Dimplementationofmaxwell’s Equationsin Matlabtostudythe Effect Of Absorption Using Pml

1-D Implementation of Maxwell’s Equations in MATLAB to Study the Effect of Absorption Using PML . Pranav K Shrivastava,Vikas Rathi, Hemant S Pokhariya Graphic Era Unversity ,Dehradun e-mail:{pranav.shantikunj,vikas.rth}@gmil.com . . Abstract: The Finite Difference Time Domain method   (FDTD)     uses     centre-difference representations   of   the   continuous   partial The 3D source free( J =0) Mxwell’s curl equations[5]  a homogeneous medium are: . ∂Ez − ∂Ey = −µ ∂Hx ∂y differential equations to create iterative numerical  dH  ∂Ex ∂z ∂Ez ∂t ∂Hy models of wave propagation. First we study the ∇×E = −µ → ∂z   − ∂x   = −µ ∂t propagation behavior of the wave in single dt  ∂Ey ∂Ex ∂Hz dimension without PML and in second part we study the absorption using PML for the same wave  ∂x   − ∂y = −µ ∂t using MATLAB environment. . I. INTRODUCTION . Finite-difference  time-domain  (FDTD)  is  a  popular computational electrodynamics modeling technique. Since it is a . ∇ × H = ε  ∂Hz d E      ∂Hx dt    ∂Hy →   ∂y ∂z  ∂x ∂Hy −   ∂z    = ε ∂Hz = −    ∂t  ε ∂Hx −   ∂y    = ε ∂Ex ∂t ∂Ey ∂t ∂Ez ∂t time-domain method, solutions can cover a wide frequency range with a single simulation run. ∂Ex   = −µ ∂Hy ∂z  ∂t ∂Hy   = −ε ∂Ex The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. The time- dependent Maxwell’s equations (in partial differential form) are discretized using central-difference approximations to the space and time partial   derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is...

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UNIT III DIMENSIONAL ANALYSIS . . . . UNIT III DIMENSIONAL ANALYSIS . The basic concepts and procedures for dimensional analysis were developed by hydraulic engineers to determine the performances of a prototype (a full-scale structure) from the data obtained by tests on a model ( a reduced-scale structure). Here we present the general method of dimensional analysis and illustrates its application to various problems of fluid machines. Some of the important principles of similarity and use of dimensionless numbers in model analysis are also studied. . . SYSTEM OF DIMENSIONS: Dimensions refer to the qualitative characteristics for physical quantities, while units are standards of comparison for quantitative measure of dimensions. The most common systems of dimensioning a physical quantity and the Mass-length-time and the Force-length-time systems referred to as the MLT and FLT systems of units. There is no direct relationship between the quantities length L, mass M and time T. These independent quantities are called fundamental quantities. In compressible fluids, one more dimension namely temperature θ is also taken as the fundamental dimension. All other quantities such as pressure, velocity and energy etc. are expressed in terms of these fundamental quantities and are called derived or secondary quantities. For example F=MLT−2:M=FT2L−1 . . Physical quantity Symbol Dimensions M-L-T System F-L-T System *Fundamental quantities . . . Mass M M FL-1T2 Length L L L Time T T T Force F MLT-2 F *Geometric quantities . . . Area A L2 L2 Volume V L3 L3 *Kinematic quantities . . . Linear velocity u,V,U LT-1 LT-1 Angular velocity ω T-1 T-1 Acceleration a LT-2 LT-2 Discharge Q,q L3 T-1 L3 T-1 Gravity g LT-2 LT-2 Kinematic viscosity ν L2 T-1 L2 T-1 *Dynamic quantities . . . Density ρ ML-3 FL-4T2 Specific Weight w ML-2T-2 FL-3 Surface tension σ...

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Binomial and Normal distributions used in business forecastingMade By:Abhay SinghRoll No.—50202BBS I ABusiness Statistics and ApplicationsTerm Paper

statistics term paper Figure 1 1 What are theoretical distributions? 3 Binomial Distribution 3 Cumulative Distribution Function 4 Why is it important? 4 (p + q)2 = p2 + 2pq +q2, or more simply, pp + 2pq + qq 4 Quick facts 4 Uses in Business 5 1. Quality Control 5 2. Public Opinion Survey 6 3. Medical Research 6 4. Insurance Sector 7 Normal Distribution 8 Uses 10 1. Modern Portfolio Theory 10 2. Human resource Management 11 Forecasting 11 1. Using the Normal Distribution to Determine the Lower 10% Limit of Delivery Times 13 2. Finding the probability of a certain type of package passing down a conveyor belt if the probability of that type of package passing by is known. 14...

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Considere La Matriz De Datos Del Ejercicio 6 Del Capítulo 1 Complete Cada Uno De Los Incisos Siguientes

PROBLEMARIO . 1.- Verifique que los dos vectores a1=[2/√5.1/√5.]            a2=[1/√5.−2/√5.] Son ortogonales entre sí. Represente gráficamente estos dos vectores en una gráfica bidimensional y trace rectas desde el origen hasta cada uno de los vectores en la gráfica. Efectuamos el producto escalar entre los dos y tenemos que: a1a2=[2/√5.1/√5.][1/√5.−2/√5.]=(2√5..)(1√5..)+(1√5)..)(−2√5..)=25..−25..=0 Por lo que efectivamente se trata de dos vectores ortogonales. . 2.- Considere la matriz de datos del ejercicio 6 del capítulo 1 Complete cada uno de los incisos siguientes. El instructor decidirá si se va a trabajar a man o tiene que usar un programa que le permita realizar las manipulaciones con matrices. a)Encuentre la traza tanto de ˆΣ b)Encuentre el determinante tanto de ˆΣ   c)Encuentre los eigenvectores y los eigenvalores tanto de ˆΣ  . Demuestre que todas las parejas de eigenvectores son ortogonales entre sí. d)Demuestre que la suma de los eigenvalores de ˆΣ  es igual a la traza de ˆΣ . Asimismo, demuestre que el producto de los eigenvalores de ˆΣ   es igual al determinante de ˆΣ . e) Calcule √ˆμμ ,√ˆμ´ˆΣ−1ˆμ, y  √(X2−ˆμ)ˆΣ−1(X2−ˆμ) .      Traza de la matriz ˆΣ =3. . . . . . . . . —- . . . . . . . . . . . . 3.- Cuarenta y ocho individuos que habían presentado solicitud de trabajo a una gran empresa fueron entrevistados y clasificados en relación con 15 criterios. Los aspirantes se clasificaron según la forma de su letra en la solicitud (FL), su aspecto (APP),su capacidad académica (AA), su amabilidad (LA),su autoconfianza (SC), su lucidez (LC),su honestidad (HON),su arte de vender(SMS), su experiencia(EXP),su empuje(DRV),su ambición (AMB),su capacidad para captar conceptos(GSP),su potencial(POT),su entusiasmo para trabajar en grupo (KJ) y su conveniencia(SUIT). Cada criterio se evalúo en una escala que va del 0 al 10,con 0 como una calificación muy insatisfactoria y con 10 como una calificación muy alta. ID FL...

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Combined Radiation And Convection

EXPERIMENT NO: 01                                                                                       DATE: 25-07-12 . COMBINED RADIATION AND CONVECTION . . AIM • To determine the heat transfer due to radiation and convection from cylinder. • To find emissivity at different temperatures. • To find natural convection coefficient. . APPARATUS REQUIRED • Thermometer • Heater • Stopwatch • Sand paper . THEORY If a surface, at a temperature above that of its surroundings, is located in stationary air at the same temperature as the surroundings then heat will be transferred from the surface to the air and surroundings. This transfer of heat will be a combination of natural convection to the air (air heated by contact with the surface becomes less dense and rises) and radiation to the surroundings. A horizontal cylinder is used in this exercise to provide a simple shape from which the heat transfer can be calculated. Note: Heat loss due to conduction is minimised by the design of the equipment and measurements mid way along the heated section of the cylinder can be assumed to be unaffected by conduction at the ends of the cylinder. Heat loss by conduction would normally be included in the analysis of a real application. . In the case of natural (free) convection the Nusselt number Nu depends on the Grashof and Prandtl numbers and the heat transfer correlation can be expressed in the form: Nusselt number, Nu = f (Gr, Pr) Rayleigh number, Ra = (Gr Pr) The average heat transfer coefficient for radiation Hrm can be calculated using the following relationship:                                                  Hrm= ΣζF(Ts4−Ta4)(Ts−Ta).. The average heat transfer coefficient for natural convection Hcm can be calculated using the following relationship:                                                   Tfilm= Ts+Ta2..                                                         β= 1Tfilm..                                                      Ngr=  gβ(Ts−Ta)D3υ2..                                                  Rad = (Grd × Pr)                                                 Num = b(Rad)n, (c and n can be obtained from the table below)                                                     Hfm= kNumD.. Note: k, Pr, and n are physical properties of the air taken at...

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