Application of Geometric Algebra to Electromagnetic - download pdf or read online

By Andrew Seagar

ISBN-10: 9811000883

ISBN-13: 9789811000881

ISBN-10: 9811000891

ISBN-13: 9789811000898

This paintings provides the Clifford-Cauchy-Dirac (CCD) strategy for fixing difficulties concerning the scattering of electromagnetic radiation from fabrics of all kinds.

It permits somebody who's to grasp concepts that bring about easier and extra effective recommendations to difficulties of electromagnetic scattering than are at the moment in use. The approach is formulated by way of the Cauchy kernel, unmarried integrals, Clifford algebra and a whole-field procedure. this can be unlike many traditional options which are formulated by way of Green's services, double integrals, vector calculus and the mixed box essential equation (CFIE). while those traditional options bring about an implementation utilizing the tactic of moments (MoM), the CCD approach is applied as alternating projections onto convex units in a Banach space.

The final final result is an fundamental formula that lends itself to a extra direct and effective resolution than conventionally is the case, and applies with out exception to all kinds of fabrics. On any specific desktop, it leads to both a swifter resolution for a given challenge or the facility to unravel difficulties of better complexity. The Clifford-Cauchy-Dirac process bargains very genuine and demanding benefits in uniformity, complexity, pace, garage, balance, consistency and accuracy.

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Additional info for Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique

Sample text

To write a single Clifford number x as a real number, a complex number, a quaternion, a full Clifford number, a vector, an oriented area, an oriented volume or an oriented entity of the fourth dimension, all distinctly, requires some eight different ways of expressing the same symbol. Such a system is flawed at the outset. The supposed clarity it is intended to bring is lost immediately any two of these entities are added or multiplied together unless additional special symbols are used for paired or triple combinations.

3. See Sect. 4 for details. 7 Casting Physical Problems into Clifford Algebra For the purpose of solving physical problems with Clifford’s algebra it is necessary to cast whatever quantities are used to describe the physical phenomena involved, and the way those quantities are observed to behave and interact with one another, into a Clifford algebraic formulation. For example, in the case of the phenomenon of electromagnetism, the quantities of most interest are the sources (the current density J and the charge density ρ) and the fields (the electric field E and the magnetic field H).

15 represents a rotation, consider now Fig. 4. 3 Rotation 45 where the v component is the projection of u onto the xy plane z = 0, and the w component is the projection of u onto the z-axis. The Cartesian coordinate system has been set in space so that the plane z = 0 coincides with the plane spanned by the two unit vectors n1 and n2 . Those unit vectors are not shown to avoid making the diagram too cluttered. However, regardless of their exact locations in the plane z = 0, their cross product stands perpendicular to the plane as shown along the z-axis.

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Application of Geometric Algebra to Electromagnetic Scattering: The Clifford-Cauchy-Dirac Technique by Andrew Seagar

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