• 제목/요약/키워드: Quasi-linear

검색결과 343건 처리시간 0.019초

최적 염소 소독 모형의 개발 및 파라미터 연구 (Development of Optimal Chlorination Model and Parameter Studies)

  • 김준현;안수영;박민우
    • 환경영향평가
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    • 제29권6호
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    • pp.403-413
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    • 2020
  • 최적의 염소 소독 전략을 구축하기 위해 8개의 연립 준선형 편미분방정식으로 구성된 수학적 모형이 제안되었다. 다차원 수치 프로그램을 개발하기 위해 상류 가중 유한요소법을 사용하였다. 프로그램은 세 가지 유형의 반응기에서 측정된 농도에 대해 검증되었다. 16개의 실험 결과에 대해 경계 조건 및 반응 속도를 보정하여 측정된 값을 재생시켰다. 모델링 결과로부터 8개의 반응 속도계수가 추정되었다. 반응 속도계수는 pH 및 온도로 표현되었다. 반응 속도계수를 추정하기 위해 수치 오차의 제곱의 합을 최소화하는 자동 최적 알고리즘의 프로그램을 개발하고 모형에 결합하였다. 최종 사용지에서 염소 및 오염물의 농도를 최소화하기 위해서는 정수장의 염소소독공정으로부터 최종 사용지까지의 수질 변화를 모형에 의해 예측하고 이를 기반으로 유입수 수질에 따라 염소소독공정을 운영하는 실시간 예측 제어 시스템이 필요하다. 본 모형을 이용하여 정수장에 이러한 시스템을 구축할 수 있을 것이다.

A Method for Estimating the Lung Clinical Target Volume DVH from IMRT with and without Respiratory Gating

  • J. H. Kung;P. Zygmanski;Park, N.;G. T. Y. Chen
    • 한국의학물리학회:학술대회논문집
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    • 한국의학물리학회 2002년도 Proceedings
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    • pp.53-60
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    • 2002
  • Motion of lung tumors from respiration has been reported in the literature to be as large as of 1-2 cm. This motion requires an additional margin between the Clinical Target Volume (CTV) and the Planning Target Volume (PTV). While such a margin is necessary, it may not be sufficient to ensure proper delivery of Intensity Modulated Radiotherapy (IMRT) to the CTV during the simultaneous movement of the DMLC. Gated treatment has been proposed to improve normal tissues sparing as well as to ensure accurate dose coverage of the tumor volume. The following questions have not been addressed in the literature: a) what is the dose error to a target volume without gated IMRT treatment\ulcorner b) what is an acceptable gating window for such treatment. In this study, we address these questions by proposing a novel technique for calculating the 3D dose error that would result if a lung IMRT plan were delivered without gating. The method is also generalized for gated treatment with an arbitrary triggering window. IMRT plans for three patients with lung tumor were studied. The treatment plans were generated with HELIOS for delivery with 6 MV on a CL2100 Varian linear accelerator with a 26 pair MLC. A CTV to PTV margin of 1 cm was used. An IMRT planning system searches for an optimized fluence map ${\Phi}$ (x,y) for each port, which is then converted into a dynamic MLC file (DMLC). The DMLC file contains information about MLC subfield shapes and the fractional Monitor Units (MUs) to be delivered for each subfield. With a lung tumor, a CTV that executes a quasi periodic motion z(t) does not receive ${\Phi}$ (x,y), but rather an Effective Incident Fluence EIF(x,y). We numerically evaluate the EIF(x,y) from a given DMLC file by a coordinate transformation to the Target's Eye View (TEV). In the TEV coordinate system, the CTV itself is stationary, and the MLC is seen to execute a motion -z(t) that is superimposed on the DMLC motion. The resulting EIF(x,y)is inputted back into the dose calculation engine to estimate the 3D dose to a moving CTV. In this study, we model respiratory motion as a sinusoidal function with an amplitude of 10 mm in the superior-inferior direction, a period of 5 seconds, and an initial phase of zero.

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한반도 상공의 오존층 변화 1985~2009 (The Variations of Stratospheric Ozone over the Korean Peninsula 1985~2009)

  • 박상서;김준;조나영;이윤곤;조희구
    • 대기
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    • 제21권4호
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    • pp.349-359
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    • 2011
  • The climatology in stratospheric ozone over the Korean Peninsula, presented in previous studies (e.g., Cho et al., 2003; Kim et al., 2005), is updated by using daily and monthly data from satellite and ground-based data through December 2009. In addition, long-term satellite data [Total Ozone Mapping Spectrometer (TOMS), Ozone Monitoring Instrument (OMI), 1979~2009] have been also analyzed in order to deduce the spatial distributions and temporal variations of the global total ozone. The global average of total ozone (1979~2009) is 298 DU which shows a minimum of about 244 DU in equatorial latitudes and increases poleward in both hemispheres to a maximum of about 391 DU in Okhotsk region. The recent period, from 2006 to 2009, shows reduction in total ozone by 6% relative to the values for the pre-1980s (1979~1982). The long-term trends were estimated by using a multiple linear regression model (e.g., WMO, 1999; Cho et al., 2003) including explanatory variables for the seasonal variation, Quasi-Biennial Oscillation (QBO) and solar cycle over three different time intervals: a whole interval from 1979 to 2009, the former interval from 1979 to 1992, and the later interval from 1993 to 2009 with a turnaround point of deep minimum in 1993 is related to the effect of Mt. Pinatubo eruption. The global trend shows -0.93% $decade^{-1}$ for the whole interval, whereas the former and the later interval trends amount to -2.59% $decade^{-1}$ and +0.95% $decade^{-1}$, respectively. Therefore, the long-term total ozone variations indicate that there are positive trends showing a recovery sign of the ozone layer in both North/South hemispheres since around 1993. Annual mean total ozone (1985~2009) is distributed from 298 DU for Jeju ($33.52^{\circ}N$) to 352 DU for Unggi ($42.32^{\circ}N$) in almost zonally symmetric pattern over the Korean Peninsula, with the latitudinal gradient of 6 DU $degree^{-1}$. It is apparent that seasonal variability of total ozone increases from Jeju toward Unggi. The annual mean total ozone for Seoul shows 323 DU, with the maximum of 359 DU in March and the minimum of 291 DU in October. It is found that the day to day variability in total ozone exhibits annual mean of 5.7% in increase and -5.2% in decrease. The variability as large as 38.4% in increase and 30.3% in decrease has been observed, respectively. The long-term trend analysis (e.g., WMO, 1999) of monthly total ozone data (1985~2009) merged by satellite and ground-based measurements over the Korean Peninsula shows increase of 1.27% $decade^{-1}$ to 0.80% $decade^{-1}$ from Jeju to Unggi, respectively, showing systematic decrease of the trend magnitude with latitude. This study also presents a new analysis of ozone density and trends in the vertical distribution of ozone for Seoul with data up to the end of 2009. The mean vertical distributions of ozone show that the maximum value of the ozone density is 16.5 DU $km^{-1}$ in the middle stratospheric layer between 24 km and 28 km. About 90.0% and 71.5% of total ozone are found in the troposphere and in the stratosphere between 15 and 33 km, respectively. The trend analysis reconfirms the previous results of significant positive ozone trend, of up to 5% $decade^{-1}$, in the troposphere and the lower stratosphere (0~24 km), with negative trend, of up to -5% $decade^{-1}$, in the stratosphere (24~38 km). In addition, the Umkehr data show a positive trend of about 3% $decade^{-1}$ in the upper stratosphere (38~48 km).