Department of Mathematics

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Author: search.filters.author.Dr. Ayesha SohailSubject: search.filters.subject.MATHEMATICS

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    Space Spectral Time Fractional Finite Difference Method along with Stability Analysis for Fractional Order Nonlinear Wave Equations
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Sarmad Arshad; SP13-PMATH-004; Dr. Ayesha Sohail; LHR TP 5299
    In this work, nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM) is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated. Afterwards, dynamical analysis of fractional order Schr dinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the solutions obtained by the two asymptotic techniques, that is, the Fractional Homotopy Analysis Transform Method and the Optimal Homotopy Analysis Method is performed to select the most accurate technique for the stated problem. Space spectral analysis with integrating factor technique and time fraction finite difference method have been implemented to study the pressure waves propagating in bubbly fluids as well as nonlinear phenomena of plasma waves. Dynamical analysis of acoustic/pressure waves propagating in bubbly fluids is of great significance. Such flows arise in many engineering problems including sonochemistry, sonochemical reactors, cavitation around hydrofoils and ultrasonic propagation in medicine and biology. Fractional approach for modeling the propagation of the pressure waves in liquids containing a large number of tiny gas bubbles is proposed. Moreover, numerical solution of the fractional order Modified Korteweg-de Vries equation governing the dynamics is approximated using a novel space spectral time fractional finite difference tool. A spectral technique for space and a multi-step finite difference scheme for time are designed and implemented. The spatial spectral discretization error and the stability bounds are discussed. The nonlinear phenomena of plasma waves are well demonstrated with the aid of graphical analysis. Stability analysis of integer and fractional order KdV equations have been discussed quantitatively with the help of Evans function approximation.
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    Analysis of Plasma Modified KdV Waves using Discrete Periodic Inverse Scattering Transformation
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Noaman Akbar; SP15-RMT-005; LHR TP 6989; Dr. Ayesha Sohail
    Discrete Periodic Inverse Scattering Transformation (DPIST) are presented in this paper for solution of the well-known Korteweg-de Vries equations that has been hypothesized hypothetically such that non-linear dispersive waves spreading on interface of length only a joined of products fluid profundity fulfill a development condition with more extreme non-linearity than ordinary Korteweg-de Vries (KdV) equations for shallow water hypothesis. In this paper non-linear Fourier investigation is processed on time and space arrangement of surface relocation create at two areas downstream of a wavering film. Comes about because of a DPIST in view of the KdV equation, that decays a flag into soliton, sinusoidal and cnoidal parts, demonstrate while the amplitude of direct modes are preserved as unsettling influence spreads among two sensors, amplitudes of nonlinear modes increment. This recommends non-linearity of such surface waves is without a doubt more grounded than that anticipated by the KdV equations.
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    Algorithm Development for the Bayesian Optimization of Complex Data Sets
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Javed Zahoor; FA18-RMT-057; LHR TP 6461; Dr. Ayesha Sohail
    Optimization is a subfield of applied mathematics and is used in the fields of nano-medicine, applied sciences and computational biology extensively. The recent trends of optimizations are focused on the algorithm development of nonlinear programs for complex data sets. During this research, an algorithm is developed for the application of “Bayesian Optimization”, for the selection of the most accurate hyper-parameter, using the Python framework as well as the MatlabTM 2020 packages. The developed model is then implemented on the experimental data sets, extracted from the online repositories. To ensure the optimalilty of the forecasting, the algorithms are exploited in detailed manner during this research.
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    Fractional Order Model of Tumor-Induced Angiogenesis
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Sufian Asgher; SP15-RMT-001; LHR TP 6936; Dr. Ayesha Sohail
    Methods of blood vessel formation is termed angiogenesis. Two distinguishing features of cancer, uncontrollable cell growth and metastasis, cannot be sustained in the absence of neovascularisation. Angiogenesis enhances the arrangement of solid tumors and their metastasis. During this research, present progress in understanding the procedure of angiogenesis in dynamic tumor development is talked about. The development of strong tumors, including neck and head squamous cell carcinomas, relies on upon the foundation of a blood supply inside the tumor (neovascularization or angiogenesis). For this procedure to occur, tumors create development components which stimulate the expansion, movement, and separation of endothelial cells. Nonlinear pde model of tumour induced angiogenesis is discussed during this research. The semi-analytic solution of this model is presented.
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    Explainable Machine Learning for Medical Imaging
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Shahid; FA18-RMT-043; LHR TP 6023; Dr. Ayesha Sohail
    In the recent literature, artificial intelligence tools have been used very suc cessfully to investigate the history of medical images, where incomplete data is available. In this thesis, data obtained from a clinical study is analyzed using medical imaging algorithms. We have used a Bayesian machine learning clas sifier i.e. Naïve Bayes to obtain the results. We have considered the medical images from 20 patients having gastric cancer. Futhermore, we have compared the accuracy of Naïve Bayes classifier to the other medical imaging techniques such as CNN.