with different kinematic conditions offer valuable insights into various fields, including Applied Mathematics, Applied Physics, Atomic Physics, Astrophysics, Plasma Physics, and Fusion Technology.
The present study uses a multiple scattering theory to examine the ionization of metastable 2S-state hydrogen atoms by non-relativistic intermediate and high-energy electrons. This theory has already proven to be successful in previous studies of DDCS results in the ground state and Triple Differential Cross Sections (TDCS) results for metastable 2S, 2P, 3P, 3S and 3D states of hydrogen atoms by electrons.
We start our work by discussing the multiple scattering theory and other relevant theories related to the ionization of hydrogen atoms by electrons. The first Born DDCS for H(2S) ionization at incident energies of 150eV and 250eV are also investigated and the results show significant curve structures. The DDCS for the ionization of metastable 2S state hydrogen atoms by electrons, taking into account the direct T-matrix element and its exchange effects in coplanar asymmetric geometry, produces intriguing curve structures.
The results of the simulation show good qualitative accord with theoretical and experimental data for the hydrogenic ground state. The physical origins of the curve shapes in the cross section results are explained clearly in the study. Further calculations using other familiar methods would also be of interest.
Description: An M.Phil. Thesis from the Department of Mathematics2023-12-19T00:00:00Z