• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권2호
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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.

• 천문학회보
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• 제35권1호
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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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• 제32권1호
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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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• 제25권1호
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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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• 제32권3호
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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.

• 한국세라믹학회지
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• 제37권8호
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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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• 제22권6호
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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.

• 대한수학회지
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• 제58권2호
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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.

• 한국광학회지
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• 제12권2호
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• pp.77-82
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• 2001

손실 200 ppm급과 30 ppm급인 두 종류의 시험 반사경을 대상으로, 지수감쇠 방법을 이용한 반사경 손실측정 시스템의 오차 특성이 조사되었다. 공진기 길이 떨림에 의한 공진기 감쇠신호의 지수함수 왜곡을 보상하기 위하여 감쇠신호 데이터 평균기법을 적용하였다. 감쇠신호 6개의 평균이 취해졌을 때 감쇠신호의 지수함수 곡선맞춤 오차개선이 뚜력시 관측되었으며 손실 200ppm급 시험 반사경의 경우 약 2.4배 손실 30ppm급 시험 반사경의 경우 약 1.3배의 반사경 손실 측정오차 개선효과를 얻을 수 있었다 시험 공진기에서의 일별(day-to-day) 반사경 손실측정 반복도 오차가 조사되었다. 손실 200ppm급 시험 반사경의 경우 약 5.0%, 30ppm급 시험 반사경의 경우 약 26.4%의 손실측정 반복도 오차가 관측되었다. 저손실 반사경 평가에서 확인된 낮은 감쇠신호 데이터 평균효과와 높은 손실측정 반복도 오차는 손실측정 시스템 자체의 측정오차 이외에 시험 반사경 표면의 불균일한 손실 공간분포와 주변 오염원 유입의 결과로 분석되었다 또한 공진기 길이 떨림의 크기와 공진기 길이 측정오차가 손실측정 시스템의 정확도에 미치는 영향을 계산을 통해 조사한 결과, 분해능 수 ppm 급 현재의 측정 시스템의 성능에 미칠수 있는 공진기 길이오차의 영향은 충분히 적은 것으로 확인되었다.

• 대한설비공학회지:설비저널
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• 제13권4호
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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.