• 대한수학회보
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• 제57권3호
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• pp.661-676
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• 2020

To understand the interaction of a fluid and a rigid body, we use the concept of B-evolution. Then in a similar way to the usual Navier-Stokes system, we obtain a Helmholtz type decomposition. Using B-evolution theory and the decomposition, we work on the semigroup to analyze the linear part of the system.

• 한국분무공학회지
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• 제2권1호
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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, $D_{32}$.

• 한국분무공학회지
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• 제1권1호
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• pp.44-54
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• 1996

A theoretical and experimental study was carried out on the prediction of drop size distribution of the pressure swirl atomizer. Drop size distribution was obtained by using maximum entropy formal ism. Several constraints in the form of the definition of mean diameter were used in this formulation in order to avoid the difficulties of the estimating source terms. In this study $D_{10}$ was only introduced into the formulation as a constraint. A drop size obtained by using linear Kelvin-Helmholtz instability theory was considered as an unknown characteristic length scale. As a result, the calculated drop size was agreed well with measured mean diameter, particularly with $D_{32}$. The predicted drop size distribution was agreed welt with experimental data measured wi th Malvern 2600.

• Structural Engineering and Mechanics
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• 제69권5호
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• pp.487-497
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• 2019

Rapid advances in the engineering applications can bring further areas to provide the opportunity to manipulate anisotropic structures for direct productivity in design of micro/nano-structures. For the first time, magnetic affected wave characteristics of nanosize plates made of anisotropic material is investigated via the three-dimensional bi-Helmholtz nonlocal strain gradient theory. Three small scale parameters are used to predict the size-dependent behavior of the nanoplates more accurately. After owing governing equations of wave motion, an analytical approach based harmonic series is utilized to fine the wave frequency as well as phase velocity. It is observed that the small scale parameters, magnetic field and wave number have considerable influence on the wave characteristics of anisotropic nanoplates. Due to the lack of any study on the mechanics of three-dimensional bi-Helmholtz gradient plates made of anisotropic materials, it is hoped that the present exact model may be used as a benchmark for future works of such nanostructures.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.1-4
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• 1999

The Helmholtz equation is very important in physics and engineering. However, solution of the Helmholtz equation is in general known as a very difficult phenomenon. For if the ${\omega}$ is negative, the FDM discretized linear system becomes indefinite, whose solution by iterative method requires a very clever preconditioner. In this paper we assume that ${\omega}$ is nonnegative, and determine the optimal ${\rho}$ parameter for the three dimensional ADI iteration for the Helmholtz equation. The ADI(Alternating Direction Implicit) method is also getting new attentions due to the fact that it is very suitable to the vector/parallel computers, for example, as a preconditioner to the Krylov subspace methods. However, classical ADI was developed for two dimensions, and for three dimensions it is known that its convergence behaviour is quite different from that in two dimensions. So far, in three dimensions the so-called Douglas-Rachford form of ADI was developed. It is known to converge for a relatively wide range of ${\rho}$ values but its convergence is very slow. In this paper we determine the necessary conditions of the ${\rho}$ parameter for the convergence and optimal ${\rho}$ for the three dimensional ADI iteration of the Peaceman-Rachford form for the real Helmholtz equation with nonnegative ${\omega}$. Also, we conducted some experiments which is in close agreement with our theory. This straightforward extension of Peaceman-rachford ADI into three dimensions will be useful as an iterative solver itself or as a preconditioner to the the Krylov subspace methods, such as CG(Conjugate Gradient) method or GMRES(m).

• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• 한국분무공학회지
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• 제3권2호
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• pp.1-13
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• 1998

A theoretical and experimental study was carried out to predict the drop size distribution of the pressure swirl atomizer. 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 that the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. Drop size distribution was obtained by using maximum entropy formalism. Seven constraints in the form of the definition of mean diameter were used in this formulation in order to avoid the difficulties of estimating source terms. In this study $D_{10}$ only was introduced into the formulation as a constraint. The predicted drop size and drop size distribution agreed well with the measured data.

• 대한화학회지
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• 제16권5호
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• pp.265-270
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• 1972

지방족 및 방향족 탄화수소의 수용액을 Jhon 등이 제창한 liquid water의 significant structure theory 를 이용하여 연구하였으며 Helmholtz free energy, internal energy, entropy, heat capacity 등의 열역학적 성질을 계산하였다. 계산결과는 문헌에 발표된 실험치와 잘 일치됨을 볼 수 있다

• 대한조선학회지
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• 제25권2호
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• pp.19-30
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• 1988

Sectional added masses of an elastic beam vibrating vertically on the free surface in higher harmonic modes are evaluated. Hydrodynamic interactions between neighboring sections, which strip theory ignores, are considered for modal wave lengths of the order of magnitude of cross-sectional dimensions of the body. An approximate solution of modified Helmholtz equation which becomes a singular perturbation problem at small wave lengths is secured to get an analytic expression for added masses attending higher harmonic modes. As a bound of the present theory, the modified Helmholtz equation is solved for the long flat plate vibrating at high frequency on the water surface without any limitations on modal frequency. Finally, extensive series of numerical calculations are carried out for ship-like forms. It is found that when modal wave length is comparable to or shorter than a typical cross-sectional dimension of a body, sectional interaction effects are large which result in considerable reductions in added masses. For a fuller section, the ratio of added mass reduction is greater. In the limit of vanishing sectional area, the added masses approach to that of flat plate of equal beam. It is shown that the added mass distribution for a Legendre modal from can be determined form the present theory and that the results agree with the extensive three-dimensional determination of Vorus and Hilarides.

• 대한화학회지
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• 제20권2호
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• pp.118-128
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• 1976

액체에 대한 significant structure theory 와 상의 전이에 대한 Bragg-Williams근사를 사용하여 액정 화합물인 p-azoxyanisole의 열역학적 성질을 nematic phase와 isotropic phase의 온도범위에 걸쳐 계산하였다. Isotropic phase는 일반적인 액체로 보았으며 nematic phase는 액체적인 성질외에도 분자쌍극자의 배열에 의한 영향도 고려하였다. p-Azoxyanisole의 액체적인 성질은 significant structure theory로 기술하였으며 분자쌍극과 배열에 의한 영향은 Bragg-Williams 근사로써 고려하였다. 부피, 증기압, 정압비열, 열팽창계수, nematic-isotropic 전이점에서의 엔트로피 엔탈피 변화, 절대엔트로피, Helmholtz free energy등을 계산하여 실험치와 비교하였다.