• Coupled systems mechanics
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• v.1 no.2
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• pp.183-204
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• 2012

A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1120-1131
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• 2003

A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

• Journal of the Korean Chemical Society
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• v.44 no.6
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• pp.587-591
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• 2000

Many theories have been suggested to obtain an equation of state for polymeric liquids. Most of them are based on the concepts of cell, hole, free volume or lattice etc. One of the most succesful theories is an equation of state theory of Flory and his coworkers based on the concept of free volume. In this work, van der Waals potential used in Flory's theory was modified, giving a new equation of state for polymeric liquids. The calculated results showed that the new equation of state gave better agreement with experimental PVT data than Flory's theory.

• Journal of Korean Society of Forest Science
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• v.85 no.1
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• pp.56-65
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• 1996

Current volume tables might underestimate or overestimate the volumes of individual trees in a specific region because the tables were made using the data from broad region. This study provides a statistical method of local correction, which is the ratio-of-means estimator, when the table is applied to the data from a specific region. Data used in this study were 411 trees of Larix leptolepis from Hongchon region. Five statistical models for individual tree volume equation were evaluated based on 3 evalation criteria and the best equation fitted to the data from Hongchon region was selected. The volume estimated by the selected equation was then compared with the volume estimated by the current volume table. From the ratio-of-means estimate based on the volumes estimated by selected equation and by current volume table, the local correction was made. The correction equation was $V_{Hongchon}=1.078$ $V_{volume\;table}$. It is also proved that the correction equation can simply and precisely estimate tree volumes of Larix leptolepis in Hongchon region using the current volume table.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.203-210
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• 2019

We present the three-dimensional volume reconstruction model using the modified Cahn-Hilliard equation with a fractional Laplacian. From two-dimensional cross section images such as computed tomography, magnetic resonance imaging slice data, we suggest an algorithm to reconstruct three-dimensional volume surface. By using Laplacian operator with the fractional one, the dynamics is changed to the macroscopic limit of Levy process. We initialize between the two cross section with linear interpolation and then smooth and reconstruct the surface by solving modified Cahn-Hilliard equation. We perform various numerical experiments to compare with the previous research.

• Composites Research
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• v.23 no.4
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• pp.7-13
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• 2010

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solids containing interacting multiple anisotropic inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. Effects of the number of anisotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy of the method is validated by solving the single inclusion problem for which solutions are available in the literature.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.81-82
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• 2007

• 한국연소학회:학술대회논문집
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• 1998.10a
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• pp.139-154
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• 1998

Under certain circumstance, premixed turbulent flame can be treated as wrinkled thin laminar flame and its motion in a hydrodynamic flow field has been investigated by employing G-equation. Past studies on G-equation successfully described certain aspects of laminar flame propagation such as effects of stretch on flame speed. In those studies, flames were regarded as a passive interface that does not influence the flow field. The experimental evidences, however, indicate that flow field can be significantly modified by the propagation of flames through the volume expansion of burned gas. In the present study, a new method to be used with G -equation is described to include the effect of volume expansion in the flame dynamics. The effect of volume expansion on the flow field is approximated by Biot-Savart law. The newly developed model is validated by comparison with existing analytical solutions of G -equation to predict flames propagating in hydrodynamic flow field without volume expansion. To further investigate the influence of volume expansion, present method was applied to initially wrinkled or planar flame propagating in an imposed velocity field and the average flame speed was evaluated from the ratio of flame surface area and projected area of unburned stream channel. It was observed that the initial wrinkling of flame cannot sustain itself without velocity disturbance and wrinkled structure decays into planar flame as the flame propagates. The rate of decay of the structure increased with volume expansion. The asymptotic change in the average burning speed occurs only with disturbed velocity field. Because volume expansion acts directly on the velocity field, the average burning speed is affected at all time when its effect is included. With relatively small temperature ratio of 3, the average flame speed increased 10%. The combined effect of volume expansion and flame stretch is also considered and the result implied that the effect of stretch is independent of volume release.

• Journal of the Optical Society of Korea
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• v.1 no.2
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• pp.67-73
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• 1997

Light wave diffraction from multiple superposed volume gratings is inestigated using a perturbative iteration method of the integral equation of Maxwell's wave equation. The host material and index gratings are anisotropic and non-coplanar multiple volume gratings are considered. In this method, the paraxial approximation and lack of backward scattering in conventional coupled mode theory are not assumed. Systematic analysis of anisotropic wave diffraction due to multiple noncoplanar volume index gratings is performed in increasing level of diffraction orders corresponding to successive iterations.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.