A class of symplectic partitioned Runge–Kutta methods

This paper deals with some relevant properties of Runge–Kutta (RK) methods and symplectic partitioned Runge–Kutta (PRK) methods. First, it is shown that the arithmetic mean of a RK method and its adjoint counterpart is symmetric. Second, the symplectic adjoint method is introduced and a simple way to construct symplectic PRK methods via the symplectic adjoint method is provided. Some relevant properties of the adjoint method and the symplectic adjoint method are discussed. Third, a class of symplectic PRK methods are proposed based on Radau IA, Radau IIA and their adjoint methods. The structure of the PRK methods is similar to that of Lobatto IIIA–IIIB pairs and is of block forms. Finally, some examples of symplectic partitioned Runge–Kutta methods are presented.     

Reanalysis of the photoassociation spectrum of 133Cs2 （6P3/2） lg state

Reanalysis of the photoassociation spectrum of the weakly binding （6S1/2 ＋ 6P3/2） lg 133Cs2 levels, reported in the previous study [J. Mol. Spectro. 255 （2009） 106], is performed by using a Lu-Fano graph coupled to the improved LeRoy- Bernstein formula including two additional modified terms. A more accurate coefficient （c3） is obtained for the leading long-range potential （-c3/R3） of a diatomic molecule.     

Monitoring the reaction between AlCl_3 and o-xylene by using terahertz spectroscopy

Terahertz time-domain spectroscopy(THz-TDS)is used to study the interaction between AlCl3and o-xylene in a temperature range from 300 K to 368 K.For comparison,the three isomers of o-,m-,and p-xylene are measured by using THz-TDS.The o-xylene carries out isomerization reaction in the presence of catalyst AlCl3.The absorption coefficient of the mixed reaction solution is extracted and analyzed in the frequency range from 0.2 THz to 1.4 THz.The temperature dependence of the absorption coefficient,which is influenced by both the dissolution of AlCl3and the production of the two other isomer resultants,is obtained,and it can indicate the process of the isomerization reaction.The results suggest that THz spectroscopy can be used to monitor the isomerization reaction and other reactions in chemical synthesis,petrochemical and biomedical fields.     

Accuracy Improvement in the Measurement of the Non-Linear Coefficient of Optical Fibers Based on Self-Phase Modulation

Abstract

A novel and simple procedure to improve the accuracy of the measurement of the third-order Kerr non-linear coefficient of optical fibers based on self-phase modulation is described. It includes an efficient method to identify the chirp of the input pulse. A standard single-mode fiber and a highly non-linear microstructure chalcogenide fiber have been measured. The accuracy of the measurement is increased to ±5% instead of ±19% with the classical self-phase modulation method in this case.     

Effect of Ethanol on the Partition Coefficient Of Cyclohexylacetate Between Bulk and Cetyltrjmethylammonium Bromide Micellar Pseudophases

Variation of the partition coefficient of cyclohexylacetate (CA) was studied by a differential absorption spectroscopic method as a function of ethanol and (CTAB) cetyltrimethylammoniumbromide concentrations. Approach used was based upon the pseudo-two phase model, including effect of ethanol concentrations on the critical micelle concentration (CMC) of CTAB. Ethanol enhanced micelle formation of CTAB at concentrations below 1% by volume, had a slight inhibitory effect at higher concentrations and totally inhibited at a concentration above 15% by volume.

Various amounts of ethanol were used with a purpose of changing the solubility of CA in water. The differential absorbance (AA), was almost zero at low concentrations of CTAB, however an increase in AA began at a certain concentration of CTAB which can accordingly be assumed to be consistent with CMC of CTAB in the presence of ethanol. As CTAB concentration increased above CMC, ΔA reached a plateau. In this plateau, ΔA can reasonably be interpreted as the saturation of CA in micellar phase.

Plateau values of ΔA decreased with increasing ethanol concentration. This showed that the fraction of CA in the micellar phase depended on the ethanol concentration in terms of changing the solubility. Partition coefficients, K_c, were obtained from the plots of 1/ΔA against 1/[C_CA] +[C³ _m], which were linear in high CTAB concentrations. It was also seen that as ΔA, K_c decreased when the ethanol percentage were increased. In other words, the lower the solubility of CA in the bulk, the higher the partition coefficient.     

Mechanistic study of the reaction of methyl peroxy radical (CH3O2) with formaldehyde (CH2O)

ABSTRACT

A direct dynamic study on the reactions of CH₃O₂?+?CH₂O was carried out over the temperature range of 300–1500?K. All stationary points were calculated with the M06-2X/6-311++G(d,p) level of theory and identified for local minimum. The energetic parameters were refined at QCISD (T)/cc-pVTZ and CCSD (T)/cc-pVTZ levels of theory. Three channels were explored and a reaction of hydrogen abstraction from CH₂O by CH₃O₂ was identified as dominant channel which involves the formation of a prereactive complex in the entrance channel. The rate coefficient of the dominant channel was calculated with TST and TST/Eck and the Eckart tunnelling effect is only important over the lower temperature region. The calculated rate coefficient of the dominant channel has positive temperature dependence and agrees reasonably with the available literature data.     

Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis

Hesitant fuzzy sets (HFSs), which allow the membership degree of an element to a set represented by several possible values, can be considered as a powerful tool to express uncertain information in the process of group decision making. We derive some correlation coefficient formulas for HFSs and apply them to clustering analysis under hesitant fuzzy environments. Two real world examples, i.e. software evaluation and classification as well as the assessment of business failure risk, are employed to illustrate the actual need of the clustering algorithm based on HFSs, which can incorporate the difference of evaluation information provided by different experts in clustering processes. In order to extend the application domain of the clustering algorithm in the framework of HFSs, we develop the interval-valued HFSs and the corresponding correlation coefficient formulas, and then demonstrate their application in clustering with interval-valued hesitant fuzzy information through a specific numerical example.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.