• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.31-40
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• 2009

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.757-762
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• 2009

In allelic model $X\;=\;(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;{\int}^t_0\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. We can also obtain a new diffusion operator $L^*$ for diffusion coefficient and we prove that unique solution for $L^*$-martingale problem exists. In this note, we define new symmetric preserving transformation. Uniqueness for martingale problem and symmetric property will be proved.

• Journal of the Korean Wood Science and Technology
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• v.31 no.3
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• pp.24-29
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• 2003

This research was performed to investigate the diffusivity of borate rods in radiata pine (Pinus radiata D. Don) conditioned to 40 percent moisture content (MC). The deepest penetration of boron were observed in the longitudinal direction, followed by the radial and the tangential directions. The boron loading on the wood face adjacent to the borate rod tended to increase with diffusion time in all directions. To mathematically quantify boron diffusion, the diffusion coefficient of boron was determined using Boltzmann's transformation by assuming that it was a function of concentration only. The values of the longitudinal diffusion coefficients were between 1.3×10^-8 cm²/sec and 9.2×10^-8 cm²/sec. The radial diffusion coefficients were between 1.4×10^-8 cm²/sec and 9.5×10^-8 cm²/sec, and the tangential diffusion coefficients were between 5.2×10^-9 cm²/sec and 1.3×10^-8 cm²/sec. The differences of diffusion coefficients between the longitudinal direction and the radial direction were slight, although their concentration profiles were markedly different. This indicates that the amount of boron loading on the wood face adjacent the borate rod is one of the most important factor for boron penetration in wood with low MC.

• Korean Journal of Soil Science and Fertilizer
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• v.28 no.3
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• pp.233-240
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• 1995

Fick's diffusion equation was transformed into algebraic subsidiary equation with its initial and boundary conditions through Laplace transformation, and the subsidiary equation was transformed back on the basis of Burington's table of inverse transformations so that it became the solution of Fick's equation. The initial and boundary condition was for upward diffusion of salts into flooding water of constant depth from uniform polder soil of infinite depth containing constant concentration of salt. The derived solution was tested through comparison for its conformability with other solutions of simpler initial and boundary conditions. The importance of shallow transplanting of rice seedlings and salt removing by growing rice was mentioned on the basis of very slow desalting rate by diffusion calculated from the derived solutions.

• Geophysics and Geophysical Exploration
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• v.17 no.3
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• pp.129-136
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• 2014

Electromagnetic (EM) methods are generally divided into frequency-domain EM (FDEM) and time-domain EM (TDEM) methods, depending on the source waveform. The FDEM and TDEM fields are mathematically related by the Fourier transformation, and the TDEM field can thus be obtained as the Fourier transformation of FDEM data. For modeling in time-domain, we can use fast frequency-domain modeling codes and then convert the results to the time domain with a suitable numerical method. Thus, frequency-to-time transformations are of interest to EM methods, which is generally attained through fast Fourier transform. However, faster frequency-to-time transformation is required for the 3D inversion of TDEM data or for the processing of vast air-borne TDEM data. The diffusion expansion method (DEM) is one of smart frequency-to-time transformation methods. In DEM, the EM field is expanded into a sequence of diffusion functions with a known frequency dependence, but with unknown diffusion-times that must be chosen based on the data to be transformed. Especially, accuracy of DEM is sensitive to the diffusion-time. In this study, we developed a method to determine the optimum range of diffusion-time values, minimizing the RMS error of the frequency-domain data approximated by the diffusion expansion. We confirmed that this method produces accurate results over a wider time range for a homogeneous half-space and two-layered model.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.91-99
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• 2004

Iwata et al. analyzed the pseudorandomness of the block cipher Serpent which is a SPN-type transformation. In this parer, we introduce a generalization of the results, which can be applied to any SPN-type transformation. For the purpose, we give several explicit definitions and prove our main theorems. We will also apply our theorems to several SPN-type transformations including Serpent, Crypton and Rijndael.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.18 no.1
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• pp.15-21
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• 2008

SiC has an excellent resistance to oxidation and corrosion, high temperature strength and good thermal conductivity. However, it is difficult to density because of its highly covalent bonding characteristics. Hot-press sintering process was applied to fabricate fully densified SiC ceramics with carbon and boron addition as a sintering additive. The addition of carbon improved the mechanical properties of SiC because it could induce a fine and homogeneous microstructure by the suppression of abnormal growth of SiC grain. Also, the addition of carbon could control the phase transformation of SiC. The phase transformation of 6H to 4H increased with sintering temperature but the addition of carbon decreased that kind of phase transformation.

• Korean Journal of Materials Research
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• v.15 no.11
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• pp.735-740
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• 2005

The phase transformation of Ni-B diffusion barrier by Cu diffusion was studied. The Ni-B diffusion barrier, thickness of 10(Inn, was electrolessly deposited on the electroplated Cu interconnect. The specimens were annealed either in Ar atmosphere or in $H_2$ atmosphere from $300^{\circ}C\;to\;800^{\circ}C$ for 30min, respectively. Although the Ni-B coated specimens showed the decomposition of $Ni_3B$ above $400^{\circ}C$ in both Ar atmosphere and $H_2$ atmosphere, Ni-B powders did not show the decomposition of $Ni_3B$. The $Ni_3B$ was decomposed to Ni and B in hi atmospherr: and the metallic Ni formed the solid solution with Cu and the free B was oxidized to $B_2O_3$. However, both the boron hydride and free B were not observed in the diffusion barrier after the annealing in $H_2$ atmos There. These results revealed that the decomposition of $Ni_3B$ by Cu made the Cu diffusion continued toward the Ni-B diffusion barrier.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2005.11a
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• pp.132-133
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• 2005

• Computers and Concrete
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• v.15 no.1
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• pp.127-140
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• 2015

The process of chloride ingress in saturated concrete was presented by a previous study that used a mathematical model for the same as that concrete. This model is to be studied chloride ion diffusion which is considered as a chemical phenomenon and is to be represented the chloride diffusion process to be a nonlinear partial differential equation (PDE). In this paper, this nonlinear PDE is solved by the Kirchhoff transformation to render into a linear PDE. This linear PDE associated with initial and boundary conditions is also solved by the Laplace transformation to obtain an analytical solution. To verify the serviceability and reliability of this proposed method, the practical application should be supplied. The input parameters were cited from the previous study. The free chloride concentration profiles obtained by the analytical solution of mathematical model for saturated concretes after 24 and 120 hrs of exposure were compared with the previous study. The predicted results obtained from proposed method have a tendency with experimental results obtained by the previous study and trend toward numerical results approximated by finite difference technique.