• Honam Mathematical Journal
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• v.44 no.4
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• pp.485-503
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• 2022

In this work, a discontinuous singular Dirac system is studied. For this system, a spectral function is constructed. Finally, by using the spectral function, a spectral expansion formula is given.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.871-888
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• 2018

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1347-1370
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• 2016

On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1{\geq}5$, $m{\equiv}0$ mod 2, we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair (${\varphi}_{{\frac{m}{2}}-1}$, ${\varphi}_{\frac{m}{2}}$) of spinor fields (called Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.06a
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• pp.623-624
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• 2008

• Korean Journal of Ecology and Environment
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• v.36 no.3 s.104
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• pp.344-355
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• 2003

Water quality model applicable paddy field was developed using field experiment during 1999 ${\sim}$ 2002. This model involves inputs from fertilization and sediment release as dirac delta function and continuous source function, respectively, and can simulate various processes such as ponded depth, surface drainage, total nitrogen concentration and total phosphorus concentration in a daily basis. The model was calibrated using data collected from field experiments which was irrigated with ground water and validated from field experiments which was irrigated with surface water. The nutrient concentration of surface water depended on the fertilization and dirac delta function can efficiently explain the valiance of nutrient concentration of surface water by fertilizer. As a result of calibration and validation, this model demonstrates good agreement. The model fit efficiencies ($R^2$) of ponded depth, surface concentration of TN and TP were 0.93,0.98 and 0.95, respectively for calibration, and those of TN and TP were 0.99 and 0.70, respectively for validation. We can apply lake and reservoir model to analysis paddy field considered with shallow ponded system, but it will need so many parameters and have much uncertainty. Fortunately, paddy field have a series of cultural practices yearly basis, such as irrigation-fertilization-forced drain-harvest with a similar time , so simple model may explain the mechanism for paddy field. Water quality model for paddy field developed in this study is simply, needs little parameters, but appeared high applicability to evaluate paddy filed drainage. We recommend this model to estimate nutrient loading from paddy field and establish best management practice.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.14-26
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• 2002

A new model for degenerate semiconductor quantum well devices was developed. In this model, the multi-subband Boltzmann transport equation was formulated by applying the Pauli exclusion principle and coupled to the Schrodinger and Poisson equations. For the solution of the resulted nonlinear system, the finite difference method and the Newton-Raphson method was used and carrier energy distribution function was obtained for each subband. The model was applied to a Si MOSFET inversion layer. The results of the simulation showed the changes of the distribution function from Boltzmann like to Fermi-Dirac like depending on the electron density in the quantum well, which presents the appropriateness of this modeling, the effectiveness of the solution method, and the importance of the Pauli -exclusion principle according to the reduced size of semiconductor devices.

• Composites Research
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• v.12 no.5
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• pp.65-79
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• 1999

This paper descrives the method to analyzed the free vibratioin of supported composite cylindrical shells with a longitudinal, interior rectangular plate. To obtain the free vibration characteristics before the combination of two structures, the energy principle based on the classical plate theory and Love's thin shell theory is adopted. The frequency equation of the combined system is formulated using the receptance method. When the line load and moment applied along the joint are assumed as the the Dirac delta and sinusolidal function, the continuity conditions at the joint of the plate and shell are proven to be satisfied. The effects on the combined shell frequencies of the length-no-radius ratios and radius-to-thickness ratios of the shell, fiber orientation angles and orthotropic modulus ratios of the composite are also examined.

• Journal of the Korea Institute of Military Science and Technology
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• v.7 no.4 s.19
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• pp.114-124
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• 2004

In this paper, we have proposed a novel method which can analysis a rotating elastically restrained blade with concentrated masses located in an arbitrary position. 1:he equations of motion are derived and transformed into a dimensionless form to investigate general phenomena. For the modeling of the multi-concentrated masses, the Dirac delta function is used for the mass density function. Simulation results show that the vibration characteristics of elastic restrained blade of according to dimensionless variables for example, multiple masses magnitude and mass location ratio. This method can be applied to an practical rotating blade system required to more accurate results.

• Journal of the Korean Magnetic Resonance Society
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• v.16 no.1
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• pp.11-21
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• 2012

The line-width of carbon nanotubes (CNTs) was studied as a function of the temperature at a frequency of 9.49 GHz in the presence of external electromagnetic radiation. The relative frequency dependence of the absorption power is obtained with the projection operator technique (POT) proposed by Kawabata. The line-width increased as the temperature increased in the high-temperature region (T>200 K). The scattering is little affected in the low-temperature region (T<200 K) because there is no correlation between the resonance field and the Fermi-Dirac distribution function. Thus, the present technique is considered to be more convenient to explain the resonant system as in the case of other optical transition problems.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.307-307
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• 2011

Graphene is the hottest topic in condensed-matter physics due to its unusual electronic structures such as Dirac cones and massless linear dispersions. Graphene can be epitaxially grown on various metal surfaces with chemical vapor deposition processes. Such epitaxial graphene shows modified electronic structures caused by substrates. Here, local geometric and electronic structures of graphene grown on Ru(0001) will be presented. Scanning tunneling microscopy (STM) and spectroscopy (STS) was used to reveal energy dependent atomic level topography and position-dependent differential conductance spectra. Both topography and spectra show variations from three different locations in rippled structures caused by lattice mismatch between graphene and substrate. Based on the observed results, structural models for graphene on Ru(0001) system were considered.