• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.3
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• pp.27-36
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• 2002

Numerical stability is studied based on numerics and mathematics. It is frequently observed in the region where velocity is zero. In that region, the Euler equation have numerous solutions and, thus, it is impossible to determine a unique solution with only governing equations. However, a unique solution can be determined by additional outer flow conditions or outer numerical discontinuity calculation since the information or a unique solution under undisturbed conditions is lost by disturbances. In this reason, the numerical scheme comsistent with Euler equations cannot remove shock instability completely.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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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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• v.5A no.2
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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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• v.41 no.6
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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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• v.51 no.4
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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.

• Journal of ILASS-Korea
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• v.3 no.3
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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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• v.20 no.4
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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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2006.05a
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• pp.135-140
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• 2006

In the experimental study of $N_2$ purge cold flow test of impinging(FOOF) injector for determining of instability region, the whistling sound which has a specific frequency is generated. The frequency of whistling is proportional to the gas flow velocity in part of the oxidizer orifice and due to the coupling of the vibrating gas column and the natural frequency of pipe-orifice shape, the discontinuous jumping phenomena arises. The whistling phenomena have no effect on the combustion instability. Compared the damping factor of 1T1L mode with the hot fire test, the instability region of $N_2$ purge cold flow test is very much like that. It means that flow instability by impinging or mixing of jet is the main reason of combustion instability of impinging injector(FOOF) in the hot firing test.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.187-199
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• 2011

The main objective of this study was investigation of natural gas flames in a lean premixed swirl-stabilized dump combustor with an attention focused on the effect of the various fuel-air mixing section geometry on the combustion instability characteristics. The multi-channel dynamic pressure transducers were located on the combustor and inlet mixing section region to observe combustion pressure oscillation and difference phase at each dynamic pressure measurement results. Dynamic pressures were also measured to investigate characteristics of combustion at the same time. The combustor and mixing section length was varied in order to have different acoustic resonance characteristics from 800 to 1800 mm in combustor and 470, 550, 870 mm in mixing section. We observed two dominant instability frequencies in this study. Lower frequencies were obtained at lower equivalence ratio region and it was associated with a fundamental longitudinal mode of combustor length. Higher frequencies were observed in higher equivalence ratio conditions. It was related to secondary longitudinal mode of coupled with the combustor and mixing section. In this instability characteristics, pressure oscillation of mixing section part was larger than pressure oscillation of combustor. As a result, combustion instability was strongly affected by acoustic characteristics of combustor and mixing section geometry.