• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권2호
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• pp.139-155
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• 2019

In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

• 한국항공우주학회지
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• 제30권3호
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• pp.27-36
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• 2002

AUSM계열 수치기법의 수치적 불안정성에 대한 원인과 해결방안에 대한 연구를 수행하였다. Euler 유동에서 수치적 불안정성은 제어면에 수직한 방향의 유동속도가 영인 영역에서 발생하며 이 영역에서 Eule r 방정식은 근본적으로 부정해를 가지게 되어 무수히 많은 해를 가지게 된다. 지배방정식 자체로는 유일해를 찾는 것이 불가능하고 주위의 유동조건이나 외부교란에 의해 유일해를 결정하게 된다. 이러한 특징은 충격파 영역에서 교란이 존재할 경우 초기 상태에 대한 정보를 상실하게 되어 충격파 불안정성을 유발하게 된다. slip유동을 정확히 계산할 수 있는, 즉 유일해를 결정할 수 없는, 수치기법은 충격파 불안정성을 근본적으로 제거할 수 없다.

• 천문학회보
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• 제37권1호
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• pp.93.1-93.1
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• 2012

In this study, we investigated the generation of consecutive electrostatic solitary waves (ESWs) using by one-dimensional electrostatic particle-in-cell (PIC) simulation. For a given Gaussian perturbation, it is found that electron two-stream instability occurs in local grids region. Thus because of this instability, the electrostatic potential grows rapidly so as to be separated into electron and ion in perturbation region, and then electrons are trapped with heating during growing instability. It is found that these heated and trapped electrons are caused the generation of ESW, and ions are reflected backward and forward at the boundary of the initial perturbation, then form cold ion beam whereas electrons are confined to inside of the potential. Furthermore backward reflected ion beam forms ion holes by ion two-stream instability. On the other hand, as the confined electrons are released, and then released electrons also form hot electron beam, which play an important role in the generation of consecutive ESWs such as broadband electrostatic noise (BEN) observed frequently in space environment. Therefore the reason of the generation of consecutive ESWs is the existence of heated electrons which can sufficiently support energy to produce ESWs.

• KIEE International Transactions on Power Engineering
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• 제5A권2호
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• pp.132-137
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• 2005

In Korea, the protection systems against the instability of the nation's power system are insufficient in contrast with many other countries. In addition, there have just been studies carried out on detecting power system instability, while only a few studies pertaining to protection plans against instability exist. This paper focuses on systems to protect against the instability phenomena in the Korean power system. In this paper, we survey possible contingencies in the Korean power system and suggest outline and specs of the SPS (System Protection Scheme) against faults on the 765 kV line, based on simulations. It is concluded that event-based SPS for transient stability is appropriate for the Korean power system. In the simulations, the most severe contingency on the Korean power system is the fault on 765 kV transmission lines. If one of these lines is tripped by a fault, synchronism may be lost on the power plants near this line because of heavy power flow carried by them. In addition, undervoltage in the Metropolitan region is a serious problem in this case since this region receives about half its total power flow through these lines. In order to prevent a synchronism loss, some power plants have to be rejected according to the situations in the simulations.

• Nuclear Engineering and Technology
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• 제41권6호
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• pp.841-848
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• 2009

A simple model to analyze non-linear density-wave instability in a sodium-cooled helically coiled steam generator is developed. The model is formulated with three regions with moving boundaries. The homogeneous equilibrium flow model is used for the two-phase region and the shell-side energy conservation is also considered for the heat flux variation in each region. The proposed model is applied to the analysis of two-phase instability in a JAEA (Japan Atomic Energy Agency) 50MWt No.2 steam generator. The steady state results show that the proposed model accurately predicts the six cases of operating temperatures on the primary and secondary sides. The sizes of three regions, the secondary side pressure drop according to the flow rate, and the temperature variation in the vertical direction are also predicted well. The temporal variations of the inlet flow rate according to the throttling coefficient, the boiling and superheating boundaries and the pressure drop in the two-phase and superheating regions are obtained from the unsteady analysis.

• Steel and Composite Structures
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• 제51권4호
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• pp.457-471
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• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• 한국분무공학회지
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• 제3권3호
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• pp.1-13
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• 1998

In this study, an experimental study was performed to investigate the breakup mechanism of vaporizing droplet. A well-controlled experimental apparatus was used to study breakup mechanisms of a monodisperse stream of drops injected into a transverse high temperature and velocity air stream. The experiments gave information$ about the microscopic structure of the liquid drop breakup process, drop breakup regimes, and drop trajectories in high temperature flow region. The breakup time, drop acceleration and wavelength of surface instability wave were measured from a high-magnification and double spark photography. The two instability theories, i.e., Kelvin-Helmholtz instability and Rayleigh-Taylor instability, were estimated by comparing the calculated data with the measurements. The results showed that the breakup time in high temperature flow condition is shortened because the surface tension is decreased by the increase of gas temperature.

• Structural Engineering and Mechanics
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• 제20권4호
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• pp.435-450
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• 2005

Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2006년도 제26회 춘계학술대회논문집
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• pp.135-140
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• 2006

충돌형(FOOF) 분사기의 불안정 영역을 결정하기 위해 질소분사 음향시험을 수행하였다. 파이프와 오리피스 형상을 가지는 분사기 내 산화제 부분에서 유동속도에 비례하고, 비정상적으로 jumping하는 특정 주파수를 가지는 whistling이 발생한다. 동일한 조건의 연소시험과 비교해 본 결과 whistling 현상은 연소현상에는 영향을 주지 않는다. 질소분사 음향시험과 연소시험에서 얻은 연소실 내 1T1L mode의 damping factor를 비교하여 불안정 영역을 구해보면, 비슷한 조건에서 불안정 영역을 가진다. 이것은 유동의 충돌, 혼합에 의한 유동불안정 현상이 연소시험에서 연소불안정을 발생시키는 주요한 인자임을 의미 한다.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2011년도 제37회 추계학술대회논문집
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• pp.187-199
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• 2011

본 연구는 희박 예혼합 연소기에서 연소실과 연료-공기 혼합부의 공진모드의 관계가 연소불안정에 어떤 영향을 미치고 있는지에 대하여 실험적으로 확인한 연구이다. 다체널 동압측정을 통하여 각각 위치에서 동압의 모드와 각 센서들간의 phase를 분석하여 연소불안정의 원인을 규명할 수 있었다. 연소실의 길이와 혼합부의 길이를 음향학적 경계로 일치시켜 연소불안정 특성을 확인해 보았을 때 두가지 서로 다른 연소불안정 모드를 확인할 수 있었는데 저주파 연소불안정 특성은 화염의 열방출 섭동과 연소실의 공진모드에 기인하며, 고주파 영역대의 연소불안정 현상은 혼합부의 길이를 변경하였을 때 발생하는 또 다른 불안정 현상임을 실험적으로 확인할 수 있었다.