• Title, Summary, Keyword: computational group theory

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Theoretical Studies on Mechanism and Kinetics of the Hydrogen-Abstraction Reaction of CF3CH2CHO with OH Radicals

  • Ci, Cheng-Gang;Yu, Hong-Bo;Wan, Su-Qin;Liu, Jing-Yao;Sun, Chia-Chung
    • Bulletin of the Korean Chemical Society
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    • v.32 no.4
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    • pp.1187-1194
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    • 2011
  • The hydrogen abstraction reaction of $CF_3CH_2CHO$ + OH has been studied theoretically by dual-level direct dynamics method. Two stable conformers, trans- and cis-$CF_3CH_2CHO$, have been located, and there are four distinct OH hydrogen-abstraction channels from t-$CF_3CH_2CHO$ and two channels from c-$CF_3CH_2CHO$. The required potential energy surface information for the kinetic calculation was obtained at the MCG3-MPWB//M06-2X/aug-cc-pVDZ level. The rate constants, which were calculated using improved canonical transitionstate theory with small-curvature tunneling correction (ICVT/SCT) were fitted by a four-parameter Arrhenius equation. It is shown that the reaction proceeds predominantly via the H-abstraction from the -CHO group over the temperature range 200-2000 K. The calculated rate constants were in good agreement with the experimental data between 263 and 358 K.

FULL NON-RIGID GROUP OF 2,3,5,6-TETRAMETHYLEPYRAZINE AS WREATH PRODUCT AND ITS SYMMETRY

  • Arezoomand, Majid;Taeri, Bijan
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.915-931
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    • 2009
  • The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to deduce the character table of the full non-rigid molecule group (f-NRG) of 2,3,5,6-Tetramethylpyrazine The f-NRG of this molecule is seen to be isomorphic to the group $\mathbb{Z}_3{\wr}(\mathbb{Z}_2{\times}\mathbb{Z}_2)$, where $\mathbb{Z}_n$ is the cyclic group of order n, of order 324 which has 45 conjugacy classes. We determine the some properties and relations between characters of the group. Also, we examine the symmetry group of this molecule and show that its symmetry group is $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

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Reliability analysis by numerical quadrature and maximum entropy method

  • Zhu, Tulong
    • Structural Engineering and Mechanics
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    • v.3 no.2
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    • pp.135-144
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    • 1995
  • Since structural systems may fail in any one of several failure modes, computation of system reliability is always difficult. A method using numerical quadrature for computing structural system reliability with either one or more than one failure mode is presented in this paper. Statistically correlated safety margin equations are transformed into a group of uncorrelated variables and the joint density function of these uncorrelated variables can be generated by using the Maximum Entropy Method. Structural system reliability is then obtained by integrating the joint density function with the transformed safety domain enclosed within a set of linear equations. The Gaussian numerical integration method is introduced in order to improve computational accuracy. This method can be used to evaluate structural system reliability for Gaussian or non-Gaussian variables with either linear or nonlinear safety boundaries. It is also valid for implicit safety margins such as computer programs. Both the theory and the examples show that this method is simple in concept and easy to implement.

A Computational Investigation of the Stability of Cyclopropyl Carbenes

  • Baik, Woon-Phil;Yoon, Cheol-Hun;Koo, Sang-Ho;Kim, Byeong-Hyo
    • Bulletin of the Korean Chemical Society
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    • v.25 no.1
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    • pp.90-96
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    • 2004
  • The conformations of dicyclopropyl, isopropyl cyclopropyl, and diisopropylcarbenes were optimized using density functional theory (B3LYP/6-31G(d)). We showed that the optimized geometries of carbenes with cyclopropyl groups are fully in accord with those expected for bisected W-shaped conformations, in which the effective hyperconjugation of a cyclopropyl group with singlet carbene can occur. The stabilization energies were evaluated at the B3LYP/6-311+G(3df, 2p)//B3LYP/6-31G(d) + ZPE level using an isodesmic equation. The relative stability of carbenes is in the order $(c-Pr)_2$C: > (i-Pr)(c-Pr)C: > $(i-Pr)_2$C:, and a cyclopropyl group stabilizes carbene more than an isopropyl group by nearly 9 kcal/mol. Energies for the decomposition of diazo compounds to carbenes increase in the order $(c-Pr)_2$ < (i-Pr)(c-Pr) < $(i-Pr)_2$ by ~9 kcal/mol each. From a singlettriplet energy gap ($E_{ST}$) calculation, the singlet level is lower than the triplet level and the $E_{ST}$ shows a trend similar to the stabilization energy calculations. For comparison, the optimized geometries and stabilization energies for the corresponding carbocations were also studied at the same level of calculation. The greater changes in geometries and the higher stabilization energies for carbocations compared to carbenes can explain the greater hyperconjugation effect.

A new meta-heuristic optimization algorithm using star graph

  • Gharebaghi, Saeed Asil;Kaveh, Ali;Ardalan Asl, Mohammad
    • Smart Structures and Systems
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    • v.20 no.1
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    • pp.99-114
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    • 2017
  • In cognitive science, it is illustrated how the collective opinions of a group of individuals answers to questions involving quantity estimation. One example of this approach is introduced in this article as Star Graph (SG) algorithm. This graph describes the details of communication among individuals to share their information and make a new decision. A new labyrinthine network of neighbors is defined in the decision-making process of the algorithm. In order to prevent getting trapped in local optima, the neighboring networks are regenerated in each iteration of the algorithm. In this algorithm, the normal distribution is utilized for a group of agents with the best results (guidance group) to replace the existing infeasible solutions. Here, some new functions are introduced to provide a high convergence for the method. These functions not only increase the local and global search capabilities but also require less computational effort. Various benchmark functions and engineering problems are examined and the results are compared with those of some other algorithms to show the capability and performance of the presented method.

Computational Study on the Conformational Characteristics of Calix[4]pyrrole Derivatives

  • Hong, Joo-Yeon;Son, Min-Kyung;Ham, Si-Hyun
    • Bulletin of the Korean Chemical Society
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    • v.30 no.2
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    • pp.423-428
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    • 2009
  • The comparative study of three calix[4]heterocycles (calix[4]pyrrole, calix[4]furan, and calix[4]thiophene) has been theoretically performed by using high-level density functional theory (DFT) at the MPWB1K/6-311G$^{**}$//B3LYP/6- 311G$^{**}$ level. The effect of different hetero-atoms (nitrogen, oxygen, and sulfur) placed in the heterocycles on the conformational flexibility, thermodynamic stability order, cavity sizes, charge distributions, and binding propensities are examined. The thermodynamic stability differences between the conformers are found to be much greater in calix[4]pyrrole compared to those in calix[4]furan and calix[4]thiophene. Relatively larger NH group and higher dipole of a pyrrole ring in calix[4]pyrrole contribute to the higher energy barrier for the conformational conversions and relatively rigid potential energy surface compared to the case of calix[4]furan and calix[4]thiophene. The computational results herein provide theoretical understanding of the conformational flexibility and the thermodynamic nature which can be applied to understand the complexation behavior of the three calix[4]heterocycles.

Computational aspects of guided wave based damage localization algorithms in flat anisotropic structures

  • Moll, Jochen;Torres-Arredondo, Miguel Angel;Fritzen, Claus-Peter
    • Smart Structures and Systems
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    • v.10 no.3
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    • pp.229-251
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    • 2012
  • Guided waves have shown a great potential for structural health monitoring (SHM) applications. In contrast to traditional non-destructive testing (NDT) methodologies, a key element of SHM approaches is the high process of automation. The monitoring system should decide autonomously whether the host structure is intact or not. A basic requirement for the realization of such a system is that the sensors are permanently installed on the host structure. Thus, baseline measurements become available that can be used for diagnostic purposes, i.e., damage detection, localization, etc. This paper contributes to guided wave-based inspection in anisotropic materials for SHM purposes. Therefore, computational strategies are described for both, the solution of the complex equations for wave propagation analysis in composite materials based on exact elasticity theory and the popular global matrix method, as well as the underlying equations of two active damage localization algorithms for anisotropic structures. The result of the global matrix method is an angular and frequency dependent wave velocity characteristic that is used subsequently in the localization procedures. Numerical simulations and experimental investigations through time-delay measurements are carried out in order to validate the proposed theoretical model. An exemplary case study including the calculation of dispersion curves and damage localization is conducted on an exemplary unidirectional composite structure where the ultrasonic signals processed in the localization step are simulated with the spectral element method. The proposed study demonstrates the capabilities of the proposed algorithms for accurate damage localization in anisotropic structures.

Degradation of Sulfonamide Antibiotic Substances by Ozonation: An Experimental and Computational Approach (설폰아미드계 항생물질의 오존산화분해에 대한 계산화학적 해석 및 실험적 검증)

  • Won, Jung Sik;Lim, Dong Hee;Seo, Gyu Tae
    • Journal of Korean Society of Environmental Engineers
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    • v.36 no.6
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    • pp.442-450
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    • 2014
  • Concern has grown over a presence of micropollutants in natural water since sulfonamide antibiotic substances such as sulfamethazine, sulfamethoxazole, sulfathiazole have been frequently detected in Nakdong River, Korea. The current work investigates the degradation of the three sulfonamide substances by using quantum chemistry calculations of density functional theory (DFT) and experimental measurement techniques of Fourier transform infrared spectroscopy (FT-IR) and ultraviolet-visible spectrophotometer (UV-VIS). DFT calculations demonstrate that the lowest energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbitals (LUMO) lies in sulfanilamide functional group of sulfonamide, implying that the sulfanilamide functional group would be the most active site for ozone oxidation. Also, UV-VIS spectra and FT-IR analysis reveal that 260 nm band originated from sulfanilamide group was absent after ozone oxidation, indicating that a functional group of amine (N-H) was removed from sulfanilamide. Both theoretical and experimental observations agree well with each other, demonstrating the DFT calculation tool can be an alternative tool for the prediction of chemical reactions in purification treatment processes.

CONVEX POLYTOPES OF GENERALIZED DOUBLY STOCHASTIC MATRICES

  • Cho, Soo-Jin;Nam, Yun-Sun
    • Communications of the Korean Mathematical Society
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    • v.16 no.4
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    • pp.679-690
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    • 2001
  • Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

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Prediction Model of the Exit Cross Sectional Shape of Workpiece in Round-Oval-Round Pass Rolling

  • Lee, Youngseog;Kim, Byung-Min;Kim, Dong-Hwan
    • Journal of Mechanical Science and Technology
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    • v.16 no.6
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    • pp.785-798
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    • 2002
  • A reliable analytic model that predicts the surface profile of the exit cross section of workpiece in round-oval (or oval-round) pass sequence is established. The presented model does not require any plasticity theory but needs the only geometric information on workpiece and roll groove. Formulation is based on the linear interpolation of the radius of curvature of an incoming workpiece and that of roll groove in the roll axis direction when the maximum spread of workpiece is known beforehand. The validity of the analytic model is examined by hot rod rolling experiment with the roll gap, specimen size, design parameter of oval groove and steel grade changed. Results revealed that the cross sectional shapes predicted by the model were in good agreement with those obtained experimentally. We found that the analytic model not only has simplicity and accuracy for practical usage but also saves a large amount of computational time in comparison with finite element method.