• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.76-107
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• 2022

In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded mollification technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.72.2-72.2
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• 2010

We use three-dimensional hydrodynamic simulations to investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a massive perturber moving on a circular orbit through a uniform gaseous medium. We assume that the background medium is non-rotating and adiabatic with index 5/3, and represent the perturber using a Plummer potential with softening radius a. This work extends our previous study where we showed that the drag force on a straight-line trajectory is proportional to a0.45 if the perturber is massive enough. This indicates that the orbital decay of supermassive black holes (SMBHs) near galaxy centers may take much longer than the prediction of the linear force formula applicable for low-mass perturbers. For the circular orbits are considered, however, we find that the nonlinear drag force becomes independent of a, but dependent instead on the orbital radius R as $\varpropto$ R0.5. This suggests not only that the choices of large values of a, for resolution issues, in recent numerical experiments for mergers of SMBH, are marginally acceptable, but also that the gaseous drag indeed provides an efficient mean for the orbtial decay of SMBHs.

• East Asian mathematical journal
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• v.32 no.1
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• pp.117-128
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Ocean and Polar Research
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• v.25 no.1
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• pp.63-74
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• 2003

The build-up of the heat field in shallow coastal water due to a point source has been investigated using an analytical solution of a time-integral form derived by extending the solutions by Holley(1969) and also presented in Harleman (1971). The uniform water depth is assumed with non-isotropic turbulent dispersion. The alongshore-flow is assumed to be uni-directional, spatially uniform and oscillatory. Due to the presence of the oscillatory alongshore-flow, the heat build-up occurs in an oscillatory manner, and the excess temperature thereby fluctuates in that course and even in the quasi-steady state. A series of calculations reveal that proper choices of the decay coefficient as well as dispersion coefficients are critical to the reliable prediction of the excess temperature field. The dispersion coefficients determine the absolute values of the excess temperature and characterize the shoreline profile, particularly within the tidal excursion distance, while the decay coefficient determines the absolute value of the excess temperature and the convergence rate to that of the quasi-steady state. Within the e-folding time scale $1/k_d$ (where $k_d$ is the heat decay coefficient), heat build-up occurs more than 90% of the quasi-steady state values in a region within a tidal excursion distance (L), while occurs increasingly less the farther we go to the downstream direction (about 80% at 1.25L, and 70% at 1.5L). Calculations with onshore and offshore discharges indicate that thermal spreading in the direction of the shoreline is reduced as the shoreline constraint which controls the lateral mixing is reduced. The importance of collecting long-term records of in situ meteorological conditions and clarifying the definition of the heat loss coefficient is addressed. Interactive use of analytical and numerical modeling is recommended as a desirable way to obtain a reliable estimate of the far-field excess temperature along with extensive field measurements.

• East Asian mathematical journal
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• v.32 no.3
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• pp.399-412
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with the following nonlinear source and time-varying delay $$u_{tt}-M(x,t,{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\int_{0}^{t}}h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\+{\parallel}u{\parallel}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Journal of the Korean Ceramic Society
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• v.37 no.8
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• pp.774-780
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• 2000

In order to improve luminescence prperty of phosphors, we have synthesized Zn2SiO4:Mn phosphors by a new chemical synthetic route, i.e., the homogeneous precipitation method. This method has featured that the formation of phosphoris completed at relatively low temperature of 105$0^{\circ}C$ and the particle morphology exhibits spherical shape to be well-dispersed and uniform size. At all the Mn concentration explored, phosphors prepared by this method have exhibited the improved emission intensities. In particular, the emission intensities of phosphors with Mn doping contents between 1 at% and 3.5 at% were higher about 40% than that of commercial phosphor. On the other hand, the decay time has been decreased from 23 ms to 11 ms with increasing Mn concentration. In addition, the phosphor composition containing 3 at% Mn has displayed the most saturated color.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• Korean Journal of Optics and Photonics
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• v.12 no.2
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• pp.77-82
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• 2001

Error characteristics of a mirror loss measurement system using an exponential decay method were studied, with the two samples having about 200-ppm-loss and 30-ppm-loss, respectively. In order to minimize the decay signal deviation from an exponential curve due to cavity length fluctuation, a data average method was tried. The data average method significantly improved the exponential curve fitting error of the decay signal, so that for a 6 decay signal data average the loss measurement error was reduced by about 2.4 times for the 200-ppm-loss mirror and 1.3 times for the 30-ppm-loss mirror compared with a single shot measurement. Day-to-day mirror loss repeatability error for the two samples was investigated. The repeatability error was measured to be about 5% for the 200-ppm-loss mirror and about 26.4% for the 30-ppm-loss mirror. Low decay signal average effect and high repeatability error in the low loss mirror measurement were explained with non-uniform spatial loss distribution of the sample and contamination from the environment, in addition to the error sources of the mirror loss measurement system itself. The influence of cavity length fluctuation and cavity length measurement error on the mirror loss measurement system performance was theoretically calculated. It confirmed that the requirement for the cavity length parameters was not so strict in the mirror loss measurement system of several ppm resolution. ution.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.13 no.4
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• pp.223-229
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• 1984

Experiments were performed for freezing of an initially superheated or nonsuperheated liquid phase in a cooled vertical tube. The liquid was placed in a copper tube whose surface maintained a uniform temperature during the data run and the freezing occurred in a copper tube. The phase change medium was n-odtadecane, a paraffin which freezes at about $61^{\circ}C$. Measurements were made which yielded information about the time dependence of the freezing front, of the amount of frozen mass, and of the various energy components extracted from the tube. The time-wise decay of the initial liquid superheat was also measured. Initial superheat of the liquid tends to moderately diminish the rozen mass and associated latent energy extraction at small times but has lit tie effect on these quantities at large tiems. Natural convection in the liquid Plays a modest role only at small times and disappears when the superheat decay to zero. Although the latent energy constitutes the largest contributor to the total extracted energy, the sensible energy components can make a significant contribution, especially at large tube wall subcoolings, large initial liquid superheating and short freezing time.