• Interaction and multiscale mechanics
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• 제1권3호
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• pp.369-379
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• 2008

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.

• Imaging Science in Dentistry
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• 제49권4호
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• pp.257-263
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• 2019

Purpose: This study was performed to evaluate the dimensional accuracy of digital dental models constructed from cone-beam computed tomographic (CBCT) scans of polyvinyl siloxane (PVS) impressions and cast scan models. Materials and Methods: A pair of PVS impressions was obtained from 20 subjects and scanned using CBCT (resolution, 0.1 mm). A cast scan model was constructed by scanning the gypsum model using a model scanner. After reconstruction of the digital models, the mesio-distal width of each tooth, inter-canine width, and inter-molar width were measured, and the Bolton ratios were calculated and compared. The 2 models were superimposed and the difference between the models was measured using 3-dimensional analysis. Results: The range of mean error between the cast scan model and the CBCT scan model was -0.15 mm to 0.13 mm in the mesio-distal width of the teeth and 0.03 mm to 0.42 mm in the width analysis. The differences in the Bolton ratios between the cast scan models and CBCT scan models were 0.87 (anterior ratio) and 0.72 (overall ratio), with no significant difference (P>0.05). The mean maxillary and mandibular difference when the cast scan model and the CBCT scan model were superimposed was 53 ㎛. Conclusion: There was no statistically significant difference in most of the measurements. The maximum tooth size difference was 0.15mm, and the average difference in model overlap was 53 ㎛. Digital models produced by scanning impressions at a high resolution using CBCT can be used in clinical practice.

• Computers and Concrete
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• 제15권1호
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• pp.103-126
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• 2015

Thermal effects are significant loads for assessing concrete dam behaviour during operation. A new methodology to estimate thermal loads on concrete dams taking into account processes which were previously unconsidered, such as: the evaporative cooling, the night radiating cooling or the shades, has been recently reported. The application of this novel approach in combination with a three-dimensional finite element method to solve the heat diffusion equation led to a precise characterization of the thermal field inside the dam. However, that approach may be computationally expensive. This paper proposes the use of a new one-dimensional model based on an explicit finite difference scheme which is improved by means of the reported methodology for computing the heat fluxes through the dam faces. The improved model has been applied to a case study where observations from 21 concrete thermometers and data of climatic variables were available. The results are compared with those from: (a) the original one-dimensional finite difference model, (b) the Stucky-Derron classical one-dimensional analytical solution, and (c) a three-dimensional finite element method. The results of the improved model match well with the observed temperatures, in addition they are similar to those obtained with (c) except in the vicinity of the abutments, although this later is a considerably more complex methodology. The improved model have a better performance than the models (a) and (b), whose results present larger error and bias when compared with the recorded data.

• 한국기계가공학회지
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• 제10권4호
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• pp.50-56
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• 2011

Injection molding process is one of the popular manufacturing methods to produce plastic parts with high efficiency and low cost. Ball seat for automobile suspension is made by an injection molding process as a part to support pivot function of ball joint consisted of ball stud and housing. It is necessary for a ball seat to have a dimensional stability in the three dimensional inner area to be contacted with ball stud. In this paper, the dimensional stability of inner surface is indirectly analyzed by checking the difference of inner diameter around the circumferential direction and the thickness variation at the top part of ball seat. Measurement was performed by using the coordinate measuring machine and the fixture to hold ball seat. Optimization of injection molding processes such as injection time, cooling time and temperatures of cylinder barrel was derived to reduce the difference of inner diameter and the thickness variation at the top part of ball seat based on the Taguchi method.

• 대한조선학회지
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• 제24권3호
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• pp.9-16
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• 1987

In this paper, the fluid flow in the two-dimensional tank is analyzed by the Finite Difference Method. The Navier-Stokes equation is modified for the tank fixed coordinate system. For the treatment of the free surface, the Volume of Fluid Method by Hirt and Nichols is adopted. The continuity equation and the Poisson equation which is derived from the Navier-Stokes equation to find the pressure are solved by the Successive-Line-Overrelaxation Method. The comparison of the calculated results with experimental data show a favorable agreement. The fluid flow in the two-dimensional tank can be predicted reasonably before the free surface reaches breaking by this numerical method.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.235-244
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• 2012

In this paper, we solve the three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind using the full multigrid (FMG) algorithm. We derive a finite difference approximations for the biharmonic equation on a 18 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at grid points. In the multigrid methods, we use a fourth order interpolation to producing a new intermediate unknown functions values on a finer grid, and the full weighting restriction operators to calculating the residuals at coarse grid points. A set of test problems gives excellent results.

• Journal of the Optical Society of Korea
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• 제13권2호
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• pp.173-177
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• 2009

Digital holographic microscopy allows optical path difference measurement. Optical path difference depends on the both refractive index and morphology of sample. We developed a dual-wavelength in-line digital holographic microscope that can measure simultaneously the refractive index and morphology of a sample, providing highly precise three-dimensional information. Here we propose theoretical and experimental methods for dual-wavelength in-line digital holographic microscopy. The measured data were reasonable, although there was data error. By improving the experimental method, we could measure the refractive index more precisely and obtain more accurate three-dimensional information on samples.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.271-289
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• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

• 산업기술연구
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• 제11권
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• pp.85-98
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• 1991

A numerical study was performed to investigate characteristics of one-dimensional consolidation of soft clay. Results of consolidation tests with the remolded normally consolidation clay of having a very high initial void ratio were analyzed by using the numerical technique of finite difference method based on the finite strain consolidation theory, to evaluate consolidational characteristics of soft clay under surcharges on the top of clay. On the other hand, a numerical parametric study on soft clay consolidated due to its self-weight was also carried out to find its effect on one-dimensional consolidation. Terzaghi's conventional consolidation theory, finite strain consolidation theories with linear and non-linear interpolation of effective stress - void ratio - permeability relation were used to analyze the test results and their results were compared to each other to figure out the difference between them. Therefore, the validity of theories was assessed.