• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.47.2-47.2
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• 2016

The protons and helium ions in the solar wind are observed to possess anisotropic temperature profiles. The anisotropy appears to be limited by various marginal instability conditions. One of the efficient methods to investigate the global dynamics and distribution of various temperature anisotropies in the large-scale solar wind models may be that based upon the macroscopic quasi-linear approach. The present paper investigates the proton and helium ion anisotropy instabilities on the basis of comparison between the quasi-linear theory versus particle-in-cell simulation. It is found that the overall dynamical development of the particle temperatures is quite accurately reproduced by the macroscopic quasi-linear scheme. The wave energy development in time, however, shows somewhat less restrictive comparisons, indicating that while the quasi-linear method is acceptable for the particle dynamics, the wave analysis probably requires higher-order physics, such as wave-wave coupling or nonlinear wave-particle interaction. We carried out comparative studies of proton firehose instability, aperiodic ordinary mode instability, and helium ion anisotropy instability. It was found that the agreement between QL theory and PIC simulation is rather good. It means that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime.

• Journal of ILASS-Korea
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• v.2 no.1
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• pp.8-17
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• 1997

A study has been carried out on the instability of a conical liquid sheet by using the linear instability theory. Various analytical methods using the Kelvin-Helmholtz instability theory were tried to examine the wave growth on cylindrical liquid sheets. Cylinderical liquid sheets were extended to the case with the conical sheets. Perturbations due to tangential motion as well as longitudinal one were taken into account. And it was assumed the the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. The predicted drop size agreed well with the measured Sauter mean diameter, $D_{32}$.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• Bulletin of the Korean Space Science Society
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• 2009.10a
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• pp.34.2-34.2
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• 2009

The relativistic Weibel instability has drawn attention as a main mechanism of the magnetic generation in the core of galaxies or in the formation of universe. The Weibel instability is not yet fully understood in the relativistic region. We investigated nonlinear saturation and decay of the relativistic Weibel instability. It is found that the early phase of the instability is in excellent agreement with the linear theory. But, an analysis based on an alternative magnetic trapping saturation theory reveals that a substantial discrepancy between the theory and simulation is revealed in the relativistic regime in contrast to an excellent agreement in the non-relativistic regime. The analysis of the Weibel instability beyond the quasilinear saturation stage shows an inverse cascade process via a nonlinear decay instability involving electrostatic fluctuation.

• Journal of ILASS-Korea
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• v.10 no.4
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• pp.32-46
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• 2005

The breakup characteristics of liquid sheets formed by the impinging and swirl type injectors were studied as increasing the Weber number (or injection condition) and the ambient gas pressure to 4.0.MPa. In the case of impinging type injector. we compared the changes of breakup lengths between laminar and turbulent sheets. which are formed by the impingement of laminar and turbulent jets. respectively. The results showed that both sheets expand as increasing the injection velocity irrespective of the ambient gas density when the gas based Weber number is low. When the Weber number is high, however, the breakup of turbulent sheet depends on the hydraulic force of jets as well as the aerodynamic force of ambient gas which determines the breakup of laminar sheet. Using the experimental results. we could suggest empirical models on the breakup lengths of laminar and turbulent sheets. In the case of swirl type injector. as $We_l$, and ambient gas density increased, the disturbances on the annular liquid sheet surface were amplified by the increase of the aerodynamic forces. and thus the liquid sheet disintegrated near from the injector exit. Finally, the measured breakup length of swirl type injector according to the ambient gas density and $We_l$, was compared with the result by the linear instability theory. We found that the corrected breakup length relation derived from linear instability theory considering the attenuation of sheet thickness agrees well with our experimental results.

• Steel and Composite Structures
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• v.31 no.2
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• pp.187-199
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• 2019

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

• 한국연소학회:학술대회논문집
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• 2003.05a
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• pp.209-214
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• 2003

The Saffman-Taylor instability mechanisms in laminar premixed flames in a Hele-Shaw cell are investigated using two-dimensional numerical simulations with Poiseuille assumption for the viscous effect. The baseline calculations considering the Darrieus-Landau and diffusive-thermal instability modes show the results consistent with the classical linear instability theory. With the Saffrnan-Taylor instability mechanism. the overall effect is to enhance the destabilizing mechanism by providing an increased viscous force in the product gas. The linear instability behavior is found to qualitatively similar to the Darrieus-Landau mechanism. However, the results in the nonlinear range demonstrate that there may exist distinct characteristic time scales associated with Darrieus-Landau and Saffman-Taylor mechanisms, such that the latter effect sustains longer in time, contributing to a higher overall flame speed.

• Ocean Systems Engineering
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• v.8 no.2
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• pp.167-182
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• 2018

RTI (Rayleigh-Taylor instability) is investigated by a multi-liquid MPS (Moving Particle Semi-implicit) method for both viscous and inviscid flows for various density differences, initial-disturbance amplitudes, viscosities, and surface tensions. The MPS simulation can be continued up to the late stage of high nonlinearity with complicated patterns and its initial developments agree well with the linear theoretical results. According to the relevant linear theory, the difference between inviscid and viscous fluids is the rising velocity at which upward-mushroom-like RTI flow with vortex formation is generated. However, with the developed MPS program, significant differences in both growing patters and developing speeds are observed. Also, more dispersion can be observed in the inviscid case. With larger Atwood (AT) number, stronger RTI flows are developed earlier, as expected, with higher potential-energy differences. With larger initial disturbances, quite different patterns of RTI-development are observed compared to the small-initial-disturbance case. If AT number is small, the surface tension tends to delay and suppress the RTI development when it is sufficiently large. Interestingly, at high AT number, the RTI-suppressions by increased surface tension become less effective.

• Steel and Composite Structures
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• v.32 no.2
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• pp.157-171
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• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.70.1-70.1
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• 2019

Multiple-harmonic electron cyclotron emissions, often known in the literature as the (n + 1∕2)fce emissions, are a common occurrence in the magnetosphere. These emissions are often interpreted in terms of the Bernstein mode instability driven by the electron loss cone velocity distribution function. Alternatively, they can be interpreted as quasi-thermal emission of electrostatic fluctuations in magnetized plasmas. The present paper carries out a one-dimensional relativistic electromagnetic particle-in-cell simulation and also employs a reduced quasi-linear kinetic theoretical analysis in order to compare against the simulation. It is found that the Bernstein mode instability is indeed excited by the loss cone distribution of electrons, but the saturation level of the electrostatic mode is quite low, and that the effects of instability on the electrons is rather minimal. This supports the interpretation of multiple-harmonic emission in the context of the spontaneous emission and reabsorption in quasi-thermal magnetized plasma in the magnetosphere.