There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

비만아 부모의 돌봄 경험: q 방법론

Finite element methods for Maxwell's equations.

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

This introduction to electromagnetics emphasizes the computation of electromagnetic fields and the development of theoretical relations. Beginning with the idea that Maxwell's equations are primary, the authors avoid the lengthy discussions of electro - and magneto - statics that are customary in texts on electromagnetism. After a chapter, therefore, on the basics of vector calculus, the discussion begins with the electromagnetic field and Maxwell's equations; the two following chapters then present the special cases of electrostatic and magnetostatic phenomena. Dynamics is introduced in chapter 5, and electromagnetic induction in chapter 6. The discussion of wave propagation and high-frequency fields emphasizes such practical matters as propagation in lossy dielectrics, waveguides, and resonators. The remaining four chapters discuss computational techniques; the finite element method, Galerkin's residual approach, software implementation, and recent developments in computer techniques.

Electromagnetics and calculation of fields

This paper addresses the problem of finding the state of switching devices (open or closed) in primary distribution networks so that the total loss is minimum. Radiality and capacity constraints are taken into account. This optimization problem is a mixed-integer nonlinear optimization problem, in which the integer variables represent the state of the switches, and the continuous variables represent the current flowing through the branches. The standard Newton method (with second derivatives) is used to compute branch currents at each stage within the integer search, which, in turn, is implemented as a simple best-first search. Although a best-first search cannot normally guarantee the optimality of the solution, the high quality of the suboptimal solutions found, together with the high processing speed, make this approach very attractive for real-size distribution systems. Results from the application of the proposed methodology to a 1128-branch, 129-switch, real-world distribution system are presented and discussed.

Fast reconfiguration of distribution systems considering loss minimization

Classical Surface Impedance Boundary Conditions Skin Effect Approximation SIBCs of the Order of Leontovich's Approximation High-Order SIBCs Rytov's Approach References General Perturbation Approach to Derivation of Surface Impedance Boundary Conditions Local Coordinates Perturbation Technique Tangential Components Normal Components Normal Derivatives Components of the Curl Operator Surface Impedance ''Toolbox'' Concept Numerical Example Appendix SIBCs in Terms of Various Formalisms Basic Equations Electric Field-Magnetic Field Formalism Magnetic Scalar Potential Formalism Magnetic Vector Potential Formalism Common Representation of Various SIBCs Using a Surface Impedance Function Surface Impedance near Corners and Edges Calculation of the Electromagnetic Field Characteristics in the Conductor's Skin Layer Distributions across the Skin Layer Resistance and Internal Inductance Forces Acting on the Conductor Derivation of SIBCs for Nonlinear and Nonhomogeneous Problems Coupled Electromagnetic-Thermal Problems Magnetic Materials Nonhomogeneous Conductors Implementation of SIBCs for the Boundary Integral Equation Method: Low-Frequency Problems Two-Dimensional Problems Three-Dimensional Problems Properties of the Surface Impedance Function Boundary Element Formulations for Two- and Three-Dimensional Problems in Invariant Form Numerical Examples Quasi-Three-Dimensional Integro-Differential Formulation for Symmetric Systems of Conductors Implementation of SIBCs for the Boundary Integral Equation Method: High-Frequency Problems Integral Representations of High-Frequency Electromagnetic Fields SIBCs for Lossy Dielectrics Direct Implementation of SIBCs into the Surface Integral Equations Implementation Using the Perturbation Technique Numerical Example Appendix Implementation of SIBCs for Volume Discretization Methods Statement of the Problem Finite-Difference Time-Domain Method Finite Integration Technique Finite-Element Method Appendix Application and Experimental Validation of the SIBC Concept Selection of the Surface Impedance Boundary Conditions for a Given Problem Experimental Validation of SIBCs Appendix A: Review of Numerical Methods Index

Nathan Ida

Papers

Introduction to the Finite Element Method

Electromagnetics and calculation of fields

Fast reconfiguration of distribution systems considering loss minimization

Surface Impedance Boundary Conditions: A Comprehensive Approach

Artificial Neural Networks and Machine Learning techniques applied to Ground Penetrating Radar: A review