• Title/Summary/Keyword: Decay rate coefficient

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ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM

  • Kim, Daewook
    • 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.

EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.659-675
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    • 2016
  • In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

Reconsideration of CN Radiation an d $C_2$ Dissociation Rate Coefficient ($C_2$의 해리 반응 계수와 CN 복사에 대한 재고찰)

  • Hyun, Seong-Yoon;Park, Chul;Chang, Keun-Shik
    • 한국전산유체공학회:학술대회논문집
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    • 2008.03b
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    • pp.92-95
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    • 2008
  • We performed the theoretical calculation of CN Violet radiation using the code SPRADIAN07 to predict the Lee et al.'s experimental measurements and to reinvestigate $C_2$ dissociation rate. CN Violet radiations are calculated under the Boltzmann and non-Boltzmann distribution using two chemical reaction sets: Park-Losev-G\"{o}kcen-Tsang and Park-Losev-G\"{o}kcen-Tsang-Lee models. Our SPRADIAN07 calculations show improvement in prediction of absolute radiation intensity of CN Violet and its decay rate by Park-Losev-G\"{o}kcen-Tsang reaction set with $C_2$ dissociation rate coefficient of $k_f$ = 1.5${\times}$10$^{16}$ exp(-71,600/$T_x$) cm$^3$ mole$^{-1}$ s$^{-1}$.

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Effect of Recalcitrant Organics on Bio-kinetic Coeffcient and Biodegradable in Box-mill Wastewater (판지공장 폐수 중 난분해성 유기물질이 동력학적 계수 및 생분해에 미치는 영향)

  • Cho, Yong Duck;Lee, Sang Wha
    • Journal of Korean Society of Water and Wastewater
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    • v.20 no.3
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    • pp.329-338
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    • 2006
  • The research aims to provide the basic data for practical applications by correlating the bio-kinetic coefficients with the load of recalcitrant organic matter in box-mill wastewater. The activated sludge process was employed to a Wastewater disposal plant in an industrial setting, increase of consequently leading to the organic load. The parameter values derived by Monod-kinetic analysis were as follows:specific substrate removal rate $K_{max}=0.17day^{-1}$, half saturation constants $K_s=60.37mg/l$, decay coefficient $K_d=0.142day^{-1}$, microbial yield coefficient y = 0.388mg/mg, and max specific growth rate ${\mu}_{max}=0.006day^{-1}$. In view of biodegradability, the $TCOD_{Mn}/TBOD_5$ ratios of inflow and outflow were 1.07 and 1.41, and the $SCOD_{Mn}/SBOD_5$ ratios of inflow and outflow were 1.10 and 1.50, respectively. The higher $TCOD_{Mn}/TBOD_5$ ratio of outflow indicated that metabolites of a microorganism have accumulated in the cells.

Application of QUAL2E Model to Water Quality Prediction of the Nam river (남강의 수질예측을 위한 QUAL2E 모델 적용)

  • Choi, Hyoung-Sub;Park, Tae-Ju;Heo, Jong-Soo
    • Korean Journal of Environmental Agriculture
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    • v.14 no.1
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    • pp.7-14
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    • 1995
  • This research was conducted to apply the QUAL2E model to be adopted to the Nam river under current water quality conditions. The survey area of total 60 Km was divided into five reaches. Each reach was then subdivided into the uniform computational elements of 1.5 Km. Based on the stream characteristics, nine sampling stations consisting of six at main streams and three at tributaries were selected. The field data were obtained from the selected stations twice during October of 1991 and May of 1992, which represented the cold weather and low flow, also the warm weather and low flow conditions, respectively. As the results of sensitivity analysis of the model, the important parameters were the rates of BOD decay, Org-N oxidation, $NH_3-N$ oxidation, Org-P decay. The calibrated and verified results by QUAL2E model were correlation coefficient of $0.45{\sim}0.94$. The results displayed a good agreement between the variables of the field measurements and the model simulations, indicating a potential use of the QUAL2E model for the water quality assessment in the Nam River.

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Treatment of Fish Processing Wastewater Using Sequencing Batch Reactor (SBR) (연속회분식 반응기를 이용한 수산물 가공폐수 처리)

  • Paik, Byeong Cheon;Shin, Hang Sik
    • Journal of Korean Society of Water and Wastewater
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    • v.8 no.1
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    • pp.18-26
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    • 1994
  • This research investigated efficient operation mode for the successful performance of SBR(sequencing batch reactor) treating fish processing wastewater, and the effect of sodium chloride (NaCl) on treatment efficiency. 2-hour-annerobic, 6-hour-aerobic and 3-hour-anoxic operation during reaction period was found an effective operating method for organic and nitrogen removal from fish processing wastewater in SBR system. The average removal efficiencies of COD, BOD, and total nitrogen in SBR operated continuousely were 91%, 95%, and 67.1%, respectively. The estimated values of biomass yield coefficient(Y), microbial decay coefficient($K_d$), and bioreaction rate constant(K) were $0.35gMLSS/gCOD_{removed}$, $0.015day^{-1}$, and $0.209hr^{-1}$, respectively. As NaCl concentration increased from 5 to 30g/L, sludge settleability was cnhanced but organic removal in the reactor was decreased. NaCl of influent had considerable relationship with COD removal, whereas it did not significant affect nitrogen removal.

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Determination of escape rate coefficients of fission products from the defective fuel rod with large defects in PWR

  • Pengtao Fu
    • Nuclear Engineering and Technology
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    • v.55 no.8
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    • pp.2977-2983
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    • 2023
  • During normal operation, some parts of the fission product in the defective fuel rods can release into the primary loops in PWR and the escape rate coefficients are widely used to assess quantitatively the release behaviors of fission products in the industry. The escape rate coefficients have been standardized and have been validated by some drilling experiments before the 1970s. In the paper, the model to determine the escape rate coefficients of fission products has been established and the typical escape rate coefficients of noble gas and iodine have been deduced based on the measured radiochemical data in one operating PWR. The result shows that the apparent escape rate coefficients vary with the release-to-birth and decay constants for different fission products of the same element. In addition, it is found that the escape rate coefficients from the defective rod with large defects are much higher than the standard escape rate coefficients, i.e., averagely 4.4 times and 1.8 times for noble gas and iodine respectively. The enhanced release of fission products from the severe secondary hydriding of several defective fuel rods in one cycle may lead to the potential risk of the temporary shutdown of the operating reactors.

Quantitative Analysis on the Variations of Ground Reaction Force during Ascent and Descent of Bus Stairs in Women

  • Hyun, Seung Hyun;Ryew, Che Cheong
    • Korean Journal of Applied Biomechanics
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    • v.27 no.3
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    • pp.181-187
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    • 2017
  • Objective: The aim of the study was to compare & analyze on the variations of ground reaction force during ascending and descending of bus stair. Method: Simulated wooden stair of bus (raiser: 37.66 cm, width: 109 cm, tread: 29 cm) and GRF system (AMTI-OR-7/ AMTI., USA) was set up within experimental room. Adult female (n=8) performed ascending & descending of simulated bus stair, and variables analyzed consisted of TT (transfer-time), PVF (peak vertical force), LR (loading rate), DR (decay rate), CV (coefficient of variation) and AI (asymmetry index). Sample data from GRF cut off at 1,000 Hz. Results: TT showed shortest variation at phase 1 during descending, but longest variation at phase 1 during ascending of stair. PVF19 (Fz2, 100%) showed large pattern during descending than that of ascending, but rather showed small pattern during ascending of stair in case of PVF2 (Fz4). LR showed larger pattern during descending than that of ascending, but rather during ascending of stair in case of DR. Variation of CV (%) did not show difference between LR and DR, but showed higher possible occurrence of variation during descending of stair. Also AI (%) showed higher index during ascending than that of descending of stair. Conclusion: Because introduction of lowered bus stair has various realistic problems, if lined up at designated bus stopage exactly, rather can solve problems of inconvenience, reduce impulsive force and secure a stability of COG during ascending & descending of stair.

Substrate Removal Condition in Activated Sludge Process of Wastewater from Acetaldehyde Manufacturing Plant (Acetaldehyde폐수의 활성오이법에 의한 기질제거조건)

  • 금영일;금두조
    • Journal of environmental and Sanitary engineering
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    • v.8 no.1
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    • pp.107-116
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    • 1993
  • This study is conducted to investigate treatability by activated sludge process for wastewater from acetaldehyde manufacturing plant. The optimum hydraulic retention time in aeration tank for removal of high strength substrate were measured. The removal efficiency were checked out by hydraulic retention time : 35hr., 40hr. and 45hr., respectively. $COD_{Cr}$, like substances were removed in all hydraulic retention time zone directed for efficiency, but non-biodegradable substances were remained. $COD_{Cr}$ biomass loading was 0.81kg $COD_{Cr}/kgMLVSS$ . day at 35hr. of retention time, 0.34 kg$COD_{Cr}$/kg MLVSS . day at 40hr., and O.l9kg$COD_Cr$/kgMLVSS . day at 45hr. And the mean $COD_{Cr}$, removal efficiency was 65.5%, 81.6% and 83.0%, respectively. And also $COD_{Cr}$, volume loading was 1.01kg$COD_{Cr}/m^3$ day, 0.87kg$COD_{Cr}/m^3$ - day, and 0.79kg$COD_{Cr}/m^3{\cdot }$day, respectively. The basic design parameter obtained is as fallows. The value of Specific substrate removal rate coefficient (k), Yield coefficient(Y) and Decay coefficient($k_d$) was $0.0013day^{-1}$, $0.505kgMLVSS/kgCOD_{Cr}$ and $0.040day^{-1}$, respectively.

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Treatability Study on the SepticTAnk Sludges

  • Byung Soo Yang
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.17 no.1
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    • pp.41-47
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    • 1981
  • The characteristics of septic tank sludges were investigated and the kinetic coefficients in the aerobic biodegradation were evaluated from bach treatability tests. Using an unbiased statistical method, the estimated values, k (substrate removal rate coefficient) =0. 0175hr-1 at 17\ulcornerC, K. (Michaelis Menten constant) = 248mg/ e, a (cell yield coefficient)=0.625, and Kd (cell decay coefficient:' =0. 00192hr-1 were obtained based on biodegradable COD(mg/ \ulcorner) and volatile suspended solids(mg/\ulcorner). The relationship between COD and BOD, COD (mg/\ulcorner) =2. 1 BOD(mg/\ulcorner) +250, also was established for the septic tank sludges. Dilution was inevitable for the grit removal because of the high viscosity of the sludges. An aerobic activated sludge process rather than anaerobic processes was recommended for the removal of soluble organics after the removal of grit and suspended solids. A multi-stage activated sludge process was adapted for this highly concentrated and not easily-degradable waste. It was estimated that a four-stage activated sludge process would require 40 hours retention time compared to 92 hours for a single-stage process, 52 hours for a double-stage process, and 46 hours for a three stage process in order to achieve an effluent quality of 84mg/ e COD( 40mg/ e BOD) with about 4, OOOmg/ \ulcorner MLSS from an influent quality of I, 500mg/ t COD(714mg/.e BOD), while multi-stages beyond four stage would not save the required retention time significantly.

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