Legendre Functions, Feynman's Disk Paradox, Electromagnetic angular momentum.
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| Title: | Legendre Functions, Feynman's Disk Paradox, Electromagnetic angular momentum. |
|---|---|
| Authors: | Khosravi, Sepand1 sepandkhosravi1@gmail.com |
| Source: | Latin-American Journal of Physics Education. Dec2025, Vol. 19 Issue 4, p1-4. 4p. |
| Subject Terms: | Lane-Emden equation, Stellar structure, Numerical solutions to equations, Equations of state, Astrophysics |
| Abstract (English): | We present numerical solutions of the Lane-Emden equation for selected polytropic indices using a fourth order Rnnge-Kutta integrator with series expansion initial conditions. The method is validated against the analytical cases n = 0 and n = 1, then applied to the astrophysically relevant indices n = 1.5 and n = 3. The computed first zeros are 𝜉1 ≈3.654 (n = 1.5) and 𝜉1 ≈6.897 (n = 3), and the resulting density profiles show that increasing n produces more extended, less centrally concentrated models. The n = 3 polytropic model yields a solar radius of the correct order of magnitude, showing that even a simplified pressure-density relation can capture the essential structural scaling of real stars like the Sun. [ABSTRACT FROM AUTHOR] |
| Abstract (Polish): | Presentamos soluciones numéricas de la ecuación de Lane-Emden para índices politrópicos seleccionados utilizando un integrador Rnnge-Kutta de cuarto orden con condiciones iniciales de expansión en serie. El método se valida frente a los casos analíticos n = 0 y n = 1, y posteriormente se aplica a los índices astrofísicamente relevantes n = 1,5 y n = 3. Los primeros ceros calculados son 𝜉1 ≈3,654 (n = 1,5) y 𝜉1 ≈6,897 (n = 3), y los perfiles de densidad resultantes muestran que al aumentar n se obtienen modelos más extendidos y con menor concentración central. El modelo politrópico n = 3 proporciona un radio solar del orden de magnitud correcto, lo que demuestra que incluso una relación presión-densidad simplificada puede capturar la escala estructural esencial de estrellas reales como el Sol. [ABSTRACT FROM AUTHOR] |
| Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 191649236 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Legendre Functions, Feynman's Disk Paradox, Electromagnetic angular momentum. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Khosravi%2C+Sepand%22">Khosravi, Sepand</searchLink><relatesTo>1</relatesTo><i> sepandkhosravi1@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Latin-American+Journal+of+Physics+Education%22">Latin-American Journal of Physics Education</searchLink>. Dec2025, Vol. 19 Issue 4, p1-4. 4p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Lane-Emden+equation%22">Lane-Emden equation</searchLink><br /><searchLink fieldCode="DE" term="%22Stellar+structure%22">Stellar structure</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+equations%22">Numerical solutions to equations</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+state%22">Equations of state</searchLink><br /><searchLink fieldCode="DE" term="%22Astrophysics%22">Astrophysics</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: We present numerical solutions of the Lane-Emden equation for selected polytropic indices using a fourth order Rnnge-Kutta integrator with series expansion initial conditions. The method is validated against the analytical cases n = 0 and n = 1, then applied to the astrophysically relevant indices n = 1.5 and n = 3. The computed first zeros are 𝜉1 ≈3.654 (n = 1.5) and 𝜉1 ≈6.897 (n = 3), and the resulting density profiles show that increasing n produces more extended, less centrally concentrated models. The n = 3 polytropic model yields a solar radius of the correct order of magnitude, showing that even a simplified pressure-density relation can capture the essential structural scaling of real stars like the Sun. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Polish) Group: Ab Data: Presentamos soluciones numéricas de la ecuación de Lane-Emden para índices politrópicos seleccionados utilizando un integrador Rnnge-Kutta de cuarto orden con condiciones iniciales de expansión en serie. El método se valida frente a los casos analíticos n = 0 y n = 1, y posteriormente se aplica a los índices astrofísicamente relevantes n = 1,5 y n = 3. Los primeros ceros calculados son 𝜉1 ≈3,654 (n = 1,5) y 𝜉1 ≈6,897 (n = 3), y los perfiles de densidad resultantes muestran que al aumentar n se obtienen modelos más extendidos y con menor concentración central. El modelo politrópico n = 3 proporciona un radio solar del orden de magnitud correcto, lo que demuestra que incluso una relación presión-densidad simplificada puede capturar la escala estructural esencial de estrellas reales como el Sol. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=191649236 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 4 StartPage: 1 Subjects: – SubjectFull: Lane-Emden equation Type: general – SubjectFull: Stellar structure Type: general – SubjectFull: Numerical solutions to equations Type: general – SubjectFull: Equations of state Type: general – SubjectFull: Astrophysics Type: general Titles: – TitleFull: Legendre Functions, Feynman's Disk Paradox, Electromagnetic angular momentum. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Khosravi, Sepand IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 18709095 Numbering: – Type: volume Value: 19 – Type: issue Value: 4 Titles: – TitleFull: Latin-American Journal of Physics Education Type: main |
| ResultId | 1 |
