• Title/Summary/Keyword: Quasi-linear

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

  • Kim, Joonhyun;Ahn, Sooyoung;Park, Minwoo
    • Journal of Environmental Impact Assessment
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    • v.29 no.6
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    • pp.403-413
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    • 2020
  • A mathematical model comprised with eight simultaneous quasi-linear partial differential equations was suggested to provide optimal chlorination strategy. Upstream weighted finite element method was employed to construct multidimensional numerical code. The code was verified against measured concentrations in three type of reactors. Boundary conditions and reaction rate were calibrated for the sixteen cases of experimental results to regenerate the measured values. Eight reaction rate coefficients were estimated from the modeling result. The reaction rate coefficients were expressed in terms of pH and temperature. Automatic optimal algorithm was invented to estimate the reaction rate coefficients by minimizing the sum of squares of the numerical errors and combined with the model. In order to minimize the concentration of chlorine and pollutants at the final usage sites, a real-time predictive control system is imperative which can predict the water quality variables from the chlorine disinfection process at the water purification plant to the customer by means of a model and operate the disinfection process according to the influent water quality. This model can be used to build such a system in water treatment plants.

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
    • Proceedings of the Korean Society of Medical Physics Conference
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    • 2002.09a
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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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The Variations of Stratospheric Ozone over the Korean Peninsula 1985~2009 (한반도 상공의 오존층 변화 1985~2009)

  • Park, Sang Seo;Kim, Jhoon;Cho, Nayeong;Lee, Yun Gon;Cho, Hi Ku
    • Atmosphere
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    • v.21 no.4
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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).