On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Polymer crystallization dynamics,as reflected by differential scanning calorimetry. Part 2: Numerical simulations

With the aid of a model for the kinetics of polymer crystallization, as put forward in previous publications, the shape of DSC-curves and their position on the temperature scale were simulated for various conditions of heat transfer in the apparatus. It turns out that the outcome is very dependent on the assumptions made with respect to these heat transfer conditions. For the ideal condition — no temperature differences between sample, pan and furnace — an invariable shape is predicted for the DSC-curves. They only shift to lower temperatures with increasing cooling rates. For more realistic conditions, the curves not only shift but become broader and their maxima decrease. They show a more familiar appearance. These calculations are very involved, however, A simple balance equation is shown to yield equivalent results, if a dimensionless characteristic number like the Nusselt number remains considerably smaller than one. This number contains an effective heat transfer coefficient between sample and furnace which, surprisingly, should not be too high. Apparently, the heat capacity of the pan does not play an important role under these conditions. This is investigated in Appendix II. Appendix I describes the procedure of the numerical simulations.     

Comparison between adsorption isotherm determination techniques and overloaded band profiles on four batches of monolithic columns

The adsorption isotherms of 4-tert.-butyl phenol were measured on four different monolithic columns, using three different techniques, classical frontal analysis (FA), the perturbation on a plateau method (PP) and the recently introduced numerical procedure known as the inverse numerical method (IN). This last approach requires only the recording of a few overloaded profiles and has the potential advantage of affording a dramatic decrease of the amounts of compounds, solvent, and time needed to determine accurate estimates of the coefficients of the isotherm. The reproducibility of the adsorption data measured on the four columns is discussed with reference to the specific techniques used for obtaining these data and to the most suitable equation used for modeling them. The data obtained for the different columns were highly consistent. The inverse numerical approach was confirmed to provide a powerful, accurate, and economic method for measuring single component adsorption data.     

旋流煤粉燃烧的一维综合数值模拟

发展了综合考虑气－固两相旋流流动，气相燃烧，颗粒相变与燃烧及两相辐射传热的旋流煤粉燃烧－维数学模型，给出了气－固两相能量方程中颗粒相就源项的计算表达式，应用这一模型对涡旋燃烧炉环形通道内多组工况的旋流气体燃烧和煤粉燃烧进行了数值模拟，计算得到的炉内温度分布和燃烧效率与实验数据基本相符，表明本文建立的模型可用于旋流煤粉燃烧的一维综合数值模拟。     

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。     

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.     

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。