التفاصيل البيبلوغرافية
| العنوان: |
A uniform spherical goat (problem): explicit solution for homologous collapse's radial evolution in time. |
| المؤلفون: |
Slepian, Zachary, Philcox, Oliver H E |
| المصدر: |
Monthly Notices of the Royal Astronomical Society: Letters; Jun2023, Vol. 522 Issue 1, pL42-L45, 4p |
| مصطلحات موضوعية: |
KEPLER'S equation, LARGE scale structure (Astronomy), NUMERICAL grid generation (Numerical analysis), DIFFERENTIAL equations, FAST Fourier transforms |
| مستخلص: |
The homologous collapse from rest of a uniform density sphere under its self gravity is a well-known toy model for the formation dynamics of astronomical objects ranging from stars to galaxies. Equally well-known is that the evolution of the radius with time cannot be explicitly obtained because of the transcendental nature of the differential equation solution. Rather, both radius and time are written parametrically in terms of the development angle θ. We here present an explicit integral solution for radius as a function of time, exploiting methods from complex analysis recently applied to the mathematically similar 'geometric goat problem.' Our solution can be efficiently evaluated using a Fast Fourier Transform and allows for arbitrary sampling in time, with a simple python implementation that is $\sim \, 100\times$ faster than using numerical root-finding to achieve arbitrary sampling. Our explicit solution is advantageous relative to the usual approach of first generating a uniform grid in θ, since this latter results in a non-uniform radial or time sampling, less useful for applications such as generation of sub-grid physics models. This solution is also of interest because it is the e = 1 case of Kepler's equation. Our subsequent work extends the method here to produce a general one for solving Kepler's equation, which turns out to be faster than any other currently extant. [ABSTRACT FROM AUTHOR] |
|
Copyright of Monthly Notices of the Royal Astronomical Society: Letters is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. 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.) |
| قاعدة البيانات: |
Complementary Index |