Period-doubling and chaotic oscillations in the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

硬木热解过程中颗粒内部二次反应的数值研究Ⅱ.数值模拟结果

为了研究生物质（硬木）热解过程中颗粒内部的二次反应，对流化床环境下单颗粒生物质热解模型进行了求解。计算针对典型大颗粒和典型小颗粒在流化床反应器反应条件下的热解过程，对不同大小颗粒内部各种产物的生成、消耗、积累以及逃逸行为进行了定量描述。计算结果表明：对于直径为2mm的小颗粒，颗粒内二次裂解的份额可以忽略，但是对于直径10mm的大颗粒，热争过程中有超过20%的一次焦油参加了颗粒内部二次反应，颗粒内二次裂解显著地改变了热解产物分布，改变了热解产物的品质。     

Swelling of poly(N-isopropylacrylamide) gels in water-aprotic solvent mixtures

The swelling volume of poly(N-isopropylacrylamide) (PIPAAm) gel in aprotic solvents (acetonitrile (AcN)-, tetrahydrofuran (THF)-, 1,4-dioxane (DO)- and dimethylsulfoxide (DMSO))-water mixtures was measured at 25°C. The gel swollen in water shrank first and then reswelled with addition of the aprotic solvents. At an intermediate mole fraction (XDMSO) range of DMSO-water mixtures, the gel demonstrated a reentrant swelling phenomenon the hydrated gel shrank first on addition of a small amount of solvent, showed a typical wide reentrant transition, and gradually reswelled in the range near pure solvent. On the other hand, the gels in AcN-, THF-, and DO-water mixtures demonstrated a reentrant-convex swelling phenomenon: the gels reswelled after a reentrant phase transition in low Xorg (XAcN, XTHF and XDO), showed a maximum swelling in the intermediate Xorg region, and shrank again gradually in the high Xorg region. Such a swelling behavior of the gel was interpreted by correlating with solution properties of the aqueous aprotic solvent mixtures.The strength of hydrogen bonding around amide groups of the homopolymer was examined in pure solvents (water, THF, and DMSO) and in all proportion of aqueous THF to observe the relation with swelling behavior of gel by spectrum analysis of the amide I and II bands of Fourier Transform Infrared Spectroscopy (FT-IR). The swelling properties of gels in solvents and the aqueous mixtures were well correlated with the peak shifts of amide groups of the homopolymer.     

Radio-frequency induction plasmas at atmospheric pressure: Mixtures of hydrogen,nitrogen, and oxygen with argon

Numerical calculations are reported which simulate atmospheric-pressure radiofrequency induction plasmas consisting of either pure argon or mixtures of argon with hydrogen, nitrogen, or oxygen. These calculations are compared to observations of laboratory plasmas generated with the same geometry and run conditions. The major features of the laboratory plasmas are predicted well by the calculations: the pure argon plasma is the largest, with the argon-oxygen plasma slightly smaller. The argon-nitrogen plasma is considerably smaller and the argon-hydrogen plasma is the shortest, although somewhat fatter than the argon-nitrogen case. The calculations are not entirely successful in predicting the exact location of the plasmas relative to the coils. A likely explanation is that there is significant uncertainty regarding the actual power coupled to the laboratory plasmas.     

Dielectric study on pure and KOH-doped tetrahydrofuran clathrate hydrates

Complex dielectric permittivities of pure and KOH-doped (x = 1.8 x 10^–4) tetrahydrofuran clathrate hydrates were measured in the temperature range 20–260 K and in the frequency range 20 Hz-1 MHz. The relaxation time of the water reorientational motion was found to decrease drastically as a result of the doping; e.g., the relaxation time of the doped sample was 10^–9 times shorter than that of the pure sample at 70 K. The activation enthalpy of the motion was reduced to 7.4 kJ mol^–1. On cooling the crystal, the value of decreased suddenly at the 62 K phase transition to the ₂ value of the pure sample and at the same time disappeared. No dispersion effect due to the guest reorientation was observed below the transition. These data indicate that both the host and guest molecules become ordered or, at least, change their mobility drastically. In the pure sample, a relaxation phenomenon of ₀₂ was found around the glass transition region. The relaxation times agreed well with those derived from the enthalpy of relaxation in a calorimetric study.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.     

The W algorithm and the D transformation for the numerical evaluation of three‐center nuclear attraction integrals

Three‐center nuclear attraction integrals over exponential‐type functions are required for ab initio molecular structure calculations and density functional theory (DFT). These integrals occur in many millions of terms, even for small molecules, and they require rapid and accurate numerical evaluation. The use of a basis set of B functions to represent atomic orbitals, combined with the Fourier transform method, led to the development of analytic expressions for these molecular integrals. Unfortunately, the numerical evaluation of the analytic expressions obtained turned out to be extremely difficult due to the presence of two‐dimensional integral representations, involving spherical Bessel integral functions. % The present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of these spherical Bessel integrals. This algorithm, which is based on the nonlinear D transformation and the W algorithm of Sidi, can be computed recursively, allowing the control of the degree of accuracy. Numerical analysis tests were performed to further improve the efficiency of our algorithm. The numerical results section demonstrates the efficiency of this new algorithm for the numerical evaluation of three‐center nuclear attraction integrals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.     

强流电子束泵浦XeCl准分子激光动力学模型

强流电子束泵浦XeCl准分子激光动力学模型由三部分组成,即电子束能量沉积的计算;电子温度、电子反应速率的计算和化学/激光动力学。这个模型可以准确地预报小信号增益、吸收等激光特征量的时间变化规律。 该模型是在文献[1]、[2]、[3]报导的动力学模型的基础上提出的。采用四阶龙格_库塔法在VAX—11/780机器上进行数值求解。 计算给出XeCl准分子激光反应过程中各种粒子浓度、小信号增益、吸收、输出光强、激发速率以及平均电子能量随时间的变化规律。计算结果表明本征效率是激发速率,电流密度和工作气体(Ne/Xe/HCl)的各分压比的函数。 该模型可为高功率准分子激光器的研制提供设计参数和最佳实验条件。     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.