• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.1
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• pp.68-74
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• 1999

The Green function method is widely used for the analysis of waves in a harbor with a constant depth. In extending this method to a wave field over arbitrary depth, a generalized and convenient method is needed to obtain unit solutions for waves emerging from a point source. For this purpose, a parabolic wave equation is derived to approximate the mild-slope equation written in terms of polar coordinates. Usefulness of the equation obtained is examined through trial computations.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.11 no.6
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• pp.33-37
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• 1974

In this paper, the radiation characteristics for the array of a circular loop antenna is studied in moving media. The medium is assumed to be homogeneous, isotropic, and to move with a constant velocity much less than the speed of light. The integral equation for the current distribution is derived and the current functions is found by means of courier Series as a solution of the integral equation. The electric field is derived from the current on circular loop antenna and the Dyadic Green's Function in moving media. The numerical calculation of the electric field concerning to the two element antenna array,, in which one element is parasitic, is carried out. The field patterns are plotted from the computed values. As a result, the field patterns in moving media, compared with the patterns in stationary media, are found to decrease in the direction of media velocity and increase in the opposite direction, and the maximum directivity is shifted.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.6
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• pp.772-778
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• 2002

A numerical analysis of turbulent gas-particle two-phase flow is performed in conjunction with the experiments of Fackrell ＆ Robins and Raupach & Legg that considered ground-level source and/or elevated source flat plate flow. K-$\omega$ turbulence model is used in order to analyze fully turbulent flow field and the concentration equation with settling velocity is adopted for the concentration field. The model of Einstein and Chien is applied that couples the velocity field and the concentration field. Turbulent eddy viscosity is re-evaluated in this model. The present numerical results have good agreement between the simulation and the experimental data for the mean flow velocities and particle concentrations. While the previous study shows about 27% error in the vicinity of the source of particle concentration, the .present study allows about 14% error. A new turbulent gas-particle flow model developed by this study is able to cut down error by 13% at a near source.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.1
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• pp.70-81
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• 1999

To predict the viscous boundary layers and wakes around a ship, the CFD techniques are commonly used. For the efficient application of CFD tools to practical hull farms, a 3-D field grid generating system is developed. The present grid generating system utilizes the solution of Poisson equation. Sorenson's method developed for 2-D is extended into 3-D to provide the forcing functions controling grid interval and orthogonality on hull surface, etc. The weighting function scheme is used for the discretization of the Poisson equation and the linear equations are solved by using MSIP salver. The trans-finite interpolation is also employed to assure the smooth transition into boundary surface grids. To rove the applicability, the field grid systems around a container ship and a VLCC with bow and stem bulb are illustrated, and the procedures for generating 3-D field grid system are explained.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.176-183
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• 2003

This paper presents a neural network based approach to disseminating information relating to experimental and field observations in engineering. Although the methodology is generic and can be applied to many areas of engineering science, attention is focussed here solely on geotechnical engineering applications. Field data relating to the settlement of foundations presented by Burland and Burbidge (1985) which led to their well known equation for calculation of settlement, now included in most text books, is re-visited. A part of the data, chosen randomly, is used to train an Artificial Neural Network (ANN), which relates foundation settlement to various causes as identified by the authors. Predictions are made for situations for which data were not used in training. These indicate sufficient accuracy when compared to the original field data. Accuracy of predictions is further improved when all the data are included in the training set. The finally trained ANN is shown to represent these data more accurately than the Burland and Burbidge equation. Based on the above heuristic example, an ANN is presented as an alternative to developing equations and design rules in geotechnical engineering practice. Significant advantages are shown to arise by using this methodology. Ease of updating the ANN, as and when additional data becomes available, being the most important one. Loss of transparency, however, seems to be the main disadvantage.

• Journal of the Semiconductor & Display Technology
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• v.8 no.3
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• pp.31-37
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• 2009

This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

• Journal of The Korean Society of Agricultural Engineers
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• v.60 no.2
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• pp.37-44
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• 2018

Universal soil loss equation (USLE) had been employed to estimate potential soil loss since it was developed from the statewide data measured and collected in the United States. The equation had an origin in average annual soil loss estimation though, it was modified or improved to provide better opportunities of soil loss estimation outside the United States. The equation has five factors, most studies modifying them to adapt regional status were focused on rainfall erosivity factor and cover management factor. While the conservation practice factor (USLE P factor) is to represent distinct features in agricultural fields, it is challenging to find studies regarding the factor improvements. Moreover, the factor is typically defined using slopes. The factor defining approach was suggested in the study, the approach is a step-by-step method allowing USLE P factor definition with given condition. The minimum condition is slope and field location to provide an opportunity for using in any GIS software and to reflect regionally distinct features. If watershed location, slope, crop type, and mulching type on furrows are given, detailed definition of the factors are possible. The approach was developed from field survey in South-Korea, it is expected to be used for potential soil loss using USLE in South-Korea.