Denis S. Ryabov¹, Igor V. Kosarev^2,3, Daxing Xiong⁴, Aleksey A. Kudreyko⁵, Sergey V. Dmitriev^2,6,*

CMC-Computers, Materials & Continua, Vol.82, No.3, pp. 3797-3820, 2025, DOI:10.32604/cmc.2025.062079 - 06 March 2025

Abstract Molecular dynamics (MD) is a powerful method widely used in materials science and solid-state physics. The accuracy of MD simulations depends on the quality of the interatomic potentials. In this work, a special class of exact solutions to the equations of motion of atoms in a body-centered cubic (bcc) lattice is analyzed. These solutions take the form of delocalized nonlinear vibrational modes (DNVMs) and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals. The accuracy of the potentials can be checked by comparing the… More >

Ömer Ekim Genel^*, Hilal Koç, Ekrem Tüfekci

CMC-Computers, Materials & Continua, Vol.82, No.2, pp. 2043-2059, 2025, DOI:10.32604/cmc.2025.060111 - 17 February 2025

Abstract Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that… More >

Hakeem Ullah¹, Mehreen Fiza^1,*, Ilyas Khan^2,*, Abd Allah A. Mosa³, Saeed Islam¹, Abdullah Mohammed⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 277-291, 2023, DOI:10.32604/cmes.2023.022289 - 05 January 2023

Abstract In this paper, we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method (OAFM) for fractional-order equations using the Caputo operator, which is named FOAFM. The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations (FWE). The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM. A rapidly convergent series solution is obtained from FOAFM and is validated by… More >

Ahmed M. Elshenhab^1,2,*, Xingtao Wang¹, Fatemah Mofarreh³, Omar Bazighifan^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 927-940, 2023, DOI:10.32604/cmes.2022.021512 - 31 August 2022

Abstract We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. More >

Hulya Durur¹, Asıf Yokuş², Doğan Kaya³, Hijaz Ahmad^4,*

Sound & Vibration, Vol.55, No.3, pp. 241-251, 2021, DOI:10.32604/sv.2021.014157 - 15 July 2021

Abstract In this paper, sub equation and expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation (LWE) in a magneto-electro-elastic circular rod. The proposed methods have been used to construct hyperbolic, rational, dark soliton and trigonometric solutions of the LWE in the magneto-electro-elastic circular rod. Arbitrary values are given to the parameters in the solutions obtained. 3D, 2D and contour graphs are presented with the help of a computer package program. Solutions attained by symbolic calculations revealed that these methods are effective, reliable and simple mathematical tool for finding solutions of More >

Nadeem Ahmad Sheikh^1,2, Dennis Ling Chuan Ching¹, Thabet Abdeljawad^3,4,5, Ilyas Khan^6,*, Muhammad Jamil^7,8, Kottakkaran Sooppy Nisar⁹

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1385-1398, 2021, DOI:10.32604/cmc.2021.011986 - 05 February 2021

Abstract An emerging definition of the fractal-fractional operator has been used in this study for the modeling of Casson fluid flow. The magnetohydrodynamics flow of Casson fluid has cogent in a channel where the motion of the upper plate generates the flow while the lower plate is at a static position. The proposed model is non-dimensionalized using the Pi-Buckingham theorem to reduce the complexity in solving the model and computation time. The non-dimensional fractal-fractional model with the power-law kernel has been solved through the Laplace transform technique. The Mathcad software has been used for illustration of… More >

Muhammad Saqib¹, Ilyas Khan^2,*, Sharidan Shafie¹, Ahmad Qushairi Mohamad¹, El-Sayed M. Sherif^3,4

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 1069-1084, 2021, DOI:10.32604/cmc.2021.012000 - 12 January 2021

Abstract In recent times, scientists and engineers have been most attracted to electrically conducted nanofluids due to their numerous applications in various fields of science and engineering. For example, they are used in cancer treatment (hyperthermia), magnetic resonance imaging (MRI), drug-delivery, and magnetic refrigeration (MR). Bearing in mind the significance and importance of electrically conducted nanofluids, this article aims to study an electrically conducted water-based nanofluid containing carbon nanotubes (CNTs). CNTs are of two types, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs). The CNTs (SWCNTs and MWCNTs) have been dispersed in regular water as… More >

Wael A. Altabey^1,2,*

Sound & Vibration, Vol.54, No.4, pp. 215-224, 2020, DOI:10.32604/sv.2020.011516 - 25 November 2020

Abstract The optimization of the acoustic silencer volume is very important to develop it and to get high-performance, the importance of the silencer was appeared in industrial field to eliminate the noise of the duct by efficient and economical method. The main goal of this research is to optimize the transmission loss (TL) by analytical method of the Double-Chamber Silencer (DCS), the TL has been selected as the main parameter in silencer because it does not based on the source or the termination impedances. First we calculated the power transmission coefficient (PTC) and the TL of More >

Wafaa Alharbi¹, Abdulrahman Aljohani¹, Essam El-Zahar^{2, 3, *}, Abdelhalim Ebaid¹

CMC-Computers, Materials & Continua, Vol.63, No.3, pp. 1143-1157, 2020, DOI:10.32604/cmc.2020.08875 - 30 April 2020

Abstract In this paper, the mathematical model describing the third-grade nonNewtonian blood flow suspended with nanoparticles through porous arteries is exactly solved. The present physical model was solved in the research literature via the optimal homotopy analysis method and the collocation method, where the obtained solution was compared with the numerical fourth-order Runge-Kutta solution. However, the present paper only introduces a new approach to obtain the exact solution of the concerned system and implements such exact solution as a reference to validate the published approximate solutions. Several remarks on the previously published results are observed and… More >

M. H. Ghasemi¹, S. Hoseinzadeh^{2, 3, *}, P. S. Heyns², D. N. Wilke²

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.1, pp. 399-414, 2020, DOI:10.32604/cmes.2020.07827 - 01 January 2020

Abstract In this study, transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition. Governing equations for the model are expressed in two-dimensional cylindrical coordinates; the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method. Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model. On the contrary, thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model. Also the effect of relaxation time in More >