• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.475-482
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• 2023

This paper studies the effect of the relaxation time on a two-dimensional thermoelastic medium which has a doubly porous structure in the presence of diffusion and gravity. The normal mode analysis is used to obtain the analytic expressions of the physical quantities, which we take the solution form in the exponential image. We have discussed a homogeneous thermoelastic half-space with double porosity with the effect of diffusion and gravity. The equations of generalized thermoelastic material with double porosity structure with one relaxation time have been developed. Moreover, the expressions of many physical quantities are explained. The general solutions, under specific boundary conditions of the problem, were found in some detail. In addition, numerical results are computed.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.15-26
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• 2009

Bass diffusion model have played a central role in studying the diffusion of the new products since 1969, the year of publication of Bass model. Almost 750 publications based on the Bass diffusion model have explored extensions and applications. Extension models can be divided into two types. One is the model containing marketing-mix variables and the other is the model containing additional parameters. This paper presents another extension model of the latter type. Our model allows the time varying coefficients of innovation and imitation. Two pieces approximation of time varying coefficients is introduced and it's parameters are estimated based on NLS(Non-Linear Mean Square) method. Empirical studies are performed and the results show that our model is superior to the basic Bass model and the NUI(Non-Uniform Influence) model which is the well-known extension of the Bass model. The model developed in this paper is, also, transformed into the Bass model with the ready potential adopters in order to enhance the descriptive power.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.02a
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• pp.280-280
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• 2012

We examined ammonia diffusion on the surface of amorphous ice film through the measurement of decreasing residual quantity of $NH_3$ molecules compared to $H_2O$. The populations of $NH_3$ molecules on the surface of amorphous ice were monitored by using the techniques of temperature programmed reactive ion scattering (TPRIS) method. The ratio of intensity between ammonia and water was examined as a function of time at controlled temperature. When ammonia molecules were externally added onto an ice film at a temperature of 80 K, ammonia coverage with regard to ice was 0.12-0.16 ML. The intensity of ammonia molecules on the surface of ice decreased as time increased and the extent of decreased intensity of ammonia increased as controlled temperature increased. Moreover, energy barrier was estimated to be $51kJmol^{-1}$ on amorphous ice film. The results of the experiment indicate that ammonia molecules have a property of vertical diffusion into amorphous ice and the energy barrier of ammonia diffusion into bulk of ice is higher than that of hydrogen bonding.

• Journal of Korean Institute of Industrial Engineers
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• v.13 no.1
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• pp.25-29
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• 1987

When the historical data are available, the diffusion model, which describes the time pattern of the adoption process of a new product or technology or service, has been used as a reasonable predictor in the telecommunication demand forecasting area. This paper shows that the diffusion model is applicable when the historical data are not available. The model used is in the form of a "logistic" function. The parameters of the function are estimated using the questionnaire and the historical data of reference products. From the questionnaire, an initial and an upper limit long run value of the market share are estimated, and the diffusion time to the upper limit value is determined by the relation between the investment and the utility.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.527-528
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• 2007

There are some rebate programs for energy efficient appliances, which are lightings, vending machines, ASDs, motors, transformers, pumps, to reduce national energy consumption in Korea. In existing studies, some diffusion models have been applied to the rebate program case. But those studies could not consider various cases in duration, amounts, whether or not, of rebates. Hence, new diffusion models considering the time-variant diffusion status are proposed for high-efficient appliance rebate programs in this paper. The case study shows the application of these model into some high-efficient appliances.

• Proceedings of the Korean Society Of Semiconductor Equipment Technology
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• 2004.05a
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• pp.55-58
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• 2004

This paper presents a 3-dimensional diffusion simulation with adaptive solution strategy. The developed diffusion simulator VLSIDIF-3 was designed to re-refine areas where difference of doping concentration between any of two nodes of each element is greater than tolerance and redo diffusion process until error is tolerable. Numerical experiment in low doping diffusion problem showed that this adaptive solution strategy is very efficient in both memory and time, and expected this scheme would be more powerful in complex diffusion model.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.1-8
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• 2019

We will deal with an n locus model in which mutation and gene conversion are taken into consideration. Also random partitions of the number n determined by chromosomes with n loci should be investigated. The diffusion process describes the time evolution of distributions of the random partitions. In this paper, we find the probability of distribution of the diffusion process with special diffusion operator $L_1$ and we show that the average probability of genes at different loci on one chromosome can be described by the rate of gene frequency of mutation and gene conversion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.9
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• pp.3015-3029
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• 1996

The notion of effective transport property of a heterogeneous medium implies that the medium is large enough that the ergodic theorem holds and local fluctuation of the property can be neglected. In case that the medium is not large enough compared to its characteristic microstructure length scale, the effective property fluctuates and differs from the value of the medium being large enough. As a representative transport phenomenon, diffusion was considered and the fluctuation of varying effective diffusion property, diffusion coarseness $C_k$, was defined as a quantifying parameter. Scaled effective diffusion property, $^*$>/k$_1$ and $C_k$ were computed for the two phase random media consisting of matrix of diffusion coefficient k$_1$ and spheres of diffusion coefficient k$_2$. Numerical simulations were performed by use of the so-called first passage time technique and data were collected for existing microstructure models of hard spheres(HS), overlapping spheres(OS) and penetrable concentric shells(PCS).

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.895-906
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• 2015

Diffusion is a mathematical tool to explain the fluctuation of financial assets and the movement of particles in a micro time scale. There are ongoing statistical trials to develop an estimation method for diffusion models based on likelihood. When we estimate diffusion models by applying the maximum likelihood estimation method on data observed at discrete time points, we need to know the transition density of the diffusion. In order to approximate the transition densities of diffusion models, we suggests the method to approximate the path integral of the random process with normal random variables, and compare the numerical properties of the method with other approximation methods.