• Title, Summary, Keyword: separatrix

Search Result 5, Processing Time 0.032 seconds

THE MEASURE OF THE UNIFORMLY HYPERBOLIC INVARIANT SET OF EXACT SEPARATRIX MAP

  • Kim, Gwang-Il;Chi, Dong-Pyo
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.3
    • /
    • pp.779-788
    • /
    • 1997
  • In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.

  • PDF

ELLIPTIC BIRKHOFF'S BILLIARDS WITH $C^2$-GENERIC GLOBAL PERTURBATIONS

  • Kim, Gwang-Il
    • Bulletin of the Korean Mathematical Society
    • /
    • v.36 no.1
    • /
    • pp.147-159
    • /
    • 1999
  • Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

  • PDF

KSTAR ICRF 가열장치의 고주파 부하저항 증가를 위한 gaspuffing

  • An, Chan-Yong;Kim, Chang-Bae;Kim, Seon-Ho;Wang, Seon-Jeong;Gwak, Jong-Gu;Kim, Seong-Gyu
    • Proceedings of the Korean Vacuum Society Conference
    • /
    • /
    • pp.135-135
    • /
    • 2010
  • Kstar (Korea Superconducting Tokamak Advanced Research, 국가핵융합연구장치) ICRF(Ion Cyclotron Range of Frequency) 가열장치를 이용한 이온가열을 추가 gas puffing 과 함께 수행할 예정이다. 안테나와 separatrix사이 간격이 좁혀질수록 안테나의 고주파 부하저항은 올라가는 것으로 알려져 있지만, 안테나에서의 sputtering을 통한 불순물 증가의 원인이 될 수 있으며, 이는 전체 플라즈마 에너지의 손실을 초래할 수 있다. 이를 보완하기 위해 고주파 입사시 플라즈마 외곽, 안테나 전면에 추가적인 연료 가스를 공급하게 되면, 안테나 주위의 플라즈마는 냉각되어 sputtering에 의한 불순물 방출을 줄일 수 있고, 안테나 전면의 플라즈마 밀도는 증가될 것이다. 이를 통한 고주파 부하저항의 증가에 의하여 동일한 고주파 최고전압의 한계 내에서 기존보다 더 큰 출력을 플라즈마에 전달할 수 있을 것이다. 본 발표에서는 단순한 외곽 플라즈마 모델에서의 고속파 전파에 따른 고주파 부하저항의 거동을 살펴봄으로써 예상할 수 있는 추가 gas puffing 효과와 출력 증대량을 설명하고, 구체적인 실험 방법을 토론하도록 하겠다.

  • PDF

An Analytical Approximation for the Pull-Out Frequency of a PLL Employing a Sinusoidal Phase Detector

  • Huque, Abu-Sayeed;Stensby, John
    • ETRI Journal
    • /
    • v.35 no.2
    • /
    • pp.218-225
    • /
    • 2013
  • The pull-out frequency of a second-order phase lock loop (PLL) is an important parameter that quantifies the loop's ability to stay frequency locked under abrupt changes in the reference input frequency. In most cases, this must be determined numerically or approximated using asymptotic techniques, both of which require special knowledge, skills, and tools. An approximating formula is derived analytically for computing the pull-out frequency for a second-order Type II PLL that employs a sinusoidal characteristic phase detector. The pull-out frequency of such PLLs can be easily approximated to satisfactory accuracy with this formula using a modern scientific calculator.

s on the Arrangement of Electrodes in Non-Uniform Magnetic Fields (비균일자장들 속에서 전극배치에 따른 저기압 방전 특성)

  • ;Ryohei Itatane
    • The Transactions of the Korean Institute of Electrical Engineers
    • /
    • v.37 no.1
    • /
    • pp.63-68
    • /
    • 1988
  • The V-I characteristics of low pressure discharges occurring between each of three kinds of anode and a fixed hot cathode in several bi-cusp magnetic fields are investigated. The results are different from those in non-magnetic fields as follows` First, both breakdown and maintaining potentials of low pressure discharges in the fields are rather depend on the arrangement of the directions of magnetic lines of force and the directions between two electrodes than on the distance between two electrodes or the size of the electrodes. Second, the maintaining potentials of the discharges in the fields are lower than those in the non-fields, and the electrical conductivity in the fields are better than those in the non-fields. Third, the breakdown potertials in the fields when the direction of magnetic lines of force is perpendicular with the direction of discharging path between two electrodes are higher than those when the two directions are parallel with each other. But the maintaining patentials in the fields are shown the contrary phenomena with before. This results are particularily conspicuous as the separatrix of the fields pass across the discharging path between two electrodes.

  • PDF