volume | PIER Journals

0000-00-00

Volterra Differential Constitutive Operators and Locality Considerations in Electromagnetic Theory

Dan Censor,

Dr. Dan Censor

Department of Electrical and Computer Engineering

Ben-Gurion University of the Negev

Israel

Homepage

Timor Melamed

Dr. Timor Melamed

Department of Electrical and Computer Engineering

Ben Gurion University of the Negev

ISRAEL

Homepage

, Vol. 36, 121-137, 2002

doi:10.2528/PIER02011001 | Google Scholar

Abstract

Macroscopic Maxwell's theory for electrodynamics is an indeterminate set of coupled, vector, partial differential equations. This infrastructure requires the supplement of constitutive equations. Recently a general framework has been suggested, taking into account dispersion, inhomogeneity and nonlinearity, in which the constitutive equations are posited as differential equations involving the differential operators based on the Volterra functional series. The validity of such representations needs to be examined. Here it is shown that for such representations to be effective, the spatiotemporal functions associated with the Volterra differential operators must be highly localized, or equivalently, widely extended in the transform space. This is achieved by exploiting Delta-function expansions, leading in a natural way to polynomial differential operators. The Four-vector Minkowski space is used throughout, facilitating general results and compact notation.

Download Full Article (182) View Full Article

Citation

Copy Export

Dan Censor, and Timor Melamed, "Volterra Differential Constitutive Operators and Locality Considerations in Electromagnetic Theory," , Vol. 36, 121-137, 2002.
doi:10.2528/PIER02011001

References

1. Censor, D., "Constitutive relations in inhomogeneous systems and the particle-field conundrum," Progress In Electromagnetics Research, J. A. Kong (Ed.), Vol. 30, 305-335, 2001. Google Scholar

2. Censor, D., "Application-oriented relativistic electrodynamics (2)," Progress In Electromagnetics Research, J. A. Kong (Ed.), Vol. 29, 107–168, 2000. Google Scholar

3. Censor, D., "A quest for systematic constitutive formulations for general field and wave systems based on the Volterra differential operators," Progress In Electromagnetics Research, J. A. Kong (Ed.), Vol. 25, 261–284, Elsevier, 2000. Abstract: Journal of Electromagnetic Waves and Applications, Vol. 14, 77–78, 2000. Google Scholar

4. Lindell, I. V., Methods for Electromagnetic Field Analysis, Oxford Science Publications, 1992.

5. Van Bladel, J., Singular Electromagnetic Fields and Sources, Clarendon Press, 1991.

6. Censor, D., "Quasi doppler effects associated with spatiotemporal translatory, moving, and active boundaries," Journal of Electromagnetic Waves and Applications, Vol. 13, 145-174, 1999.
doi:10.1163/156939399X00790 Google Scholar

7. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, 1989.

8. Von Hippel, A., Dielectric Materials and Their Applications, Artech House, 1994.

9. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media, Artech House, 1994.

10. Segev, T., "Locality and continuity in constitutive theory," Archive for Rational Mechanics and Analysis, Vol. 101, 29-39, 1988.
doi:10.1007/BF00281781 Google Scholar