• The Bulletin of The Korean Astronomical Society
• /
• v.38 no.2
• /
• pp.60.1-60.1
• /
• 2013

We study tidal disruption and subsequent mass fallback process for stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that the mass fallback rate decays with the expected -5/3 power of time for parabolic orbits, albeit with a slight deviation due to the self-gravity of the stellar debris. For eccentric orbits, however, there is a critical value of the orbital eccentricity, significantly below which all of the stellar debris is bound to the supermassive black hole. All the mass therefore falls back to the supermassive black hole in a much shorter time than in the standard, parabolic case. The resultant mass fallback rate considerably exceeds the Eddington accretion rate and substantially differs from the -5/3 power of time. We also show that general relativistic precession is crucial for accretion disk formation via circularization of stellar debris from stars on moderately eccentric orbits.

• East Asian mathematical journal
• /
• v.27 no.5
• /
• pp.521-525
• /
• 2011

We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.395-408
• /
• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.42 no.3
• /
• pp.270-278
• /
• 2014

This paper describes an improvement of space objects orbit prediction. To screen possible collisions between operational satellites and space objects, the TLE (Two-Line Element) was used as pseudo-measurement and than the orbit determination and orbit prediction were performed through the flight dynamics system. For determining the orbits, the state vectors were assumed by a series of TLEs within a certain period. The propagation error was analyzed according to the fitting period and a number of pseudo-observations. In order to find out the improvement of orbit prediction with the proposed method, KOMPSAT-2, 3 having the precise orbit in the meter-level range were first applied. Then the result applied to space objects under the same conditions was analyzed. As a result of the RMS error comparison with the orbit prediction of space object, the precision of orbit prediction was improved by approximately 90% for seven days prediction. The improved orbit prediction of space objects can be utilized in the daily analysis for initial screening of the close space objects at high risk.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.53-65
• /
• 2019

Recently, Chung and Lee [2] introduced the notion of topological stability for a finitely generated group action, and proved a group action version of the Walters's stability theorem. In this paper, we introduce the concepts of continuous shadowing and continuous inverse shadowing of a finitely generated group action on a compact metric space X with respect to various classes of admissible pseudo orbits and study the relationships between topological stability and continuous shadowing and continuous inverse shadowing property of group actions. Moreover, we introduce the notion of structural stability for a finitely generated group action, and we prove that an expansive action on a compact manifold is structurally stable if and only if it is continuous inverse shadowing.