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Hierarchical Methods Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics 1st Edition by V Kulish ISBN 1402007574 9781402007576

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Hierarchical Methods Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics 1st Edition V. Kulish Digital Instant Download

Author(s): V. Kulish
ISBN(s): 9781402007576, 1402007574
Edition: 1
File Details: PDF, 5.65 MB
Year: 2002
Language: english
SKU: EB-1526538 Category: Tag:

Hierarchical Methods Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics 1st Edition by V Kulish – Ebook PDF Instant Download/Delivery:1402007574, 9781402007576
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Product details: 

ISBN 10: 1402007574 

ISBN 13: 9781402007576

Author: V. Kulish

The book consists of two Volumes. The first (the preceding volume) is devoted to the general nonlinear theory of the hierarchical dynamic oscillative–wave systems. This theory has been called the theory of hi- archical oscillations and waves. Here two aspects of the proposed theory are discussed. The first aspects concern the fundamental nature and the basic c- cepts and ideas of a new hierarchical approach to studying hierarchical dynamic systems. A new hierarchical paradigm is proposed as a – sis of a new point of view of such types of systems. In turn, a set of hierarchical principles is formulated as the fundamental basis of this paradigm. Therein the self-resemblance (holographic) principle plays a key role here. An adequate mathematic description (factorization) of the proposed paradigm is carried out. The concepts of structural and dynamic (functional) operators are put into the basis of this descr- tion. Electrodynamics is chosen as a convenient basis for an obvious demonstration of some key points of the proposed new theory. The second aspect has a purely mathematical nature. It is related to the form of factorization (i.e., mathematical description) of hier- chical types of dynamic models, and discussion of the methods of their mathematical analysis. A set of the hierarchical asymptotic analytical– numerical methods is given as an evidence of the practical effectiveness of the proposed version of hierarchical theory.

Table of contents: 

Introduction to Hierarchical Methods

Definition and Importance

Historical Context in Electrodynamics

Scope and Objectives of the Book

Fundamentals of Hierarchy in Physical Systems

The Concept of Hierarchical Structures

Hierarchical Principles in Nature

Multi-Scale Phenomena

Mathematical Foundations of Hierarchical Methods

Asymptotic Expansions and Perturbation Theory

Hierarchical Decomposition of Complex Systems

Dimensional Analysis in Hierarchical Models

Electrodynamics and Hierarchical Models

Classical Electrodynamics Revisited

Maxwell’s Equations in a Hierarchical Framework

Multi-Scale Electromagnetic Field Analysis

Hierarchical Asymptotic Methods

Small and Large Parameter Expansions

Approximation Techniques for Electromagnetic Waves

Boundary Layer Approximations

Applications in Wave Propagation and Scattering

Hierarchical Approaches in Optical Systems

Multi-Scale Scattering Problems

Electromagnetic Wave Interaction with Complex Media

Numerical and Computational Aspects

Hierarchical Finite Element Methods

Multi-Scale Computational Models

Numerical Stability and Convergence

Hierarchy in Nonlinear Electrodynamics

Nonlinear Wave Equations in Electromagnetism

Self-Organizing Hierarchical Structures

Chaotic and Fractal Electromagnetic Systems

Experimental Validation and Practical Applications

Laboratory Techniques for Hierarchical Systems

Applications in Antenna Theory and Wireless Communication

Nanotechnology and Hierarchical Electromagnetics

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