The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

Like‐Charge Attraction: A Combined Electrostatic–Hydrodynamic Approach

Abstract

This article discusses the like‐charge attraction of colloidal spheres close to a charged plate and compares results produced by an electrostatic and a hydrodynamic model with experimental data. Hydrodynamic coupling is shown to be the dominating effect, while the electrostatic influence may often be neglected. Some observations, however, can be explained only by means of a combined electrostatic–hydrodynamic model, which is derived in this work. The combined model is able to predict not only the attractive force between particles of similar charge close to a charged plate but also the change to a purely repulsive force once the sphere‐plate distance is further reduced. This prediction matches qualitatively results of experiments reported in the literature.     

Excitation functions of the analyzing power in elastic proton-proton scattering from 0.45 to 2.5 GeV

Excitation functions A_N(p_lab,_c.m.) of the analyzing power in elastic proton-proton scattering have been measured in an internal target experiment at the Cooler Synchrotron COSY with an unpolarized proton beam and a polarized atomic hydrogen target. Data were taken continuously during the acceleration and deceleration for proton kinetic energies T_lab (momenta p_lab) between 0.45 and 2.5 GeV (1.0 and 3.3 GeV/c) and scattering angles 30 ^° _c.m. 90^°. The results provide excitation functions and angular distributions of high precision and internal consistency. The data can be used as calibration standard between 0.45 and 2.5 GeV. They have significant impact on phase shift solutions, in particular on the spin triplet phase shifts between 1.0 and 1.8 GeV.     

On the equation of state of classical one-component systems with long-range forces

Several definitions of the pressure are introduced for one-component systems and shown to be nonequivalent in the presence of a rigid neutralizing background. Relations between these pressures are derived for finite and infinite systems; these relations depend on the asymptotic behavior of the force at infinity, with the Coulomb force at the borderline between different properties. It is argued that only one of those definitions is physically acceptable and its properties are discussed in relation to the asymptotic behavior of the force. It is seen in particular that a knowledge of the state of the infinite system is not sufficient to determine its thermodynamic properties. The results are illustrated by some typical examples.For example, for two-dimensional systems with three-dimensional Coulomb interaction see refs. 2–4.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

取压方式对微通道内单相摩擦阻力特性的影响

本文以去离子水和氮气为工质,在水平圆形微通道(dh=0．336 mm)中采用两种直接取压方式-缝隙取压和小孔取压,对单相摩擦阻力特性进行了实验研究,并通过改变缝隙宽度,研究缝隙宽度对压降测量偏差的影响．     

Complementary energy principle for large elastic deformation

Using the “base forces” as the fundamental unknowns to determine the state of an elastic system, the complementary energy principle for large elastic deformation is constructed for the conjugate quantities being displacement gradients, which possesses exactly the same form as that of classical linear elasticity. It is revealed that the complementary energy contains deformation part and rotation part.