Diffusion in Lorentz lattice gas automata with backscattering

The probability of first return to the initial intervalx and the diffusion tensorD _x are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values forx andD _x apply also to a regular space lattice with a fraction of sites occupied by a scatterer in the limit of a small concentration of scatterers. If backscattering occurs, the results are very different from the Boltzmann approximation. The theory is applied to different types of lattices and different types of scatterers having rotational or mirror symmetries.     

Self-consistent-field – Hartree–Fock method with finite nuclear mass corrections

We have upgraded a Self-consistent-field – Hartree–Fock routine to include a finite nuclear mass correction for molecules developed in our laboratory. The new routine can handle isotopomers without calculating any nuclear kinetic energy matrix element. Tests on H₂, LiH, HF, F₂, and H₂O isotopomers indicate the equivalence of our correction to the standard diagonal adiabatic correction. A further original application to C₂H₆ illustrates the usefulness of the method for polyatomic molecules. The resulting molecular orbitals carry the nuclear mass signature, exemplified with Koopmans ionization potentials.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.     

Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

On laplace continued fraction for the normal integral

The Laplace continued fraction is derived through a power series. It provides both upper bounds and lower bounds of the normal tail probability % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x), it is simple, it converges for x>0, and it is by far the best approximation for x3. The Laplace continued fraction is rederived as an extreme case of admissible bounds of the Mills' ratio, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x)/(x), in the family of ratios of two polynomials subject to a monotone decreasing absolute error. However, it is not optimal at any finite x. Convergence at the origin and local optimality of a subclass of admissible bounds are investigated. A modified continued fraction is proposed. It is the sharpest tail bound of the Mills' ratio, it has a satisfactory convergence rate for x1 and it is recommended for the entire range of x if a maximum absolute error of 10^-4 is required.The efforts of the author were supported by the NSERC of Canada.     

Modified AutoDock for accurate docking of protein kinase inhibitors

Protein kinases are an important class of enzymes controlling virtually all cellular signaling pathways. Consequently, selective inhibitors of protein kinases have attracted significant interest as potential new drugs for many diseases. Computational methods, including molecular docking, have increasingly been used in the inhibitor design process [1]. We have considered several docking packages in order to strengthen our kinase inhibitor work with computational capabilities. In our experience, AutoDock offered a reasonable combination of accuracy and speed, as opposed to methods that specialize either in fast database searches or detailed and computationally intensive calculations.However, AutoDock did not perform well in cases where extensive hydrophobic contacts were involved, such as docking of SB203580 to its target protein kinase p38. Another shortcoming was a hydrogen bonding energy function, which underestimated the attraction component and, thus, did not allow for sufficiently accurate modeling of the key hydrogen bonds in the kinase-inhibitor complexes.We have modified the parameter set used to model hydrogen bonds, which increased the accuracy of AutoDock and appeared to be generally applicable to many kinase-inhibitor pairs without customization. Binding to largely hydrophobic sites, such as the active site of p38, was significantly improved by introducing a correction factor selectively affecting only carbon and hydrogen energy grids, thus, providing an effective, although approximate, treatment of solvation.     

对称广义中心对称矩阵模型修正的矩阵逼近法及其扰动性

X,B是实测的位移矩阵和载荷矩阵,C是有限元方法得到的估计矩阵,给出了AX=B的对称广义中心对称矩阵解集合ζ的表达式,对于逼近问题||C-A||F=min A∈ζ||C-A||F的解A,给出了它的表达式并分析了解A的扰动性,数值结果表明方法是行之有效的.     

Thermodynamic Properties of Crystalline Cellulose Allomorphs Studied with Dispersion-Corrected Density Functional Methods

The phonon properties and thermodynamics of four crystalline cellulose allomorphs, Iα, Iβ, II, and III1, have been investigated using dispersion-corrected density functional theory (DFT). In line with experimental findings, the free energy differences between the studied cellulose allomorphs are small, less than 1 kJ/mol per atom. The calculated specific heat at constant volume (Cv) has been compared with the available experimental data in the temperature range 10–300 K. Quasiharmonic approximation has been employed to study thermodynamics and specific heat at constant pressure (Cp). For the studied temperature range of 10–400 K, the specific heat of all cellulose allomorphs shows very similar behavior. The calculated and experimental specific heat agree well at low temperatures below 100 K, but the deviation between theory and experiment increases with temperature. This may be due to increasing phonon anharmonicity as the temperature increases.     

Quantum Chaos,Random Matrices,and Irreversibility in Interacting Many-Body Quantum Systems

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.     

电推力器流动模拟中的电子处理方法

分析了电子的准中性假设、玻耳兹曼分布假设、粒子模型在电推力器流动模拟中的适用性和优劣性,提出了一种新的电子处理方法——电子漂移扩散近似,采用该方法模拟了离子发动机栅极光学系统等离子体运动过程。结果表明:该方法得出的电势分布、离子相空间分布及电子数密度分布与经典的电子玻耳兹曼分布假设处理方法计算结果一致,验证了该方法可以很好地应用于电推力器栅极光学系统模拟。