• 비파괴검사학회지
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• 제36권2호
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• pp.112-120
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• 2016

The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter ${\beta}$. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of ${\beta}$ on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved ${\beta}$ values can be obtained by considering the diffraction effects.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 2009년도 한국우주과학회보 제18권2호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2006년도 하계종합학술대회
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• pp.905-906
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• 2006

In this paper, we propose an attractive novel numerical int egration method that is largely devoid of ill conditioning and is suitable for any nonlinear problem. Since the method is exact for linear problems, it is especially precise for quasilinear problems, which are frequently encountered in the real world. The method is based on a new approach to the computat ion of a matrix exponential. It does not require excessive computational resources and lends itself to a short and robust piece of software that can be easily inserted into large simulation packages.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.48.3-48
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• 2001

A gain-scheduled autopilot design for a bank-to-turn (BTT) missile is developed by using the Linear Matrix Inequality (LMI) optimization technique and a state-space lineal interpolation method. The missile dynamics are brought to a quasilinear parameter varying (quasi-LPV) form. Robust linear control design method is used to obtain state feedback controllers for the LPV systems with exogenous disturbances at the frozen values of the scheduling parameters. Two gam-scheduled controllers for the pitch axis and the yaw/roll axis are constructed by linearly interpolating the robust state-feedback gains. The designed controller is applied to a nonlinear six-degree-of-freedom (6-DOF) simulations.

• 대한수학회논문집
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• 제34권4호
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• 대한수학회보
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• 제61권2호
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• pp.541-556
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• 2024

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝ^N, where 2 ≤ p < 2^*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L^∞ estimate, we study the existence of positive solutions. Here, we construct the L^∞ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• 천문학회보
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• 제41권1호
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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 Astronomy and Space Sciences
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• 제36권2호
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• pp.45-60
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• 2019

The Earth's outer radiation belt has long received considerable attention mainly because the MeV electron flux in the belt varies often dramatically and at various time scales. It is now widely accepted that the wave-particle interaction is one of the major mechanisms responsible for such flux variations. The wave-particle interaction can accelerate electrons to MeV energies, explaining the observed flux increase events, and can also scatter the electrons' motion into the loss cone, resulting in atmospheric precipitation and thus contributing to flux dropouts. In this paper, we provide a review of the current state of research on relativistic electron scattering and precipitation due to the interaction with electromagnetic ion cyclotron (EMIC) waves in the inner magnetosphere. The review is intended to cover progress made over the last ~15 years in the theory and simulations of various issues, including quasilinear resonance diffusion, nonlinear interactions, nonresonant interactions, effects of finite normal angle on pitch angle scattering, effects due to rising tone emission, and ways to scatter near-equatorial pitch angle electrons. The review concludes with suggestions of a few promising topics for future research.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1995년도 춘계학술대회
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• pp.27-33
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• 1995

A time-dependent large deformation fracture theory is developed for application to soft biological tissues. The theory uses the quasilinear viscoelastic theory of Fung, and particularizes it to constitutive assumptions on polyvinyl-chloride (PVC) (Part I) and cartilage (Part II). This constitutive theory is used in a general viscoelastic theory by Christensen and Naghdi and an energy balance to develop an expression for the fracture toughness of the materials. Experimental methods are developed for measuring the required constitutive parameters and fracture data for the materials. Elastic stress and reduced relaxation functions were determined using tensile and shear tests at high loading rates with rise times of 25-30 msec, and test times of 150 sec. The developed method was validated, using an engineering material, PVC to separate the error in the testing method from the inherent variation of the biological tissues. It was found that the the proposed constitutive modeling can predict the nonlinear stress-strain and the time-dependent behavior of the material. As an approximation method, a pseudo-elastic theory using the J-integral concept, assuming that the material is a time-independent large deformation elastic material, was also developed and compared with the time-dependent fracture theory. For PVC. the predicted fracture toughness is $1.2{\pm}0.41$ and $1.5{\pm}0.23\;kN/m$ for the time-dependent theory and the pseudo-elastic theory, respectively. The methods should be of value in quantifying fracture properties of soft biological tissues. In Part II, an application of the developed method to a biological soft tissue was made by using bovine humeral articular cartilage.