Wave propagation induced by body forces for free microtubules using cylindrical shell model

Muhammad Taj, Ikram Ahmad, Mohamed Amine Khadimallah, Hamdi Ayed, Rana Muhammad Akram Muntazir, Abir Mouldi, Manahil Maqsood, Essam Mohammed Banoqitah, Muzamal Hussain, Abeera Talib, Hajra Khanam and Zafer Iqbal

Abstract

This paper examines the wave velocity of protein microtubules using a elasticity model that incorporates body forces, based on the structure of these hollow cylinder-like structures., the governing equations are analytically solved to determine how the body forces effect the wave velocity. To analyze the microtubule waves velocity, use microtubules with simply supported ends. The electric field of a dipole vibrating at the same frequency as microtubule vibrations approximates the electric field generated by the rhythmic motion of every charge. The numerical findings for the three modes of frequencies in the longitudinal, radial, and torsional directions for the current conditions are compared with the results of previous calculations.

Key Words

electric field; microtubule; oscillatory motion; simply supported; wave velocity

Address

(1) Muhammad Taj: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; (2) Ikram Ahmad, Manahil Maqsood: Department of Chemistry, University of Sahiwal, Sahiwal, 57000, Pakistan; (3) Mohamed Amine Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia; (4) Hamdi Ayed: Department of Civil Engineering, College of Engineering, King Khalid University, Abha - 61421, Saudi Arabia; (5) Rana Muhammad Akram Muntazir, Abeera Talib, Hajra Khanam; Department of Mathematics, Lahore Leads University, 54792, Lahore, Pakistan; (6) Abir Mouldi: Department of Industrial Engineering, College of Engineering, King Khalid University, Abha - 61421, Saudi Arabia; (7) Essam Mohammed Banoqitah: Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Jeddah 21589, Saudi Arabia; (8) Muzamal Hussain: Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Pakistan; (9) Zafer Iqbal: Department of Mathematics, University of Sargodha, Sargodha, Punjab, Pakistan; (10) Zafer Iqbal: Department of Mathematics, University of Mianwali, Punjab, Pakistan.

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