Browsing by Author "Uddin, Mahtab"

Now showing 1 - 6 of 6

Modulation Instability Analysis, and Characterize Time-dependent Variable Coefficient Solutions in Electromagnetic Transmission and Biological Field
(Elsevier, 2024-06-10) Chakrabarty, Anuz Kumar; Akter, Sonia; Uddin, Mahtab; Roshid, Md. Mamunur; Abdeljabbar, Alrazi; Or-Roshid, Harun
This study integrates the telegraph model with the traveling wave coefficient. This model characterizes planar random motion of particles in fluid flow, pressure waves from pulsatile blood flow in arteries, electrical impulses in nerve and muscle cell axons, and electromagnetic waves in superconducting media. Using the efficient and well-established Enhanced Modified Simple Equation (EMSE) method, we investigate solitary wave solution with the variable coefficient of the telegraph model. To investigate the variable coefficient solitary wave solution, we apply a transformation variable η = h(t)x + g(t), which is dependent on the time variable function. The diverse functions of h(t) and g(t) yield many novel and exclusive solutions. Numerical solutions are plotted in 3D, density, and 2D. instanton soliton, kinky periodic wave, lump wave, kink wave, anti-kink wave, double periodic wave, diverse types periodic wave, lump with bell wave periodic wave, periodic lump wave, etc. Solitary waves explain complex wave phenomena through nonlinear effects like self-interaction and dispersion. Due to the classical nonlinear telegraph model's wave dynamics, they are used in brain function and communication system design. We conclude by testing the governing model's modulation instability. Dispersive and nonlinear processes modulating the stable state cause instability in high-order nonlinear equations. Examining the wave movement role and modulation instability analysis to assess solution stability shows that all solutions are accurate and stable. The computational difficulties and results demonstrate the approaches' clarity, effectiveness, and simplicity, suggesting they can be applied to evolutionary dynamic and static nonlinear equations in computational physics, other real-world situations, and numerous academic disciplines.
Numerical study on continuous algebraic riccati equation arising from large-scale sparse descriptor systems
(Department of Mathematics, 2020-02-11) Uddin, Mahtab; Khan, Dr. Md. Abdul Hakim
The mathematical models derived from the physical models are the pivot ingredient in science and engineering, especially, in the control theory. Most of the physical models have a large number of components with critical combinations and sophisticated designs. These models are infeasible for the computing tools ac-cording to the time dealing and memory allocation. To nd the remedy of current adversity and attain desired execution results, the models are to be approximated as structure-preserving Reduced-Order Models (ROM) and machine-executable designs. Memory allocation and time management are the most eye-catching factors in the simulations of the large-scale sparse Linear Time-Invariant (LTI) systems, especially, the descriptor systems. Numerical techniques can be applied practically to control, stabilize and optimize the physical models. In this thesis, rstly, the projection-based Rational Krylov Subspace Method (RKSM) has been proposed to compute the solution of Continuous Algebraic Riccati Equations (CARE) governed from large sparse index-1 descriptor systems. Iterative RKSM is not only time saving but also computationally feasible for mem-ory allocation in nding the solution of the CAREs utilizing the Reduced-Order Models (ROM). The novelties of RKSM are sparsity preserving techniques and the implementation of time convenient recursive adaptive shift parameters. Secondly, the machine-independent Alternating Direction Implicit (ADI) technique based nested iterative Kleinman-Newton (KN) method has been modi ed and adjusted to solve the CAREs governed from large sparse index-1 descriptor systems. Then compare results achieved by the Kleinman-Newton method with that of using the RKSM. The objective has been mainly focused on nding optimal feedback matrix for Riccati based feedback stabilization for the unstable index-1 descriptor systems applying the proposed methods. The applicability and adaptability of the pro-posed methods have been justified through the power system models and their transient behaviors have been analyzed. Finally, numerical results have been shown both in tabular and graphical form to verify the robustness and accuracy of the proposed methods In addition, their comparative analysis for the target models has been illustrated in detail.
Optimize task distribution in grid computing
(BRAC University, 2008-08) Shikder, Shyen Muhabbat; Uddin, Mahtab; Islam, Syed Saiful
Grid computing is designed to use free cycles of computer to perform large calculations by using free cycles of computer. Grid computing does not need dedicated computers to perform calculations instead it uses free cycles of computer in a network. It works like a virtual super computer, but it doesn’t involve extra hardware cost. As, it’s a cost effective its popularity is increasing day by day. Now a day’s popular applications are being made to support grid computing. For example Oracle database 10g is designed to support grid computing. Although grid computing is so popular, but implementing software for grid based system is tough. It needs task distribution among computers. So it uses different programming techniques and needs to use special API. The software we are currently using may not support grid environment. Software companies need to convert their programs to support grid environment that involves development cost. On other hand users are not able to use their current software in grid environment. So, they need to buy another program that involves extra cost. The objective of this project is to run traditional programs in grid system without any modification, so that we can run any executable program in grid system with parallel speeding performance. It will increase program compatibility and reduce cost.
Simulation of optical wave propagation of perturbed nonlinear Schrodinger’s equation with truncated -fractional derivative
(Scopus, 2024-06-27) Akter, Mosammat Arifa; Mostafa, Golam; Uddin, Mahtab; Roshid, Md Mamunur; Roshid, Harun Or
This work aims to investigate some novel optical soliton solutions of fractional perturbed nonlinear Schrödinger’s equation (PNLSE) with Kerr law nonlinearity. Here, the local derivative is used as the conformable wisdom known as the truncated -fractional derivative. We also deliberated on some assets satisfied by the derivative. To analyze the dynamic conduct of the optical self-control wave pattern of PNLSE, we used a newly effective analytic method, namely the unified method combined with a truncated fractional derivative. For special values of the free parameters, different types of new soliton solutions were obtained such as dark and bright bell soliton, anti-kink and kink soliton, periodic soliton, interaction of periodic and lump soliton, and periodic lump soliton wave solutions that were verified through maple with a three-dimensional plot along with density and a two-dimensional plot. For the manifestation of the effect of fractional derivative, we plotted the three-dimensional graph and also showed the comparative effect in two-dimensional plots along both the x-axis and t-axis. Exploring these single systems creates new opportunities for signal processing and optical communications applications. This technique presents a strong possibility for addressing similar issues in the future. The visualization of several findings demonstrates how the proposed technique effectively constructs solutions with well-understood physical phenomena. When it comes to solving perturbed nonlinear fractional complex equations, the aforementioned method is simpler, more dependable, and more efficient than the others. Both two- and three-dimensional graphs displaying the results will be presented.
Simulation of Optical Wave Propagation of Perturbed Nonlinear Schrodinger’s Equation with Truncatedm-fractional Derivative
(Springer Nature, 2024-06-27) Akter, Mosammat Arifa; Mostafa, Golam; Uddin, Mahtab; Roshid, Md Mamunur; Roshid, Harun Or
This work aims to investigate some novel optical soliton solutions of fractional perturbed nonlinear Schrödinger’s equation (PNLSE) with Kerr law nonlinearity. Here, the local derivative is used as the conformable wisdom known as the truncated -fractional derivative. We also deliberated on some assets satisfied by the derivative. To analyze the dynamic conduct of the optical self-control wave pattern of PNLSE, we used a newly effective analytic method, namely the unified method combined with a truncated fractional derivative. For special values of the free parameters, different types of new soliton solutions were obtained such as dark and bright bell soliton, anti-kink and kink soliton, periodic soliton, interaction of periodic and lump soliton, and periodic lump soliton wave solutions that were verified through maple with a three-dimensional plot along with density and a two-dimensional plot. For the manifestation of the effect of fractional derivative, we plotted the three-dimensional graph and also showed the comparative effect in two-dimensional plots along both the x-axis and t-axis. Exploring these single systems creates new opportunities for signal processing and optical communications applications. This technique presents a strong possibility for addressing similar issues in the future. The visualization of several findings demonstrates how the proposed technique effectively constructs solutions with well-understood physical phenomena. When it comes to solving perturbed nonlinear fractional complex equations, the aforementioned method is simpler, more dependable, and more efficient than the others. Both two- and three-dimensional graphs displaying the results will be presented.
Simulation of Optical Wave Propagation of Perturbed Nonlinear Schrodinger’s Equation with Truncatedm-fractional Derivative
(Springer Nature, 2024-06-27) Akter, Mosammat Arifa; Mostafa, Golam; Uddin, Mahtab; Roshid, Md Mamunur; Roshid, Harun Or
This work aims to investigate some novel optical soliton solutions of fractional perturbed nonlinear Schrödinger’s equation (PNLSE) with Kerr law nonlinearity. Here, the local derivative is used as the conformable wisdom known as the truncated -fractional derivative. We also deliberated on some assets satisfied by the derivative. To analyze the dynamic conduct of the optical self-control wave pattern of PNLSE, we used a newly effective analytic method, namely the unified method combined with a truncated fractional derivative. For special values of the free parameters, different types of new soliton solutions were obtained such as dark and bright bell soliton, anti-kink and kink soliton, periodic soliton, interaction of periodic and lump soliton, and periodic lump soliton wave solutions that were verified through maple with a three-dimensional plot along with density and a two-dimensional plot. For the manifestation of the effect of fractional derivative, we plotted the three-dimensional graph and also showed the comparative effect in two-dimensional plots along both the x-axis and t-axis. Exploring these single systems creates new opportunities for signal processing and optical communications applications. This technique presents a strong possibility for addressing similar issues in the future. The visualization of several findings demonstrates how the proposed technique effectively constructs solutions with well-understood physical phenomena. When it comes to solving perturbed nonlinear fractional complex equations, the aforementioned method is simpler, more dependable, and more efficient than the others. Both two- and three-dimensional graphs displaying the results will be presented.