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jovian Problem: Performance of Some High-Order Numerical Integrators

American Journal of Computational Mathematics 2013年第3期3卷 195-204页

作者： Shafiq Ur Rehman Department of Mathematics The University of Auckland Auckland New Zealand 2Department of Mathematics University of Engineering and Technology Lahore Pakistan

N-body simulations of the Sun, the planets, and small celestial bodies are frequently used to model the evolution of the Solar System. Large numbers of numerical integrators for performing such simulations have been developed and used;see, for example, [1,2]. The primary objective of this paper is to analyse and compare the efficiency and the error growth for different numerical integrators. Throughout the paper, the error growth is examined in terms of the global errors in the positions and velocities, and the relative errors in the energy and angular momentum of the system. We performed numerical experiments for the different integrators applied to the jovian problem over a long interval of duration, as long as one million years, with the local error tolerance ranging from 10-16 to 10-18.

关键词： N-Body Simulations jovian Problem Numerical Integrators CPU-Time

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Radiation belt electron scattering by whistler-mode chorus in the jovian magnetosphere: Importance of ambient and wave parameters

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Earth and Planetary Physics 2018年第1期2卷 1-14页

作者： BinBin Ni Jing Huang YaSong Ge Jun Cui Yong Wei XuDong Gu Song Fu Zheng Xiang ZhengYu Zhao Department of Space Physics School of Electronic Information Wuhan University Lunar and Planetary Science Laboratory Macao University of Science and Technology-Partner Laboratory of Key Laboratory of Lunar and Deep Space Exploration Chinese Academy of Sciences Key Laboratory of Earth and Planetary Physics Institute of Geology and Geophysics Chinese Academy of Sciences School of Atmospheric Sciences Sun Yat-Sen University

Whistler-mode chorus waves are regarded as an important acceleration mechanism contributing to the formation of relativistic and ultra-relativistic electrons in the jovian radiation belts. Quantitative determination of the chorus wave driven electron scattering effect in the jovian magnetosphere requires detailed information of both ambient magnetic field and plasma density and wave spectral property, which however cannot be always readily acquired from observations of existed missions to Jupiter. We therefore perform a comprehensive analysis of the sensitivity of chorus induced electron scattering rates to ambient magnetospheric and wave parameters in the jovian radiation belts to elaborate to which extent the diffusion coefficients depend on a number of key input parameters. It is found that quasi-linear electron scattering rates by chorus can be strongly affected by the ambient magnetic field intensity, the wave latitudinal coverage, and the peak frequency and bandwidth of the wave spectral distribution in the jovian magnetosphere, while they only rely slightly on the background plasma density profile and the peak wave normal angle, especially when the wave emissions are confined at lower latitudes. Given the chorus wave amplitude, chorus induced electron scattering rates strongly depend on jovian L-shell to exhibit a tendency approximately proportional to L_J^3. Our comprehensive analysis explicitly demonstrates the importance of reliable information of both the ambient magnetospheric state and wave distribution property to understanding the dynamic electron evolution in the jovian radiation belts and therefore has implications for future mission planning to explore the extreme particle radiation environment of Jupiter and its satellites.

关键词： jovian radiation belts whistler-mode chorus resonant wave-particle interactions magnetospheric state

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Gravitationally Quantized Orbits in the Solar System: Computations Based on the Global Polytropic Model

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International Journal of Astronomy and Astrophysics 2014年第3期4卷 464-473页

作者： Vassilis Geroyannis Florendia Valvi Themis Dallas Department of History Archaeology and Social Anthropology University of Thessaly Volos Greece Department of Mathematics University of Patras Patras Greece Department of Physics University of Patras Patras Greece

The so-called “global polytropic model” is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet’s system of statellites (like the jovian system), described by the Lane-Emden differential equation. A polytropic sphere of polytropic index?n?and radius?R1?represents the central component?S1?(Sun or planet) of a polytropic configuration with further components the polytropic spherical shells?S2,?S3,?..., defined by the pairs of radi (R1,?R2), (R2,?R3),?..., respectively.?R1,?R2,?R3,?..., are the roots of the real part Re(θ) of the complex Lane-Emden function?θ. Each polytropic shell is assumed to be an appropriate place for a planet, or a planet’s satellite, to be “born” and “live”. This scenario has been studied numerically for the cases of the solar and the jovian systems. In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code DCRKF54 (modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane along complex paths). We include in our numerical study some trans-Neptunian objects.

关键词： Complex-Plane Strategy Global Polytropic Model jovian System Quantized Orbits Solar System Trans-Neptunian Objects

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