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Classical Critical Behaviors and Ginzburg Criteria for Polymer Mixtures
조준한 한국고분자학회 2021 Macromolecular Research Vol.29 No.10
We provide a pedagogical argument on classical critical behaviors of polymer mixtures, which include an ordinary critical point and several multicritical points such as tricritical, isotropic Lifshitz, and isotropic Lifshitz tricritical points. Various scaling exponents and singularities near those critical points are first derived through analyzing Landau free energies in general but suitable forms. A simple binary blend of A and B homopolymers in the mean-field picture is taken as an example of the ordinary critical point to verify its critical exponents and scaling laws by formulating its Landau free energy with the explicit vertex coefficients. A ternary blend consisting of A and B homopolymers of the same sizes and also symmetric A-B diblock copolymer is then employed to get the classical critical exponents and scaling laws for the multicritical points through directly evaluating phase equilibria and scattering functions with varying chain length ratios. In addition, the validity of the meanfield description in the vicinity of those critical points is discussed based on Ginzburg criteria and upper critical dimensions.
조준한,김성호,한종현,이병생 대한교통학회 2006 大韓交通學會誌 Vol.24 No.6
This research is to the selection of optimal probability distribution as well as the estimation for design hourly factor in consideration of traffic characteristic, such as road function, lane number and AADT. To accomplish the objectives, we are applied to various probability distribution using traffic data that observed at permanent traffic count points in 2005. The parameters of the selected 14 probability distribution were estimated based on the method of maximum likelihood and the validity condition of the estimated parameter. The goodness-of-fit test, such as chi-square test, was performed as well as the estimation of design hourly factor. As a result, An appropriate distributions of each case were selected : Pearson Ⅴ for two lane of rural roads, LogLogistic for the four lane of rural roads, LogLogistic for the urban roads, Extreme value for recreation roads. And optimal K factor are as following : 0.1~0.2 for two lane of rural roads, 0.09~0.14 for the four lane of rural roads, 0.07~0.13 for the urban roads, 0.1~0.2 for recreation roads. 본 연구는 도로의 기능 및 통행특성, 차로수, 연평균일교통량 등을 고려하여 설계시간계수와의 관계를 살펴보고 적정 확률분포형 선정과 K값을 추정하였다. 이를 위해 2005년도 상시 교통량 조사지점에서 수집된 교통자료를 이용하여 14개의 확률분포형을 적용하였다. 각 확률분포형은 최우도법을 이용하여 매개변수를 추정하였으며 각 분포형별로 매개변수 적합성 조건을 검토하였다. 적정 확률분포형의 결정은 chi-square검정을 통하여 대상 분포형의 기각유무를 판단하였으며, 그 결과에 대해 우선순위를 정하여 적정 확률분포형을 선정하였다. 그리고 각 유형별 AADT에 따른 적정 K계수를 추정하였다. 그 결과, 지방부 2차로 및 4차로, 도시부, 관광부도로의 적정 확률분포형은 각각 Pearson V, LogLogistic, LogLogistic, Extreme value 분포로 분석되었으며, 적정 K계수는 각각 0.1~0.2, 0.09~0.14, 0.07~0.13, 0.1~0.2로 추정되었다.