• 제목/요약/키워드: logarithmic free energy

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A NONLINEAR CONVEX SPLITTING FOURIER SPECTRAL SCHEME FOR THE CAHN-HILLIARD EQUATION WITH A LOGARITHMIC FREE ENERGY

  • Kim, Junseok;Lee, Hyun Geun
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.265-276
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    • 2019
  • For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn-Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn-Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

Experimental Study of the Free Roll Decay Test for the Evaluation of Roll Damping Coefficients (감쇠계수 산출을 위한 자유 횡동요 감쇠실험 연구)

  • Kim, Namwoo;Kim, Yong Jig;Ha, Youngrok
    • Journal of the Society of Naval Architects of Korea
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    • v.52 no.6
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    • pp.460-470
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    • 2015
  • In general ships and FPSOs, roll damping is very small and consequently roll motion is very large at the roll resonance frequency. Proper evaluation of the roll damping coefficient at the resonance frequency is an important task in the study of roll motion and usually it is done by the analysis of free roll decay tests. The relative decrement method based on energy relation has been used mainly for the evaluation of roll damping coefficient from the roll decay test so far. As another method, the logarithmic decrement method based on equivalent linear decay assumption can be used for the same purpose and it is relatively simple. In this paper, both of the relative decrement method and the logarithmic decrement method are used for the evaluation of roll damping coefficient including quadratic damping from the free roll decay tests, and their results are cross-checked for verifying the obtained damping coefficients. Through applications to a box-type floating body equiped with bilge keels, it is shown that the two methods give almost the same damping coefficients in a practical view point and the cross-check of their results is to be a good tool to prevent a possible error. And also the quantitative effects of the bilge keels on the roll damping of box-type floating body are shown and discussed.

A study on design for free cooling system using dry cooler (드라이쿨러를 적용한 외기냉수냉방 시스템 설계에 관한 연구)

  • Yoon, Jung-In;Baek, Seung-Moon;Heo, Jeong-Ho;Kim, Young-Min;Son, Chang-Hyo
    • Journal of Advanced Marine Engineering and Technology
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    • v.38 no.9
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    • pp.1027-1031
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    • 2014
  • Free cooling system is used to reduce energy consumption of cooling system. Free cooling system is consisted of cooling group and dry-cooler in which heat exchange of chilled water and out air is conducted. Although this system has an excellent energy saving effect in place having cooling load regularly, data or material of design for free cooling system is lacked. In this study, characteristics analysis of free cooling system is conducted through software HYSYS with changing some facts. The main result is following as : Dry-cooler capacity is influenced by out air temperature, required chilled water temperature and LMTD(Logarithmic Mean Temperature Difference) of heat exchanger. As out air temperature is more low, dry-cooler capacity become increased. in addition, as required chilled water temperature is more high and LMTD is more low, the out air temperature range is widened for using dry-cooler. If out air temperature is below $0^{\circ}C$, antifreeze need to be used because freeze and burst can be occurred. In case of South Korea, antifreeze of 34% of ethylene glycol concentration is proper. When compressor load of R22, R134a and R407C is compared, considering environmental regulation and energy consumption, R134a is best working fluid.

A Study on the Effect of Large Coherent Structures to the Skin Friction by POD Analysis (적합직교분해(POD)기법을 사용한 난류 응집구조 거동에 관한 연구)

  • Shin, Seong-Yun;Jung, Kwang-Hyo;Kang, Yong-Duck;Suh, Sung-Bu;Kim, Jin;An, Nam-Hyun
    • Journal of the Society of Naval Architects of Korea
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    • v.54 no.5
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    • pp.406-414
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    • 2017
  • An experimental study in a recirculating water channel was carried out to investigate the effect of large coherent structures to the skin friction on a flat plate. Particle Image Velocimetry (PIV) technique was used to quantify characteristic features of coherent structures growing to the boundary layer. In the PIV measurement, it is difficult to calculate the friction velocity near the wall region due to laser deflection and uncertainty so that Clauser fitting method at the logarithmic region was adopted to compute the friction velocity and compared with the one directly measured by the dynamometer. With changing the free-stream velocity from 0.5 m/s to 1.0 m/s, the activity of coherent structures in the logarithmic region was increased over three times in terms of Reynolds stress. The flow field was separated by Variable Interval Time Averaging (VITA) technique into the weak and the strong structure case depending on the existence large coherent structures in order to validate its effectiveness. The stream-wise velocity fluctuation was scanned through at the boundary thickness whether it had a large deviation from background flow. With coherent structures connected from near-wall to the boundary layer, mean wall shear stress was higher than that of weak structure case. Proper Orthogonal Decomposition (POD) analysis was also applied to compare the energy budget between them at each free-stream velocity.

Development of Vibraction and Impact Noise Dampling Wood-based Composites(I) -Dynamic Mechanical and Vibration Damping Properties of Plasticized PVC- (진동.충격음 흡수성능을 지니는 목질계 복합재료의 개발(I) -가소화 폴리염화비닐의 동적점탄성과 진동흡수성능-)

  • 이현종
    • Journal of Korea Foresty Energy
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    • v.17 no.1
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    • pp.36-46
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    • 1998
  • The aim of this study was to develop the noise and vibration damping wood-based composites by using viscoelastic polymer materials. Polyvinylchloride(PVC) was plasticized with 20-140 phr bis(2-ethylhexyl) phthalate(DOP) and the dynamic tensile mechanical properties were measured at 110Hz and approximate temperature range -100 to 150$^{\circ}$ using a Rheovibron Instrument. The PVC/DOP blends were shown to be compatible in all proportions, and both T(E”$_{max}$) and T(tan${\delta}_{max}$) shifted to the lower temperature side as the DOP content increased. The vibration damping properties of wood/polymer composites were measured using the Rheovibron instrument in a bending mode. The composite damping factor(tan ${\delta}_{c}$) of wood /PVC-DOP/wood sandwich structure correlated with the loss factor and that of the coated structure correlated with the loss modulus(E”) of the polymer layer. In addition, the sandwich structure was found to be more effective in damping than the coated structure. The logarithmic decrement (${\Delta}$c) curve of a sandwich structure, which was determined by the free-free flexural vibration method was similar in shape to the tan ${\delta}_{c}$ curve.

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Experimental Study on Combustion Noise Characteristics in Turbulent Jet Diffusion Flames (난류 제트확산화염의 연소소음 특성에 관한 실험연구)

  • 김호석;오상헌
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.5
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    • pp.1253-1263
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    • 1994
  • The experimental study is carried out to identify the combustion generated noise mechanism in free turbulent jet diffusion flames. Axial mean fluctuating velocities in cold and reacting flow fields were measured using hot-wire anemometer and LDv.The overall sound pressure level and their spectral distribution in far field with and without combustion were also measured in an anechoic chamber. The axial mean velocity is 10-25% faster and turbulent intensities are about 10 to 15% smaller near active reacting zone than those in nonreacting flow fields. And sound pressure level is about 10-20% higher in reacting flow fields. It is also shown that the spectra of the combustion noise has lower frequency characteristics over a broadband spectrum. These results indicate that the combustion noise characteristics in jet diffusion flames are dominated by energy containing large scale eddies and the combusting flow field itself. Scaling laws correlating the gas velocity and heat of combustion show that the acoustic power of the combustion noise is linearly proportional to the 3.8th power of the mean axial velocity rather than 8th power in nonreacting flow fields, and the SPL increases linearly with logarithmic 1/2th power of the heat of combustion.

Chain Transfer to Monomer and Polymer in the Radical Polymerization of Vinyl Neo-decanoate

  • Balic, Robert;Fellows, Christopher M.;Van Herk, Alex M.
    • Macromolecular Research
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    • v.12 no.4
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    • pp.325-335
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    • 2004
  • Molecular weight distributions of poly(vinyl neo-decanoate) produced by the bulk polymerization of the monomer to low conversions were investigated to obtain values of the rate constants for the chain transfer to monomer ( $C_{M}$). The value of $C_{M}$ of 7.5($\pm$0.6)${\times}$10$^{-4}$ was obtained from a logarithmic plot of the number distribution at 5,25, and 5$0^{\circ}C$, which suggests that the activation energy for chain transfer is on the order of 20-25 kJ ㏖$^{-1}$ . These plots were linear between the number and weight-average degrees of polymerization, but not over the whole molecular weight range for which a significant signal was observed in the gel permeation chromatography (GPC) trace. Modeling suggests that the deviations observed at high molecular weights can be explained by branching of the chains through chain transfer to the polymer, with a branching density as low as 10$^{-5}$ , without affecting the slope at low values of the number of monomer unit, N. This deviation from the expected distribution of linear chains was used to estimate the branching densities at low conversion.ion.

Development of a Daily Solar Major Flare Occurrence Probability Model Based on Vector Parameters from SDO/HMI

  • Lim, Daye;Moon, Yong-Jae;Park, Jongyeob;Lee, Kangjin;Lee, Jin-Yi
    • The Bulletin of The Korean Astronomical Society
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    • v.42 no.2
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    • pp.59.5-60
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    • 2017
  • We present the relationship between vector magnetic field parameters and solar major flare occurrence rate. Based on this, we are developing a forecast model of major flare (M and X-class) occurrence rate within a day using hourly vector magnetic field data of Space-weather HMI Active Region Patch (SHARP) from May 2010 to April 2017. In order to reduce the projection effect, we use SHARP data whose longitudes are within ${\pm}60$ degrees. We consider six SHARP magnetic parameters (the total unsigned current helicity, the total photospheric magnetic free energy density, the total unsigned vertical current, the absolute value of the net current helicity, the sum of the net current emanating from each polarity, and the total unsigned magnetic flux) with high F-scores as useful predictors of flaring activity from Bobra and Couvidat (2015). We have considered two cases. In case 1, we have divided the data into two sets separated in chronological order. 75% of the data before a given day are used for setting up a flare model and 25% of the data after that day are used for test. In case 2, the data are divided into two sets every year in order to reduce the solar cycle (SC) phase effect. All magnetic parameters are divided into 100 groups to estimate the corresponding flare occurrence rates. The flare identification is determined by using LMSAL flare locations, giving more numbers of flares than the NGDC flare list. Major results are as follows. First, major flare occurrence rates are well correlated with six magnetic parameters. Second, the occurrence rate ranges from 0.001 to 1 for M and X-class flares. Third, the logarithmic values of flaring rates are well approximated by two linear equations with different slopes: steeper one at lower values and lower one at higher values. Fourth, the sum of the net current emanating from each polarity gives the minimum RMS error between observed flare rates and predicted ones. Fifth, the RMS error for case 2, which is taken to reduce SC phase effect, are smaller than those for case 1.

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Mechanical and Rheological Properties of Rice Plant (수도(水稻)의 역학적(力學的) 및 리올러지 특성(特性)에 관(關)한 연구(硏究))

  • Huh, Yun Kun;Cha, Gyun Do
    • Korean Journal of Agricultural Science
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    • v.14 no.1
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    • pp.98-133
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    • 1987
  • The mechanical and rheological properties of agricultural materials are important for engineering design and analysis of their mechanical harvesting, handling, transporting and processing systems. Agricultural materials, which composed of structural members and fluids do not react in a purely elastic manner, and their response when subjected to stress and strain is a combination of elastic and viscous behavior so called viscoelastic behavior. Many researchers have conducted studies on the mechanical and rheological properties of the various agricultural products, but a few researcher has studied those properties of rice plant, and also those data are available only for foreign varieties of rice plant. This study are conducted to experimentally determine the mechanical and the rheological properties such as axial compressive strength, tensile strength, bending and shear strength, stress relaxation and creep behavior of rice stems, and grain detachment strength. The rheological models for the rice stem were developed from the test data. The shearing characteristics were examined at some different levels of portion, cross-sectional area, moisture content of rice stem and shearing angle. The results obtained from this study were summarized as follows 1. The mechanical properties of the stems of the J aponica types were greater than those of the Indica ${\times}$ Japonica hybrid in compression, tension, bendingand shearing. 2. The mean value of the compressive force was 80.5 N in the Japonica types and 55.5 N in the Indica ${\times}$ Japonica hybrid which was about 70 percent to that of the Japonica types, and then the value increased progressively at the lower portion of the stems generally. 3. The average tensile force was about 226.6 N in the Japonica types and 123.6 N in the Indica ${\times}$ Japonica hybrid which was about 55 percent to that of the Japonica types. 4. The bending moment was $0.19N{\cdot}m$ in the Japonica types and $0.13N{\cdot}m$ in the Indica ${\times}$ Japonica hybrid which was 68 percent to that of the Japonica types and the bending strength was 7.7 MPa in the Japonica types and 6.5 MPa in the Indica ${\times}$ Japonica hybrid respectively. 5. The shearing force was 141.1 N in Jinju, the Japonica type and 101.4 N in Taebaeg, the Indica ${\times}$ Japonica hybrid which was 72 percent to that of Jinju, and the shearing strength of Taebaeg was 63 percent to that of Jinju. 6. The shearing force and the shearing energy along the stem portion in Jinju increased progressively together at the lower portions, meanwhile in Taebaeg the shearing force showed the maximum value at the intermediate portion and the shearing energy was the greatest at the portion of 21 cm from the ground level, and also the shearing strength and the shearing energy per unit cross-sectional area of the stem were the greater values at the intermediate portion than at any other portions. 7. The shearing force and the shearing energy increased with increase of the cross-sectional area of the rice stem and with decrease of the shearing angie from $90^{\circ}$ to $50^{\circ}$. 8. The shearing forces showed the minimum values of 110 N at Jinju and of 60 N at Taebaeg, the shearing energy at the moisture content decreased about 15 percent point from initial moisture content showed value of 50 mJ in Jinju and of 30 mJ in Taebaeg, respectively. 9. The stress relaxation behavior could be described by the generalized Maxwell model and also the compression creep behavior by Burger's model, respectively in the rice stem. 10. With increase of loading rate, the stress relaxation intensity increased, meanwhile the relaxation time and residual stress decreased. 11. In the compression creep test, the logarithmic creep occured at the stress less than 2.0 MPa and the steady-state creep at the stress larger than 2.0 MPa. 12. The stress level had not a significant effect on the relaxation time, while the relaxation intensity and residual stress increased with increase of the stress level. 13. In the compression creep test of the rice stem, the instantaneous elastic modulus of Burger's model showed the range of 60 to 80 MPa and the viscosities of the free dashpot were very large numerical value which was well explained that the rice stem was viscoelastic material. 14. The tensile detachment forces were about 1.7 to 2.3 N in the Japonica types while about 1.0 to 1.3 N in Indica ${\times}$ Japonica hybrid corresponding to 58 percent of Japonica types, and the bending detachment forces were about 0.6 to 1.1 N corresponding to 30 to 50 percent of the tensile detachment forces, and the bending detachment of the Indica ${\times}$ Japonica hybrid was 0.1 to 0.3 N which was 7 to 21 percent of Japonica types. 15. The detachment force of the lower portion was little bigger than that of the upper portion in a penicle and was not significantly affected by the harvesting period from September 28 to October 20. 16. The tensile and bending detachment forces decreased with decrease of the moisture content from 23 to 13 percent (w.b.) by the natural drying, and the decreasing rate of detachment forces along the moisture content was the greater in the bending detachment force than the tensile detachment force.

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