Schwarzschild–Milne equations

E46433
integro-differential equations radiative transfer equations

The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.

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Observed surface forms (3)

Surface form Occurrences
Eddington approximation 1
Milne problem in radiative transfer 1
Schwarzschild equation in radiative transfer 1

Statements (46)

Predicate Object
instanceOf integro-differential equations ⓘ
radiative transfer equations ⓘ
appliesTo absorbing media ⓘ
emitting media ⓘ
plane-parallel media ⓘ
scattering media ⓘ
assumes one-dimensional variation with optical depth ⓘ
radiative transfer in local thermodynamic equilibrium in some formulations ⓘ
assumesGeometry plane-parallel slab ⓘ
context theory of stellar atmospheres ⓘ
transfer of monochromatic radiation ⓘ
dependsOn absorption coefficient ⓘ
emission coefficient ⓘ
scattering coefficient ⓘ
describes propagation of radiation in a medium ⓘ
scattering of radiation in a medium ⓘ
field radiative transfer theory ⓘ
hasForm coupled integro-differential equations for intensity and source function ⓘ
includes boundary conditions at slab surfaces ⓘ
integral over angles ⓘ
integral over optical depth ⓘ
scattering kernel ⓘ
mathematicalDomain applied mathematics ⓘ
mathematical physics ⓘ
namedAfter Edward Arthur Milne ⓘ
Karl Schwarzschild ⓘ
relatedTo Schwarzschild–Milne equations self-linksurface differs ⓘ
surface form: Milne problem in radiative transfer

Schwarzschild–Milne equations self-linksurface differs ⓘ
surface form: Schwarzschild equation in radiative transfer

radiative transfer equation ⓘ
relatesQuantity optical depth ⓘ
radiative flux ⓘ
scattering albedo ⓘ
source function ⓘ
specific intensity of radiation ⓘ
solutionMethods Feautrier method ⓘ
discrete ordinates methods ⓘ
numerical integration ⓘ
variational methods ⓘ
usedFor computing emergent intensity from a slab ⓘ
computing reflection and transmission of radiation ⓘ
determining source function in scattering atmospheres ⓘ
modeling multiple scattering ⓘ
usedIn astrophysics ⓘ
atmospheric radiative transfer ⓘ
optical physics ⓘ
stellar atmosphere modeling ⓘ

Referenced by (4)

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

Arthur Stanley Eddington → knownFor → Schwarzschild–Milne equations ⓘ
this entity surface form: Eddington approximation
Radiative Transfer → relatedConcept → Schwarzschild–Milne equations ⓘ
Schwarzschild–Milne equations → relatedTo → Schwarzschild–Milne equations self-linksurface differs ⓘ
this entity surface form: Milne problem in radiative transfer
Schwarzschild–Milne equations → relatedTo → Schwarzschild–Milne equations self-linksurface differs ⓘ
this entity surface form: Schwarzschild equation in radiative transfer