dr muhammad afzal (Math)

Dr. M. Afzal


Dr. Muhammad Afzal is an applied mathematician with a strong interest in wave mechanics, specifically in modelling, analyzing, and applying wave phenomena in various scientific and engineering fields. Since obtaining his PhD in Mathematics from Quaid-i-Azam University in 2015, he has dedicated his research efforts to the broad area of applied mathematics, focusing particularly on the theoretical understanding of wave processes. Dr. Afzal research activities primarily revolve around the scattering of acoustic or electromagnetic waves from geometric or material discontinuities, which have wide-ranging applications in acoustics, elasticity, water wave theory, and electromagnetic wave propagation problems. He has extensively worked on the application and development of mode-matching methods and Non-Sturm-Liouville systems. Further, he has extended the mode-matching approach by incorporating Galerkin procedures, low-frequency approximations, and multimodal formulations. Dr. Afzal has published over 25 articles in high-impact journals and contributed a book chapter in a publication by the American Mathematical Society, USA. He is recognized as an approved supervisor by the Higher Education Commission of Pakistan (HEC) and has successfully supervised 4 PhD and 13 MPhil students.

PhD Mathematics Quaid-e-Azam University, Islamabad, Pakistan 2015
MPhil Mathematics Quaid-e-Azam University, Islamabad, Pakistan 2011
MSc Mathematics University of the Punjab, Lahore 2008
Associate Professor Capital University of Science and Technology (CUST), Islamabad Since – 2022
Assistant Professor Capital University of Science and Technology (CUST), Islamabad 2015 – 2022
1. Acoustics and Electromagnetic Waves Scattering
2. Structural Acoustic, Diffraction Theory
3. Mode-Matching Technique
4. Low Frequency Approximation
1. MPhil Acoustic Scattering and Absorption in Discontinuous Waveguide Involving Porosity
2. MPhil Acoustic Scattering in Bifurcated Waveguide Containing Porous Material
3. PhD Scattering Analysis of Discontinuous flexible panels with different edge conditions(In progress)
4. PhD Acoustics Wave Scattering in Trifurcated Waveguide Containing Structural Discontinuities and Change of Material Properties (In progress)
5. PhD Analysis of Transmission Loss in Active and Passive Devices using Mode-Matching Technique (In progress)
6. PhD Effect of Vertical Flexible Walls of Expansion Chamber in Reactive Silencer: A Tailored Galerkin Approach (In progress)
7. MPhil Analysis of Vertical Membrane Bounded Cavity: A Modal Approach (In progress)
8. MPhil Scattering analysis in discontinuous Cylindrical Waveguide by using Mode-Matching Approach (In progress)
9. MPhil Multimodal analysis of Cavity backed channel (In progress)
M. Afzal and S. Shafique, Attenuation analysis of flexural modes with absorbent lined flanges and different edge conditions, Journal of the Acoustical Society of America, 148, 85 (2020). https://doi:
S. Shafique, M. Afzal and R. Nawaz, On the attenuation of fluid structure coupled modes in a nonplanar waveguide, Mathematics and Mechanics of Solids, 25(10), 1-20 (2020)
M. Afzal, J. U. Satti and R. Nawaz, Scattering characteristics of non-planar trifurcated waveguides, Meccanica, 55, 977-988 (2020).
J. U. Satti, M. Afzal and R. Nawaz, Scattering analysis of a partitioned wave-bearing cavity containing different material properties, Physica Scripta (2019)
T. Nawaz, M. Afzal and R. Nawaz, The scattering analysis of trifurcated waveguide involving structural discontinuities, Advances in Mechanical Engineering, 11(7), 1-11 (2019)
H. Bilal and M. Afzal, Acoustic wave scattering from a wave-bearing cavity in a rectangular waveguide, Journal of the Acoustical Society of America, 144, 1681 (2018)
Rab Nawaz, Aasim Ullah Jan and Muhammad Afzal, Fluid-structure coupled wave scattering in a flexible duct at the junction of planar discontinuities, Advances in Mechanical Engineering, 9(7), 1–11 (2017).
Sajid Shafique, Muhammad Afzal and Rab Nawaz, On mode matching analysis of fluid-structure coupled wave scattering between two flexible waveguides, Canadian Journal of Physics, 95(6), 581-589 (2017).
J. B. Lawrie and M. Afzal, Acoustic scattering in a waveguide with a height discontinuity bridged by a membrane: a tailored Galerkin approach. Journal of Engineering Mathematics, 1-17 (2016).
M. Afzal, R. Nawaz, Asim Ullah, Attenuation of dissipative device involving coupled wave scattering and change in material properties, Applied Mathematics and Computations, 290 (2016) 154–163.
R. Nawaz, M. Afzal and M. Ayub, Acoustic propagation in two-dimensional waveguide for membrane bounded ducts, CNSNS 20 (2015), pp. 421-433.
M. Afzal, R. Nawaz, M. Ayub and A. Wahab, Acoustic scattering in flexible waveguide involving step discontinuity, PLOS One, 9(8): 2014: Paper ID. e103807.
M. Afzal, J. U. Satti and R. Nawaz, The wave scattering analysis in a flexible trifurcated waveguide, has been submitted in “Applied Mathematical Modelling” journal for possible publication.
M. Afzal and Touqeer Nawaz, The scattering analysis in trifurcated waveguide involving porosity and structural discontinuities has been submitted in “Mathematical Methods in Applied Sciences” journal for possible publication.
M. Afzal, Touqeer Nawaz and R Nawaz, Analysis of acoustics wave scattering in trifurcated waveguide for generalized boundary conditions, has been submitted in “Applied Mathematics and Computations” journal for possible publication.
M. Afzal, U. Camci, and K. Saifullah, Integrability conditions for conformal Ricci collineation equations, “Proceedings of 13th Regional Conference on Mathematical Physics, Antalya, Turkey: World Scientific, Mathematical Physics: pp. 103-115. (2012)

Other Members