Table Of Contents:
Introduction xiii

Mathematical Preliminaries 1(30)

Vector Analysis 1(3)

Vector Addition 2(1)

Dot Product 2(1)

Cross Product 3(1)

Triple Vector Product 4(1)

Vector Derivatives 4(3)

Gradient of a Scalar Field 4(1)

Divergence of a Vector Field 5(1)

Curl of a Vector Field 6(1)

The Scalar Laplacian 7(9)

Cartesian Coordinates 7(1)

Cylindrical Coordinates 8(1)

Bicylindrical Coordinates 8(1)

Elliptic Cylindrical Coordinates 9(2)

Spherical Coordinates 11(1)

Oblate Spheroidal Coordinates 11(1)

Prolate Spheroidal Coordinates 12(4)

Torroidal Coordinates 16(1)

The Vector Laplacian 16(1)

Integral Theorems 17(1)

Divergence Theorem 17(1)

Stokes' Theorem 18(1)

Gradient Theorem 18(1)

Integral Transforms 18(3)

Laplace Transform 18(1)

Inverse Laplace Transform 19(2)

Fourier Transform 21(1)

Fast Fourier Transform 21(1)

The Dirac Delta Function 21(4)

Special Functions 25(6)

Bessel Functions 25(1)

Modified Bessel Functions 25(1)

Airy Functions 26(1)

Exercises 27(4)

Solutions to Laplace's Equation 31(26)

Separation of Variables 31(7)

Cartesian Coordinates 31(3)

Cylindrical Coordinates 34(1)

Bicylindrical Coordinates 35(1)

Elliptic Cylindrical Coordinates 35(1)

Spherical Coordinates 35(1)

Prolate Spheroidal Coordinates 36(1)

Oblate Spheroidal Coordinates 37(1)

Toroidal Coordinates 37(1)

Conformal Mapping 38(4)

Finite Difference Methods 42(4)

Monte Carlo Method 46(4)

Finite Element Method 50(7)

Exercises 54(3)

A Walk Through QuickField 57(24)

What is QuickField? 57(4)

Basic Organization of QuickField 61(1)

Specifying Problem Types and Properties 62(1)

Model Construction 63(2)

Problem Solving and Post Processing 65(1)

Electrostatics Simulation 66(6)

Magnetostatics Simulation 72(9)

Exercises 79(2)

Electrostatics 81(32)

Coulomb's Law and the Superposition Principle 81(2)

Electric Flux and Gauss' Law 83(3)

Electric Flux 83(1)

Gauss' Law 83(1)

Calculation of the Electric Field from Gauss' Law 84(1)

Divergence of the Electric Field 85(1)

Electric Potential 86(1)

Delta Function Charge Distribution 87(1)

QuickField Electrostatic Calculation 87(7)

Boundary Conditions 88(2)

Material Properties 90(1)

Vertex Conditions 90(1)

Uniform Electric Field and Dipole Sources 90(1)

Integral Quantities 91(1)

Point Charge Inside a Conical Cavity in a Dielectric 92(1)

Charged Needle Threading a Circular Hole in a Conducting Sheet 92(2)

Calculation of Capacitance 94(2)

Motion of Charged Particles in Static Electric Fields 96(17)

Exercises 101(12)

Magnetostatics 113(28)

Biot-Savart Law 113(1)

Ampere's Law 114(1)

Gauss' Law for Magnetic Fields 115(1)

Magnetic Scalar Potential 116(1)

Spherical Permanent Magnet 116(1)

Magnetic Vector Potential 117(2)

QuickField Magnetostatic Analysis 119(6)

Magnetic Material Properties 120(2)

Boundary Conditions 122(2)

Vertex Conditions 124(1)

Inductance Calculations 125(1)

Uniform Magnetic Fields 125(2)

Uniform Field in x-y Symmetry 125(1)

Uniform Field in Axisymmetry 126(1)

Dipole Sources 127(2)

Modeling a Line Current Source 127(1)

Current Dipole 128(1)

Current Density 128(1)

Magnetic Dipole 128(1)

Shielding Applications 129(1)

Magnetic Shielding by a Highly Permeable Tube 129(1)

Magnetic Monopoles 130(11)

Exercises 132(9)

Time-harmonic Magnetics 141(42)

Faraday's Law and Maxwell's Displacement Current 141(2)

Time-harmonic Maxwell's Equations 143(3)

Current Sheet Above a Conducting Half-Space 144(2)

Vector Potential Formulation 146(11)

Circular Coil Above a Conducting Half-Space 147(5)

Circular Coil Above a Conducting Sphere 152(5)

Time-harmonic Analysis in QuickField 157(5)

Boundary Conditions 157(1)

Material Properties 158(2)

Integral Quantities 160(1)

Inductance Calculations 160(2)

Current Loop Inside a Conducting Sphere 162(1)

Eddy Current Nondestructive Testing Applications 162(6)

Change in Magnetic Field and Coil Impedance Due to a Defect in Pipe Inspection 163(1)

Pipe Inspection 164(4)

Metal Detectors 168(2)

Geophysical Applications 170(1)

Magnetotellurics 170(1)

Induction Logging 170(1)

Transformer Applications 170(13)

Exercises 173(10)

Transient Magnetics 183(28)

Time-dependent Maxwell's Equations 183(4)

Current Sheet Above a Conducting Half-Space 183(4)

Finite Difference Time-domain Method 187(2)

Fields Inside a Cylindrical Cavity 187(2)

Resonant Frequencies 189(1)

Vector Potential Formulation 189(3)

Circular Coil Above a Conducting Half-Space 189(3)

Time-dependent Magnetics in QuickField 192(10)

Integral Quantities 192(1)

Material Properties and Boundary Conditions 193(1)

Time-dependent Quantities 193(1)

Conducting Cylinder in a Transient Magnetic Field 194(3)

Current Sheet Above a Conducting Plane 197(1)

Current Loop Surrounding a Conducting Sphere 197(5)

Pulsed Eddy Current Nondestructive Testing Applications 202(1)

Maxwell's Equations with Monopole Source Term 202(9)

Monopole Moving in Crossed Electric and Magnetic Fields 203(1)

Exercises 204(7)

Superconductivity 211(22)

Theoretical Background 211(2)

Modeling Superconductors 212(1)

London Theory and the Meissner Effect 213(2)

Flux Quantization 215(1)

Type-I and Type-II Superconductors 216(1)

Superconducting Geometries and Boundary Conditions 217(1)

Geometric Effects 217(1)

Nonlinear Superconductors 217(1)

Boundary Conditions 217(1)

Calculation of Supercurrent Density 217(1)

Mesh Requirements 218(1)

Superconducting Plates 218(2)

Superconducting Strip 218(2)

Superconducting Disk 220(1)

Hollow Superconducting Shells 220(4)

Zero Field Cooling 220(1)

Flux Trapping 220(1)

Superconducting Ring 221(1)

Superconducting Tube 222(2)

Layered Superconducting and Permeable Shields 224(1)

Superconducting & Highly Permeable Metal Sandwich 225(1)

Modeling Type-II Superconductors 225(8)

Exercises 228(5)

DC Conduction Analysis 233(20)

DC Current Flow Theory 233(1)

DC Conduction Analysis in QuickField 234(4)

Boundary Conditions 234(1)

Material Properties 235(1)

Vertex Conditions 235(2)

Ellipsoidal Crack in a Current Carrying Plate 237(1)

Alternative Energy Applications 238(7)

Batteries 238(1)

Fuel Cells 239(6)

Resistivity Measurements 245(1)

Printed Circuit Boards 245(8)

Exercises 249(4)

AC Current Flow 253(20)

AC Conduction Theory 253(1)

AC Conduction Analysis in QuickField 254(3)

Integral Quantities 254(1)

Material Properties 255(1)

Boundary Conditions 256(1)

Vertex Conditions 257(1)

Application to Biophysical Measurements 257(16)

Measurement of Effective Conductivity and Permittivity 257(1)

Dielectric Spectroscopy of Cells in Suspension and Tissue 258(2)

Living Cells in Alternating Electric Fields 260(2)

Cellular Organelles in Alternating Electric Fields 262(1)

Spherical Mitochondrion Model 263(1)

Mitochondrion with Complex Geometry 264(1)

Mitochondrion with Periodic Structure 264(5)

Exercises 269(4)

Thermal Analysis 273(30)

The Heat Equation 273(1)

Steady State Heat Flow 274(3)

Temperature Distribution in a Semi-Infinite Plate 275(1)

Temperature Distribution in a Circular Plate 276(1)

Conformal Transformation 276(1)

Transient Heat Transfer 277(1)

Thermal Analysis in QuickField 278(8)

Material Properties 279(3)

Boundary Conditions 282(1)

Vertex Conditions 283(1)

Calculated Values 283(1)

Steady State Heat Flow in a Sphere 284(1)

Transient Heat Flow in a Cylinder 285(1)

Coupled Time Varying Magnetic and Heat Transfer Problems 286(1)

Modeling Hyperthermia in Oncology 287(1)

Coupled Current Flow and Heat transfer Problems 287(16)

Temperature Distribution in a Fuel Cell Stack 287(1)

Fuel Cell in Open-circuit Mode 288(1)

Fuel Cell with Zero Load 288(6)

Exercises 294(9)

Stress Analysis 303(40)

Stress and Strain 303(2)

Young's Modulus 303(1)

Shear Modulus 304(1)

Poisson's Ratio 304(1)

Beams 305(2)

Stress Analysis in QuickField 307(11)

X-Y Symmetry 307(2)

Axisymmetry 309(1)

Thermal Strain 310(1)

Material Properties and Loading Sources 311(2)

Boundary Conditions 313(1)

Vertex Conditions 313(1)

Calculated Values 313(3)

Integral Values 316(1)

Stress Distribution Near a Crack 317(1)

Coupled Thermal and Stress Analysis 318(6)

Space Capsule Simulations 318(2)

Launch Abort System 320(1)

Atmospheric Reentry 320(4)

Stress Analysis with Electric Forces 324(1)

Stress Analysis with Magnetic Forces 325(3)

Coupled Electric Current, Thermal and Stress Analysis 328(15)

Exercises 332(11)

Electrical Circuits 343(34)

Electrical Current and Ohm's Law 343(1)

Kirchhoff s Laws 344(2)

Resistances in Parallel and Series 346(2)

Capacitances in Parallel and Series 348(1)

Impedances in AC Circuits 349(1)

Transient Currents in Electrical Circuits 350(4)

RL circuit 350(1)

LC circuit 351(1)

RLC circuit 352(1)

Multiple Loop Circuits 353(1)

Electrical Circuit Modeling in QuickField 354(6)

Building the Circuit 354(1)

Running the Circuit Simulation 354(4)

Using Label Mover 358(2)

Filter Applications 360(1)

Electrical Circuit Models of Biological Systems 361(6)

Modeling the Passive Response of Neurons to Electrical Stimuli 361(2)

Debye Relaxation Model 363(1)

Maxwell-Wagner Model 363(2)

Modeling Skin Impedance 365(1)

Modeling Electrode Polarization 366(1)

Chua's Chaotic Circuit 367(10)

Exercises 371(6)
Appendix 1. A Walk Through MATLAB 377(8)
Appendix 2. Laplace Transform of Pulsed and Periodic Functions 385(2)
Appendix 3. Table of Conformal Mappings 387(4)
Appendix 4. Engineering Material Properties 391(4)
Appendix 5. Biological Material Properties 395(4)
Appendix 6. About the CD-ROM 399(2)
Index 401