• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.691-725
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• 1998

무한차원 상공간에서의 디리클레 형식과 이에 관계된 확산과정에 대한 일반 이론을 소개하고, 이 이론을 물리학의 통계역학 모델에 적용하였다. 구체적으로, 고전 비유계 스핀계에 대한 통계역학적인 모델, 연속체 공간에서 상호 작용하는 무한 입자계에 대한 통계역학적인 모델에 응용하였다. 아울러서 확률 미분 방정식과 같은 디리클레 형식에 관련된 연구분야에 대해서도 간단히 알아보았다.

• Journal of the Korean Electrochemical Society
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• v.16 no.4
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• pp.217-224
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• 2013

In this paper, we have investigated the characteristics of cyclic voltammetry of a self-assembled mono-layer(SAM) electrode which was modified by 3-Mercaptopropionic acid (3-MPA) on gold nanoparticle(AuNP)-deposited electrode. Also, the transport phenomena of electrons and ions around the electrode have been analyzed. The governing equation and its boundary conditions by adopting the semi-infinite diffusion model were formulated for the mass-transfer dominant system. In order to obtain the numerical solutions of cyclic voltammetry(CV) on SAM electrodes, MATLAB program was implemented by applying the explicit finite difference method. Resulting CV program for the SAM-modified electrode was verified in good agreements with the experimental CV results for the 3-MPA on AuNP electrode.

• Economic and Environmental Geology
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• v.45 no.2
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• pp.71-78
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• 2012

Illite-smectite mixed layers (I-S) occurring authigenically in diagenetic and hydrothermal environments reacts toward more illite-rich phases as temperature and potassium ion concentration increase. For that reason, I-S is often used as geothermometry and/or geochronometry at the field of hydrocarbons or ore minerals exploration. Generally, I-S shows X-ray powder diffraction (XRD) patterns of ultra-thin lamellar structures, which consist of restricted numbers of sillicate layers (normally, 5 ~ 15 layers) stacked in parallel to a-b planes. This ultra-thinness is known to decrease I-S expandability (%S) rather than theoretically expected one (short-stacking effect). We attempt here to quantify the short stacking effect of I-S using the difference of two types of expandability: one type is a maximum expandability ($%S_{Max}$) of infinite stacks of fundamental particles (physically inseparable smallest units), and the other type is an expandability of finite particle stacks normally measured using X-ray powder diffraction (XRD) ($%S_{XRD}$). Eleven I-S samples from the Geumseongsan volcanic complex, Uiseong, Gyeongbuk, have been analyzed for measuring $%S_{XRD}$ and average coherent scattering thickness (CST) after size separation under 1 ${\mu}m$. Average fundamental particle thickness ($N_f$) and $%S_{Max}$ have been determined from $%S_{XRD}$ and CST using inter-parameter relationships of I-S layer structures. The discrepancy between $%S_{Max}$ and $%S_{XRD}$ (${\Delta}%S$) suggests that the maximum short-stacking effect happens approximately at 20 $%S_{XRD}$, of which point represents I-S layer structures consisting of ca. average 3-layered fundamental particles ($N_f{\approx}3$). As a result of inferring the $%S_{XRD}$ range of each Reichweite using the $%S_{XRD}$ vs. $N_f$ diagram of Kang et al. (2002), we can confirms that the fundamental particle thickness is a determinant factor for I-S Reichweite, and also that the short-stacking effect shifts the $%S_{XRD}$ range of each Reichweite toward smaller $%S_{XRD}$ values than those that can be theoretically prospected using junction probability.