An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

偶极积分与Boys法分子轨道定域化

定域分子轨道在分子体系的化学图象和物理图象之间充当重要的桥梁作用,它的产生依赖于定域化准则,其中最普遍使用的是Foster-Boys和Edmiston-Ruedenberg(E—R)提出的两种定域化准则。这两种定域化准则是等价的,因而结果也是一致的。但对于E—R定域化来说,由于涉及到大量的多中心积分的计算,计算极为费时,因而远不如Foster-Boys定     

A new algorithm to evaluate bielectronic integrals with 1s Slater‐type orbitals obtained by the integral transforms

This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12|34), with 1s Slater‐type orbitals. It is proved that it is possible to define, out of the expression of (12|34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) = (12|34). Therefore, F(q) may be used to calculate (12|34). It is shown that the evaluation of F(Q) turns out to be simpler than the three‐dimensional integral involved in the calculation of (12|34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10^?3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

化学反应动力学研究法──自函数回归法及其应用

由完全非线性函数经变换得到自函数递推方程．根据回归分析理论，建立了一种化学反应动力学研究法──自函数回归法．应用该法在25℃水溶液中研究了乙酸乙酯和了酸乙酯的皂化反应的动力学常数．     

On a New Formulation of the Real-Time Propagator

The development of theoretical tools for the study of dynamical phenomena of many-particle systems on the quantum level is a fundamental challenge since many decades. A lot of efforts have been invested on Feynman's path integral approach, however, no computationally tractable method for investigating realistic systems could be developed up to now. In this paper we propose an alternative representation of the real-time many-body evolution operator formulated within the framework of the auxiliary field formalism. Our goal is to derive a new auxiliary field functional integral representation, in which the large oscillations of the functional integrand are reduced, in order to render the auxiliary field approach more attractive for real-time computation. This objective is attained using a generalized version of the method of Gaussian equivalent representation of Efimov and Ganbold [Phys. Stat. Sol. 168 (1991) 165], which eliminates the low-order fluctuations of the auxiliary field from the interaction functional.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Approximate formulae for calculation of the integral òT0Tmexp(-E/RT)dT

Summary In this paper two approximate formulae have been developed for calculation of the integral ò^T₀T^mexp(-E/RT)dT by using integration-by-parts approaches. They are in the following forms: I(m,T) = (RT^m+2)/(E+(m+2)RT)exp(-E/RT) I(m,T) = (RT^m+2)/(E+(m+2)(0.00099441E+0.93695599RT)exp(-E/RT) The validity of the two formulae has been confirmed and their accuracies have been tested with data from numerical calculating. In contrast to existing other integral methods, both the present approaches are simply used, accurate, and can be used for arbitrary values of m.     

Chemical reaction dynamics of PeCB and TCDD decomposition: A tight‐binding quantum chemical molecular dynamics study with first‐principles parameterization

The decomposition reaction dynamics of 2,3,4,4′,5‐penta‐chlorinated biphenyl (2,3,4,4′,5‐PeCB), 3,3′,4,4′,5‐penta‐chlorinated biphenyl (3,3′,4,4′,5‐PeCB), and 2,3,7,8‐tetra‐chlorinated dibenzo‐p‐dioxin (2,3,7,8‐TCDD) was clarified for the first time at atomic and electronic levels, using our novel tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization. The calculation speed of our new method is over 5000 times faster than that of the conventional first‐principles molecular dynamics method. We confirmed that the structure, energy, and electronic states of the above molecules calculated by our new method are quantitatively consistent with those by first‐principles calculations. After the confirmation of our methodology, we investigated the decomposition reaction dynamics of the above molecules and the calculated dynamic behaviors indicate that the oxidation of the 2,3,4,4′,5‐PeCB, 3,3′,4,4′,5‐PeCB, and 2,3,7,8‐TCDD proceeds through an epoxide intermediate, which is in good agreement with the previous experimental reports and consistent with our static density functional theory calculations. These results proved that our new tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization is an effective tool to clarify the chemical reaction dynamics at reaction temperatures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005