Prof. EL MAHDI ASSAID: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=19482
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 20 Oct 2021 10:54:43 GMTWed, 20 Oct 2021 10:54:43 GMTNew applications published by Prof. EL MAHDI ASSAIDhttps://www.maplesoft.com/images/Application_center_hp.jpgProf. EL MAHDI ASSAID: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=19482
Polarization of Dielectric Sphere .....
https://www.maplesoft.com/applications/view.aspx?SID=154296&ref=Feed
In this worksheet, we investigate the polarization of a dielectric sphere (dot) with a relative permittivitty "epsilon[Dot]" embedded in a dielectric matrix with a relative permittivitty "epsilon[Matrix]" and submitted to an uniform electrostatic field F oriented in z-axis direction. It's a fondamental and popular problem present in most of electromagnetism textbooks. First of all, we express Poisson equation in appropriate coordinates system:
"Delta V(r,theta,phi) = 0". We proceed to a full separation of variables and derive general expression of scalar electrostatic potential V(r,theta,phi). Then we particularize to a dielectric sphere surrounded by a dielectric matrix and give expressions of electrostatic potential V(r,theta) in the meridian plane (x0z) inside and outside the sphere by taking into account:
i) invariance property of the system under rotation around z-axis,
ii) choice of the plane z=0 as a reference of scalar electrostatic potential,
iii) regularity of V(r,theta) at the origine and very far from the sphere,
iv) continuity condition of scalar electrostatic potential V(r,theta) at the sphere surface,
v) continuity condition of normal components of electric displacement field D at the sphere surface.
The obtained expressions of V(r,theta) inside and outside the sphere allows as to derive expressions of electrostatic field F, electric displacement field D and polarization field P inside and outside dielectric dot in spherical coordinates as well as in cartesian rectangular coordinates. The paper is a proof of Maple algebraic and graphical capabilities in tackling the resolution of Poisson equation as a second order partial differential equation and also in displaying scalar electrostatic potential contourplot, electrostatic field lines as well as fieldplots of F, D and P inside and outside dielectric sphere.<img src="https://www.maplesoft.com/view.aspx?si=154296/fieldplot.PNG" alt="Polarization of Dielectric Sphere ....." style="max-width: 25%;" align="left"/>In this worksheet, we investigate the polarization of a dielectric sphere (dot) with a relative permittivitty "epsilon[Dot]" embedded in a dielectric matrix with a relative permittivitty "epsilon[Matrix]" and submitted to an uniform electrostatic field F oriented in z-axis direction. It's a fondamental and popular problem present in most of electromagnetism textbooks. First of all, we express Poisson equation in appropriate coordinates system:
"Delta V(r,theta,phi) = 0". We proceed to a full separation of variables and derive general expression of scalar electrostatic potential V(r,theta,phi). Then we particularize to a dielectric sphere surrounded by a dielectric matrix and give expressions of electrostatic potential V(r,theta) in the meridian plane (x0z) inside and outside the sphere by taking into account:
i) invariance property of the system under rotation around z-axis,
ii) choice of the plane z=0 as a reference of scalar electrostatic potential,
iii) regularity of V(r,theta) at the origine and very far from the sphere,
iv) continuity condition of scalar electrostatic potential V(r,theta) at the sphere surface,
v) continuity condition of normal components of electric displacement field D at the sphere surface.
The obtained expressions of V(r,theta) inside and outside the sphere allows as to derive expressions of electrostatic field F, electric displacement field D and polarization field P inside and outside dielectric dot in spherical coordinates as well as in cartesian rectangular coordinates. The paper is a proof of Maple algebraic and graphical capabilities in tackling the resolution of Poisson equation as a second order partial differential equation and also in displaying scalar electrostatic potential contourplot, electrostatic field lines as well as fieldplots of F, D and P inside and outside dielectric sphere.https://www.maplesoft.com/applications/view.aspx?SID=154296&ref=FeedMon, 18 Sep 2017 04:00:00 ZE. H. EL HAROUNY, A. IBRAL, S. NAKRA MOHAJER and J. EL KHAMKHAMIE. H. EL HAROUNY, A. IBRAL, S. NAKRA MOHAJER and J. EL KHAMKHAMIPhysics of Silicon Based P-N Junction
https://www.maplesoft.com/applications/view.aspx?SID=154248&ref=Feed
In this worksheet, the physics of Silicon based P-N junction in thermal equilibrium is investigated. Special attention is devoted to the case where no bias voltage is applied to the junction. Poisson equation governing the electrostatic potential throughout the P-N junction is solved using two different approaches. According the first approach, the thin layer which extends on both sides of the junction is considered as depleted and Poisson equation is simplified and solved analytically. According to the second approach, a rigorous numerical resolution of Poisson equation is performed without resorting to any simplifying hypothesis. The worksheet presents a demonstration of Maple's capabilities in tackling the resolution of Poisson equation as a second order nonlinear nonhomogeneous ordinary differential equation and also in extracting, in addition to electrostatic potential, important physical quantities such as electrostatic field, negative and positive charge carriers densities, total charge as well as electric currents densities.<img src="https://www.maplesoft.com/view.aspx?si=154248/PN_Junction.png" alt="Physics of Silicon Based P-N Junction" style="max-width: 25%;" align="left"/>In this worksheet, the physics of Silicon based P-N junction in thermal equilibrium is investigated. Special attention is devoted to the case where no bias voltage is applied to the junction. Poisson equation governing the electrostatic potential throughout the P-N junction is solved using two different approaches. According the first approach, the thin layer which extends on both sides of the junction is considered as depleted and Poisson equation is simplified and solved analytically. According to the second approach, a rigorous numerical resolution of Poisson equation is performed without resorting to any simplifying hypothesis. The worksheet presents a demonstration of Maple's capabilities in tackling the resolution of Poisson equation as a second order nonlinear nonhomogeneous ordinary differential equation and also in extracting, in addition to electrostatic potential, important physical quantities such as electrostatic field, negative and positive charge carriers densities, total charge as well as electric currents densities.https://www.maplesoft.com/applications/view.aspx?SID=154248&ref=FeedThu, 25 May 2017 04:00:00 ZH. EL ACHOUBY, M. ZAIMI, A. IBRALH. EL ACHOUBY, M. ZAIMI, A. IBRALThe Real Photovoltaic Solar Cell
https://www.maplesoft.com/applications/view.aspx?SID=33045&ref=Feed
<p>In this contribution, we use Maple software to study a solar cell modeled by an electronic circuit containing five physical parameters. The physical parameters are: the series resistance, the reverse saturation current, the ideality factor, the shunt resistance and the photocurrent. First, we solve the characteristic equation giving the output current <br />
as a function of the output voltage of the solar cell. Then, we determine the analytical expressions of the short circuit current, the open circuit voltage, the dynamical resistance <br />
of the solar cell and the different kinds of powers involved : the output power, the power dissipated by Joule Effect in the internal components of the solar cell and the solar cell total power.</p>
<p>Next, we determine a new expression of the optimal load resistance corresponding to the maximal power point. Finally, we investigate the effects of the different physical parameters on the current-voltage characteristic I[out] = f(V[out]) and on the output power P[out](I[out]) of the solar cell.</p><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The Real Photovoltaic Solar Cell" style="max-width: 25%;" align="left"/><p>In this contribution, we use Maple software to study a solar cell modeled by an electronic circuit containing five physical parameters. The physical parameters are: the series resistance, the reverse saturation current, the ideality factor, the shunt resistance and the photocurrent. First, we solve the characteristic equation giving the output current <br />
as a function of the output voltage of the solar cell. Then, we determine the analytical expressions of the short circuit current, the open circuit voltage, the dynamical resistance <br />
of the solar cell and the different kinds of powers involved : the output power, the power dissipated by Joule Effect in the internal components of the solar cell and the solar cell total power.</p>
<p>Next, we determine a new expression of the optimal load resistance corresponding to the maximal power point. Finally, we investigate the effects of the different physical parameters on the current-voltage characteristic I[out] = f(V[out]) and on the output power P[out](I[out]) of the solar cell.</p>https://www.maplesoft.com/applications/view.aspx?SID=33045&ref=FeedMon, 25 May 2009 04:00:00 ZProf. EL MAHDI ASSAIDProf. EL MAHDI ASSAIDExact Analytical Solutions Of Diodes Bridge
https://www.maplesoft.com/applications/view.aspx?SID=4861&ref=Feed
In this application worksheet, we use Maple software to determine exact analytical solutions for the current flows through the different branches of the circuit known as Graëtz bridge. This circuit is used in electronics as full wave rectifier, it is formed by four non-ideal diodes and one diagonal resistance. Then, we derive analytical expressions for the voltages at the terminals of all elements in the circuit. Finally, we calculate the dynamical resistances of different diodes in the circuit. The proposed analytical solutions are all expressed as functions of the Lambert W function.<img src="https://www.maplesoft.com/view.aspx?si=4861/GraetzBridge_186.jpg" alt="Exact Analytical Solutions Of Diodes Bridge" style="max-width: 25%;" align="left"/>In this application worksheet, we use Maple software to determine exact analytical solutions for the current flows through the different branches of the circuit known as Graëtz bridge. This circuit is used in electronics as full wave rectifier, it is formed by four non-ideal diodes and one diagonal resistance. Then, we derive analytical expressions for the voltages at the terminals of all elements in the circuit. Finally, we calculate the dynamical resistances of different diodes in the circuit. The proposed analytical solutions are all expressed as functions of the Lambert W function.https://www.maplesoft.com/applications/view.aspx?SID=4861&ref=FeedFri, 26 Jan 2007 00:00:00 ZProf. EL MAHDI ASSAIDProf. EL MAHDI ASSAIDfibre optique à saut d'indice
https://www.maplesoft.com/applications/view.aspx?SID=4856&ref=Feed
This worksheet presents a demonstration of Maple software's capabilities in the resolution of differential equations governing the propagation of an electromagnetic wave in a step-index optical fiber with a core radius of the order of magnitude of the incident radiation wavelength. It also presents the two and three dimensions graphical functionalities given by Maple which allows :
i) To access directly to the eigenvalue equation solutions.
ii) To check easily the continuity conditions of the electric E and magnetic H tangent components at the core-cladding boundary.
iii) To show in the three dimensions space the E and H vector fields.
iv) To show in the fiber transverse plane the light intensity distribution.<img src="https://www.maplesoft.com/view.aspx?si=4856/fibre_optique.jpg" alt="fibre optique à saut d'indice" style="max-width: 25%;" align="left"/>This worksheet presents a demonstration of Maple software's capabilities in the resolution of differential equations governing the propagation of an electromagnetic wave in a step-index optical fiber with a core radius of the order of magnitude of the incident radiation wavelength. It also presents the two and three dimensions graphical functionalities given by Maple which allows :
i) To access directly to the eigenvalue equation solutions.
ii) To check easily the continuity conditions of the electric E and magnetic H tangent components at the core-cladding boundary.
iii) To show in the three dimensions space the E and H vector fields.
iv) To show in the fiber transverse plane the light intensity distribution.https://www.maplesoft.com/applications/view.aspx?SID=4856&ref=FeedFri, 12 Jan 2007 00:00:00 ZProf. EL MAHDI ASSAIDProf. EL MAHDI ASSAIDLa Fibre Optique Multimode à Gradient d'Indice
https://www.maplesoft.com/applications/view.aspx?SID=4844&ref=Feed
This worksheet presents a demonstration of Maple's capabilities in the resolution of non-linear differential equations system governing the propagation of light in multimode graded-index optical fiber. It also presents the possibilities given by Maple in the composition of the solutions and the plot of a three dimensional curve representing the light's route in the fiber's core.
Cette feuille présente les capacités de Maple dans la résolution d'un système d'équations différentielles non linéaires régissant la propagation de la lumière dans une fibre optique multimode à gradient d'indice. Elle présente aussi les possibilités offertes par Maple dans la composition des solutions et le tracé d'une courbe à trois dimensions représentant le trajet de la lumière dans le coeur de la fibre.<img src="https://www.maplesoft.com/view.aspx?si=4844/fibre.jpg" alt="La Fibre Optique Multimode à Gradient d'Indice" style="max-width: 25%;" align="left"/>This worksheet presents a demonstration of Maple's capabilities in the resolution of non-linear differential equations system governing the propagation of light in multimode graded-index optical fiber. It also presents the possibilities given by Maple in the composition of the solutions and the plot of a three dimensional curve representing the light's route in the fiber's core.
Cette feuille présente les capacités de Maple dans la résolution d'un système d'équations différentielles non linéaires régissant la propagation de la lumière dans une fibre optique multimode à gradient d'indice. Elle présente aussi les possibilités offertes par Maple dans la composition des solutions et le tracé d'une courbe à trois dimensions représentant le trajet de la lumière dans le coeur de la fibre.https://www.maplesoft.com/applications/view.aspx?SID=4844&ref=FeedWed, 15 Nov 2006 00:00:00 ZProf. EL MAHDI ASSAIDProf. EL MAHDI ASSAID