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Related Experiment Videos

Nonradiating sources with connections to the adjoint problem.

Edwin A Marengo1, Anthony J Devaney

  • 1Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
Summary

Localized nonradiating (NR) sources are described for any linear partial differential equation (PDE). A key finding is that NR sources must satisfy specific orthogonality conditions with solutions of the adjoint PDE.

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Area of Science:

  • Mathematical Physics
  • Electromagnetics
  • Wave Theory

Background:

  • Nonradiating (NR) sources generate fields confined to their support.
  • Existing descriptions of NR sources are often limited to specific PDEs, such as those in wave theory.

Purpose of the Study:

  • To develop a general description of localized nonradiating sources applicable to any linear partial differential equation (PDE).
  • To establish necessary and sufficient conditions for a source to be nonradiating.

Main Methods:

  • Derivation of the description in the context of both the governing PDE and its corresponding adjoint PDE.
  • Analysis of formally self-adjoint and non-self-adjoint linear partial differential operators (PDOs).

Main Results:

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  • A general condition for NR sources is established: they must satisfy an orthogonality relation with solutions of the homogeneous adjoint PDE within the source's support.
  • For real linear PDOs, a more relaxed condition includes an additional orthogonality relation with solutions of the homogeneous governing PDE.

Conclusions:

  • The developed framework provides a unified description of nonradiating sources across various linear PDEs.
  • The orthogonality conditions offer a fundamental criterion for identifying and characterizing nonradiating sources.