Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

Momentum density and molecular geometry. Bent BH 2 − and linear BH 2 +

Based on a special form of the molecular virial theorem, the recently proposed method of momentum density for interatomic interactions is here applied to the problem of molecular geometry. Two molecules BH ₂ ^– and BH ₂ ⁺ , which have the same nuclear framework but favor respectively bent and linear conformations, are comparatively studied. Using an approximate Hartree-Fock momentum density, the total molecular energy (including the nuclear repulsion) is partitioned into orbital components, and a geometry correlation diagram is derived. An atom-bond partitioning of the total energy is also examined based on the one- and two-center decomposition of the momentum density.     

用格子Boltzmann模型模拟激波现象

根据微观和宏观之间的质量、动量、能量守恒准则,建立了一个两维的D2Q13格子Boltzmann模型,可从该D2Q13模型出发推导出宏观的流体力学方程,所得动量方程和Navier-Stokes方程相比,在黏性输运项上有明显的改进,用该模型对冲击波在障碍物表面上的折射和反射现象的数值模拟都得到了比较满意的结果,而且数值稳定性也很好.证明了D2Q13模型的适宜性 关键词： Boltzmann模型 分布函数 冲击波 流体力学方程     

信息在测量之前就已经存在了吗?——答逯还新、吴盛俊、刘克家三位先生的评论

在详尽地分析了逯-吴-刘三位先生在评论我们前文2时所提出的问题(文1)后,本文重申我们关于抽象的量子态不包含任何信息的观点.信息只是在测量时才被主体与客体共同制造出来,而作为相应的“虚拟测量”几率幅的波函数则给出了统计性的预言.     

基于AHP和动量BP神经网络的工程项目承包商选择模型

运用BP神经网络技术,采用动量BP算法,构建了基于动量BP神经网络的工程项目承包商选择模型,并将AHP的评价结果作为学习样本,对BP神经网络模型进行训练和测试.结果表明,基于AHP和动量BP神经网络的工程项目承包商选择模型是可行的,该模型具有较高的自组织、自适应和自学习能力以及较强的容错功能,能够为一般的工程项目承包商选择活动提供有效的参考和依据.     

Rigidity of Hamiltonian actions on Poisson manifolds

This paper is about the rigidity of compact group actions in the Poisson context. The main result is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash–Moser normal form theorem for closed subgroups of SCI type. This Nash–Moser normal form has other applications to stability results that we will explore in a future paper. We also review some classical rigidity results for differentiable actions of compact Lie groups and export it to the case of symplectic actions of compact Lie groups on symplectic manifolds.     

A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier–Stokes equations in time-varying complex geometries

A dispersion-relation-preserving dual-compact scheme developed in Cartesian grids is applied together with the immersed boundary method to solve the flow equations in irregular and time-varying domains. The artificial momentum forcing term applied at certain points in cells containing fluid and solid allows an imposition of velocity condition to account for the motion of solid body. We develop in this study a differential-based interpolation scheme which can be easily extended to three-dimensional simulation. The results simulated from the proposed immersed boundary method agree well with other numerical and experimental results for the chosen benchmark problems. The accuracy and fidelity of the IB flow solver developed to predict flows with irregular boundaries are therefore demonstrated.     

The momentum interpolation method based on the time-marching algorithm for All-Speed flows

The time-marching approach has clear physical meaning and strict mathematical nature and has been applied in computation of compressible flows widely and extended to many uniform algorithms for All-Speed flows. Remedy for its weakness in the problem of checkerboard decoupling of pressure field for incompressible flows is envisaged with the time-marching momentum interpolation method (MIM) taken into account in this paper. Existing preconditioning methods for suppressing decoupling and time-marching MIM are analyzed for this purpose, and algorithms of time-marching MIM are proposed for steady and unsteady flows and for All-Speed flows. Asymptotic analysis shows that the supposed time-marching MIM has at least a third-order accuracy, better than the existing time-marching coupling methods, which only have an accuracy of the same order as the adopted scheme has. Effects of the time step sizes on the ability of the time-marching MIM to suppress the checkerboard pressure decoupling are particularly discussed in terms of the dual-time stepping approach, and it is revealed how the decreased sizes of either the pseudo- or physical-time step increases the possibility of decoupling and how Choi’s modification, in which the history of the interface velocity is decided by itself instead of the arithmetic average of the velocities on its adjacent nodes, removes the unphysical pressure oscillation with small size of the physical time step but leads to divergence with the pseudo-time step as well. As a remedy for the pseudo-time step, such methods are recommended as implicit methods and the local-time step method with a proposed modification of the time-marching MIM preventing accuracy loss due to very large time step size. Numerical experiments support the theoretical analyses and show the validity of the time-marching MIM proposed.     

Fractional monodromy: parallel transport of homology cycles

A 2n-dimensional completely integrable system gives rise to a singular fibration whose generic fiber is the n-torus Tⁿ. In the classical setting, it is possible to define a parallel transport of elements of the fundamental group of a fiber along a path, when the path describes a loop around a singular fiber, it defines an automorphism of π₁(Tⁿ) called monodromy transformation [J.J. Duistermaat, On global action-angle coordinates, Communications on Pure and Applied Mathematics 33 (6) (1980) 687–706]. Some systems give rise to a non-classical setting, in which the path can wind around a singular fiber only by crossing a codimension 1 submanifold of special singular fibers (a wall), in this case a non-classical parallel transport can be defined on a subgroup of the fundamental group. This gives rise to what is known as monodromy with fractional coefficients [N. Nekhoroshev, D. Sadovskiì, B. Zhilinskiì, Fractional monodromy of resonant classical and quantum oscillators, Comptes Rendus Mathematique 335 (11) (2002) 985–988]. In this article, we give a precise meaning to the non-classical parallel transport. In particular we show that it is a homologic process and not a homotopic one. We justify this statement by describing the type of singular fibers that generate a wall that can be crossed, by describing the parallel transport in a semi-local neighbourhood of the wall of singularities, and by producing a family of 4-dimensional examples.     

On the use of the stratified momentum balance for the deduction of shear stress in horizontal gas–liquid pipe flow

The use of the stratified flow momentum balance for the deduction of interfacial and liquid wall shear stresses from experimental measurements is examined. A systematic error analysis is applied to the governing equations using the principle of maximum uncertainty. A series of air–water experiments were conducted in 50 and 80 mm diameter pipes, in which gas pressure drop, liquid height and gas wall shear stress were measured. A framework for the correlation of the deduced shear stresses is proposed from the experimental measurements. The uncertainty analysis is used to show that the definition of mean liquid height does not significantly influence the overall results. The development of empirical equations based on such methods may lead to total uncertainties of up to 40%, irrespective of accuracy of the experimental data or the appropriateness of the correlating technique. Comparisons with state-of-the-art correlations for the liquid wall and interfacial friction factor data showed even larger discrepancies between measurement and prediction.