596 research outputs found
Nonradiating sources of Maxwell's equations
This paper presents a thorough investigation into nonradiating sources of
Maxwell's equations. Various characterizations are developed to clarify the
properties of nonradiating sources, considering their varying degrees of
regularity. Furthermore, the characterizations are examined on far-field
patterns and near-field data of the electric field, along with the null spaces
of integral operators. The study includes the explicit construction of several
illustrative examples to demonstrate the presence of nonradiating sources in
different null spaces
Nonradiating sources of the biharmonic wave equation
This paper offers an extensive exploration of nonradiating sources for the
two- and three-dimensional biharmonic wave equations. Various equivalent
characterizations are derived to reveal the nature of a nonradiating source.
Additionally, we establish the connection between nonradiating sources in the
biharmonic wave equation and those in the Helmholtz equation as well as the
modified Helmholtz equation. Several illustrative examples are explicitly
constructed to showcase the existence of nonradiating sources. One significant
implication of the existence of nonradiating sources is that it undermines the
uniqueness of the inverse source problem when utilizing boundary data at a
fixed frequency
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