• 천문학회보
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• 제38권2호
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• pp.60.1-60.1
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• 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
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• 제27권5호
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• pp.521-525
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• 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].

• 대한수학회지
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• 제61권2호
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• pp.395-408
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• 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.

• 한국항공우주학회지
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• 제42권3호
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• pp.270-278
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• 2014

본 논문에서는 우주물체 궤도예측의 개선 방안에 관하여 기술하였다. 운용위성과 우주물체와의 근접 가능성 여부를 확인하기 위해 이용되는 TLE(Two-Line Element)를 가관측으로 사용하였고, 비행역학시스템을 통해 궤도결정 및 예측을 수행하였다. 궤도를 결정함에 있어 일정기간 내 일련의 TLE를 이용하여 상태벡터를 가정하였고, 결정기간 및 가관측수(pseudo-observations)에 따른 예측결과 오차를 분석하였다. 또한, 제안된 방식을 적용할 경우 궤도예측 정밀도가 향상 되는지를 알아보기 위해 수 미터 수준의 정밀궤도 확인이 가능한 아리랑위성 2, 3호를 대상으로 먼저 적용하였으며, 동일한 조건으로 우주물체에 적용한 결과를 분석하였다. 우주물체 궤도예측의 RMS 오차 비교 결과, 7일 전파기준으로 궤도 예측 정밀도를 약 90% 향상시킬 수 있었다. 우주물체의 개선된 궤도예측은 매일 수행되는 충돌가능성 분석에 이용되어 위험성이 높은 근접 우주물체의 1차적인 선별에 활용가능 할 것이다.

• 대한수학회지
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• 제56권1호
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• pp.53-65
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• 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.