Sommerfeld radiation condition

E234762

The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.

All labels observed (1)

Label Occurrences
Sommerfeld radiation condition canonical 2

How this entity was disambiguated

Statements (51)

Predicate Object
instanceOf boundary condition ⓘ
concept in scattering theory ⓘ
concept in wave theory ⓘ
mathematical condition ⓘ
radiation condition ⓘ
appliesTo Helmholtz equation ⓘ
acoustic waves ⓘ
electromagnetic waves ⓘ
scalar wave equation in frequency domain ⓘ
scattering problems ⓘ
time-harmonic wave fields ⓘ
assumes time dependence e^{-iωt} ⓘ
characterizes outgoing waves at infinity ⓘ
contrastsWith Dirichlet boundary condition at finite distance ⓘ
Neumann boundary condition at finite distance ⓘ
incoming radiation condition ⓘ
periodic boundary conditions ⓘ
domain mathematical physics ⓘ
partial differential equations ⓘ
scattering theory ⓘ
wave propagation ⓘ
ensures causal radiation behavior in frequency domain ⓘ
finite energy flux at infinity ⓘ
uniqueness of the scattered field ⓘ
generalizationOf radiation conditions for other elliptic operators ⓘ
hasConsequence existence of far-field pattern ⓘ
representation of solutions via asymptotic expansions ⓘ
well-posedness of exterior scattering problems ⓘ
imposes asymptotic behavior on wave fields ⓘ
mathematicalForm lim_{r→∞} r(∂u/∂r - iku) = 0 in three dimensions ⓘ
lim_{r→∞} r^{(d-1)/2}(∂u/∂r - iku) = 0 for d-dimensional space ⓘ
namedAfter Arnold Sommerfeld ⓘ
purpose to enforce outward-radiating behavior at infinity ⓘ
to ensure uniqueness of solutions to exterior boundary value problems ⓘ
to exclude incoming waves from infinity ⓘ
to select physically meaningful solutions of the Helmholtz equation ⓘ
relatedTo Lippmann–Schwinger equation ⓘ
limiting absorption principle ⓘ
outgoing Green's function of the Helmholtz operator ⓘ
relatesTo far-field behavior of solutions ⓘ
radiation of energy to infinity ⓘ
timePeriod early 20th century ⓘ
usedBy applied mathematicians ⓘ
engineers ⓘ
physicists ⓘ
usedIn acoustic scattering by obstacles ⓘ
antenna theory ⓘ
electromagnetic scattering by conductors ⓘ
exterior Dirichlet problems ⓘ
exterior Neumann problems ⓘ
seismology wave propagation models ⓘ

How these facts were elicited

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Arnold Sommerfeld → knownFor → Sommerfeld radiation condition ⓘ
Rayleigh–Sommerfeld diffraction theory → satisfies → Sommerfeld radiation condition ⓘ