Ter-Antonyan function (original) (raw)
The Ter-Antonyan function parameterizes the energy spectra of primary cosmic rays in the "knee" region ( eV) by the continuously differentiable function of energy taking into account the rate of change of spectral slope. The function is expressed as: Function can be re-written as: where and is the “knee” shaping function describing the change of the spectral slope. Examples of for are presented above. The rate of change of spectral slope from to with respect to energy is derived from as: , where , , and is the sharpness-independent spectral slope at the knee energy. , where
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| dbo:abstract | The Ter-Antonyan function parameterizes the energy spectra of primary cosmic rays in the "knee" region ( eV) by the continuously differentiable function of energy taking into account the rate of change of spectral slope. The function is expressed as: where is a scale factor, and are the asymptotic slopes of the function (orspectral slopes) in a logarithmic scale at and respectively for a given energy (the so-called "knee" energy). The rate of change of spectral slopes is set in function by the "sharpness of knee" parameter, . Function was proposed in ANI'98 Workshop (1998) by Samvel Ter-Antonyan for both the interpolation of primary energy spectra in the energy range 1—100 PeV and the search of parametrized solutions of inverse problem to reconstruct primary cosmic ray energy spectra. Function is also used for the interpolation of observed Extensive Air Shower spectra in the knee region. Function can be re-written as: where and is the “knee” shaping function describing the change of the spectral slope. Examples of for are presented above. The rate of change of spectral slope from to with respect to energy is derived from as: , where , , and is the sharpness-independent spectral slope at the knee energy. Function coincides with B. Petersspectra for andasymptotically approaches the broken power law of cosmic ray energy spectra for : , where (en) |
| dbo:thumbnail | wiki-commons:Special:FilePath/Knee_shaping_function.png?width=300 |
| dbo:wikiPageID | 62672363 (xsd:integer) |
| dbo:wikiPageLength | 3918 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1103095636 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Power_law dbr:Interpolation dbr:Inverse_problem dbr:Cosmic_ray dbr:Spectral_slope dbr:Logarithmic_scale dbr:Slope dbr:Parametric_equation dbr:Spectrum dbr:Air_shower_(physics) dbc:Cosmic_rays dbr:Asymptotic_analysis dbr:Rate_(mathematics) dbr:Scale_factor dbr:File:Knee_shaping_function.png |
| dbp:wikiPageUsesTemplate | dbt:NumBlk dbt:Orphan dbt:Reflist dbt:EquationRef dbt:EquationNote |
| dct:subject | dbc:Cosmic_rays |
| rdfs:comment | The Ter-Antonyan function parameterizes the energy spectra of primary cosmic rays in the "knee" region ( eV) by the continuously differentiable function of energy taking into account the rate of change of spectral slope. The function is expressed as: Function can be re-written as: where and is the “knee” shaping function describing the change of the spectral slope. Examples of for are presented above. The rate of change of spectral slope from to with respect to energy is derived from as: , where , , and is the sharpness-independent spectral slope at the knee energy. , where (en) |
| rdfs:label | Ter-Antonyan function (en) |
| owl:sameAs | wikidata:Ter-Antonyan function https://global.dbpedia.org/id/BvxgZ |
| prov:wasDerivedFrom | wikipedia-en:Ter-Antonyan_function?oldid=1103095636&ns=0 |
| foaf:depiction | wiki-commons:Special:FilePath/Knee_shaping_function.png |
| foaf:isPrimaryTopicOf | wikipedia-en:Ter-Antonyan_function |
| is foaf:primaryTopic of | wikipedia-en:Ter-Antonyan_function |
