Journey to the cosmos: Navigating stellar evolution with differential equations
Abstract
Differential equations are a fundamental and versatile mathematical tool that finds widespread application across diverse academic disciplines, from physics and biology to economics and engineering. The primary objectives of this report are to demonstrate the application of differential equations in stellar evolution, construct a mathematical model to demonstrate nuclear reactions in a star, and illustrate energy transport within a star. Triangulation was used to prepare this report, with literature studies being the primary method. This study includes several documents and field data analyzed using qualitative research. Through research and observations, two hypothetical case studies illustrate the indispensable application of differential equations in modeling energy transport and nuclear reactions within stars through which the value of luminosity was calculated in a particular star due to both radiative energy transport and convective energy transport while in another star, the helium abundance in the core was estimated to approach a value of 1.195*1077. These differential equations are not only limited to the growth of a lead but also have broader applications that are essential for understanding the chemical composition of the universe and its prolonged evolution. The report also underscores the enduring importance of differential equations in advancing our understanding of the cosmos and their vital role in space exploration and technological innovations.
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References
Abbas, F., Kitanov, P., & Longo, S. (2019). Approximate solutions to lane-emden equation for stellar configuration. Appl. Math. Inf. Sci, 13(2), 143–152. https://doi.org/10.18576/amis/130201
Adelberger, E. G., García, A., Robertson, R. G. H., Snover, K. A., Balantekin, A. B., Heeger, K., Ramsey-Musolf, M. J., Bemmerer, D., Junghans, A., & Bertulani, C. A. (2011). Solar fusion cross sections. II. The p p chain and CNO cycles. Reviews of Modern Physics, 83(1), 195–245. https://doi.org/10.1103/RevModPhys.83.195
Alhassid, Y. (2021). Nuclear level densities: From empirical models to microscopic methods. Compound-Nuclear Reactions: Proceedings of the 6th International Workshop on Compound-Nuclear Reactions and Related Topics CNR* 18, 97–112. https://doi.org/10.1007/978-3-030-58082-7_12
Altshuler, B. L. (2021). Andrei Sakharov's research work and modern physics. Physics-Uspekhi, 64(5), 427. https://doi.org/10.3367/UFNe.2021.02.038946
Amarsi, A. M., Grevesse, N., Asplund, M., & Collet, R. (2021). The solar carbon, nitrogen, and oxygen abundances from a 3D LTE analysis of molecular lines. Astronomy & Astrophysics, 656, A113. https://doi.org/10.1051/0004-6361/202141384
Arnett, W. D., Meakin, C., Viallet, M., Campbell, S. W., Lattanzio, J. C., & Mocak, M. (2015). Beyond mixing-length theory: a step toward 321D. The Astrophysical Journal, 809(1), 30. https://doi.org/10.1088/0004-637X/809/1/30
Augustson, K. C., Brown, B. P., Brun, A. S., Miesch, M. S., & Toomre, J. (2012). Convection and differential rotation in F-type stars. The Astrophysical Journal, 756(2), 1–23. https://doi.org/10.1088/0004-637X/756/2/169
Baskarada, S. (2014). Qualitative case study guidelines. Baškarada, S.(2014). Qualitative Case Studies Guidelines. The Qualitative Report, 19(40), 1–25. https://ssrn.com/abstract=2559424
Bogopane, L. P. (2013). A critical review of pertinent qualitative research processes, approaches, and tools in social sciences. Journal of Social Sciences, 35(3), 217–229. https://doi.org/10.1080/09718923.2013.11893161
Clarkson, O., & Herwig, F. (2021). Convective H–He interactions in massive population III stellar evolution models. Monthly Notices of the Royal Astronomical Society, 500(2), 2685–2703. https://doi.org/10.1093/mnras/staa3328
Cruz, R. F., & Tantia, J. F. (2017). Reading and understanding qualitative research. American Journal of Dance Therapy, 39, 79–92. https://doi.org/10.1007/s10465-016-9219-z
Dale, J. E. (2015). The modeling of feedback in star formation simulations. New Astronomy Reviews, 68(10), 1–33. https://doi.org/10.1016/j.newar.2015.06.001
Doebling, A., & Kazerouni, A. M. (2021). Patterns of academic help-seeking in undergraduate computing students. Proceedings of the 21st Koli Calling International Conference on Computing Education Research, 1–10. https://doi.org/10.1145/3488042.3488052
Ernst, R. E., Bond, D. P. G., Zhang, S., Buchan, K. L., Grasby, S. E., Youbi, N., El Bilali, H., Bekker, A., & Doucet, L. S. (2021). Large igneous province record through time and implications for secular environmental changes and geological timescale boundaries. Large Igneous Provinces: A Driver of Global Environmental and Biotic Changes, 1–26. https://doi.org/10.1002/9781119507444.ch1
Feiden, G. A., & Chaboyer, B. (2013). Magnetic inhibition of convection and the fundamental properties of low-mass stars. I. Stars with a radiative core. The Astrophysical Journal, 779(2), 1–25. https://doi.org/10.1088/0004-637X/779/2/183
Harrison, H., Birks, M., Franklin, R., & Mills, J. (2017). Case study research: Foundations and methodological orientations. Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 18(1), 1–17. https://doi.org/10.17169/fqs-18.1.2655
Hauck, C., & Heningburg, V. (2019). Filtered discrete ordinates equations for radiative transport. Journal of Scientific Computing, 80(1), 614–648. https://doi.org/10.1007/s10915-019-00950-1
Hodson, D., & Wong, S. L. (2014). From the Horse's Mouth: Why scientists' views are crucial to nature of science understanding. International Journal of Science Education, 36(16), 2639–2665. https://doi.org/10.1080/09500693.2014.927936
Hou, M.-F., Wu, C.-Y., & Hong, Y.-B. (2015). A closed-form solution of differential approximation for radiative transfer in a planar refractive medium. International Journal of Heat and Mass Transfer, 83(1), 229–234. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.004
Jermyn, A. S., Chitre, S. M., Lesaffre, P., & Tout, C. A. (2020). Convective differential rotation in stars and planets–I. Theory. Monthly Notices of the Royal Astronomical Society, 498(3), 3758–3781. https://doi.org/10.1093/mnras/staa2323
Johnson, H. L. (2012). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. The Journal of Mathematical Behavior, 31(3), 313–330. https://doi.org/10.1016/j.jmathb.2012.01.001
Kaltenborn, M. A. R. (2023). Smoothed-Particle Hydrodynamic Simulations of Compact Mergers, Mass Transfer, and Accretion Disk Formation. The George Washington University.
Kippenhahn, R., Weigert, A., & Weiss, A. (2012). Stellar structure and evolution (Vol. 192). Springer. https://doi.org/10.1007/978-3-642-30304-3
Mohajan, H. K. (2018). Qualitative research methodology in social sciences and related subjects. Journal of Economic Development, Environment, and People, 7(1), 23–48. https://www.ceeol.com/search/article-detail?id=640546
Pasetto, S., Chiosi, C., Chiosi, E., Cropper, M., & Weiss, A. (2016). Theory of stellar convection–II. First stellar models. Monthly Notices of the Royal Astronomical Society, 459(3), 3182–3202. https://doi.org/10.1093/mnras/stw858
Penprase, B. E., & Penprase, B. E. (2017). The development of modern cosmology. The Power of Stars, 283–331. https://doi.org/10.1007/978-3-319-52597-6_9
Potekhin, A. Y. (2014). Atmospheres and radiating surfaces of neutron stars. Physics-Uspekhi, 57(8), 1–43. https://doi.org/10.3367/UFNe.0184.201408a.0793
Roychoudhuri, C. (2011). Appreciation of the nature of light demands enhancement over the prevailing scientific epistemology. The Nature of Light: What Are Photons? IV, 8121, 621–637. https://doi.org/10.1117/12.895123
Steinacker, J., Baes, M., & Gordon, K. D. (2013). Three-dimensional dust radiative transfer. Annual Review of Astronomy and Astrophysics, 51, 63–104. https://www.annualreviews.org/doi/abs/10.1146/annurev-astro-082812-141042
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