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Keywords = cardinal sine

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25 pages, 3204 KiB  
Article
Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics
by Waleed Mohammed Abdelfattah, Ola Ragb, Mohamed Salah, Mohamed S. Matbuly and Mokhtar Mohamed
Fractal Fract. 2024, 8(12), 729; https://doi.org/10.3390/fractalfract8120729 - 12 Dec 2024
Viewed by 1023
Abstract
This paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-type fractional derivative, offers a significant [...] Read more.
This paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-type fractional derivative, offers a significant improvement in accuracy and efficiency over traditional methods. By employing a block-marching technique, we effectively address the time-dependent nature of the governing equations. The efficacy of the proposed method is validated through rigorous numerical simulations and comparisons with existing analytical and numerical solutions. Each scheme’s computational characteristics are tailored to achieve high accuracy, ensuring an error margin on the order of 108  or less. Additionally, a comprehensive parametric study is conducted to investigate the impact of key parameters on device performance. These parameters include supporting conditions, time evolution, carrier mobilities, charge carrier densities, geminate pair distances, recombination rate constants, and generation efficiency. The findings of this research offer valuable insights for optimizing and enhancing the performance of organic polymer solar cell devices. Full article
(This article belongs to the Special Issue Fractional Mathematical Modelling: Theory, Methods and Applications)
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17 pages, 7542 KiB  
Article
Analysis of Generalized Nonlinear Quadrature for Novel Fractional-Order Chaotic Systems Using Sinc Shape Function
by Abdelfattah Mustafa, Reda S. Salama and Mokhtar Mohamed
Mathematics 2023, 11(8), 1932; https://doi.org/10.3390/math11081932 - 19 Apr 2023
Cited by 5 | Viewed by 1546
Abstract
This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine [...] Read more.
This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine shape function, which is used in combination with the fractional operator of the generalized Caputo kind to convert nonlinear fractional differential equations into a nonlinear algebraic system. The nonlinearity problem is then solved using an iterative approach. Numerical results for a variety of chaotic systems are introduced using the MATLAB program and compared with previous theoretical and numerical results to ensure their reliability, convergence, accuracy, and efficiency. The fractional parameters play an effective role in studying the proposed problems. The achieved solutions prove the viability of the presented method and demonstrate that this method is easy to implement, effective, highly accurate, and appropriate for studying fractional differential equations emerging in fields related to chaotic systems and generalized Caputo-type fractional problems in the future. Full article
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15 pages, 3417 KiB  
Article
Comparison of Brillouin Light Scattering and Density of States in a Supported Layer: Analytical and Experimental Study
by Ossama El Abouti, John Cuffe, El Houssaine El Boudouti, Clivia M. Sotomayor Torres, Emigdio Chavez-Angel, Bahram Djafari-Rouhani and Francesc Alzina
Crystals 2022, 12(9), 1212; https://doi.org/10.3390/cryst12091212 - 28 Aug 2022
Cited by 4 | Viewed by 2266
Abstract
We provide a detailed analytical calculation of the Brillouin light scattering (BLS) intensity of a layer on a substrate, taking into account both photoelastic and moving boundary (ripple effect) mechanisms, and give a comparison between BLS intensity and density of states (DOS) to [...] Read more.
We provide a detailed analytical calculation of the Brillouin light scattering (BLS) intensity of a layer on a substrate, taking into account both photoelastic and moving boundary (ripple effect) mechanisms, and give a comparison between BLS intensity and density of states (DOS) to determine the dispersion curves of longitudinal guided modes in the supported layer. In particular, in the case where the mismatch between the elastic parameters of the substrate and the adsorbed layer is high, such as in a PMMA layer on a Si substrate, we derive closed-form expressions of BLS and DOS and demonstrate a simple relationship between these two quantities. A very good agreement between experimental and theoretical BLS spectra was found and compared to theoretical DOS spectra. In particular, we show that while the peaks in the DOS present a uniform behavior, the BLS spectra follows a sine cardinal (sinc) function shape around a given frequency fixed by the chosen laser wavelength. The theoretical calculation is performed within the framework of the Green’s function approach. Full article
(This article belongs to the Special Issue Advances in Phononic Crystals and Elastic Metamaterials)
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