Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

A van der Waals density functional theory study of poly(vinylidene difluoride) crystalline phases

Ferroelectric polymers, such as poly(vinylidene difluoride) (PVDF), have many potential applications in flexible electronic devices. PVDF has six experimentally observed polymorphs, three of which are ferroelectric. In this work we use density functional theory to investigate the structural properties, energetics and polarisation of the stable α-phase, its ferroelectric analogue, the δ-phase, and the β-phase, which has the best ferroelectric properties. The results from a variety of exchange and correlation functionals were compared and it was found that van der Waals (vdW) interactions have an important effect on the calculated crystal structures and energetics, with the vdW-DF functional giving the best agreement with experimental lattice parameters. The spontaneous polarisation was found to strongly correlate with the unit cell volumes, which depend on the functional used. While the relative phase energies were not strongly dependent on the functional, the cohesive energies were significantly underestimated using the PBE functional. The inclusion of vdW interactions is, therefore, important to obtain the correct lattice structures, polarisation and energetics of PVDF polymorphs.     

On the resolution of singularities of multiple Mellin–Barnes integrals

One of the two existing strategies of resolving singularities of multifold Mellin–Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.m     

First integrals of the discrete nonconservative and nonholonomic systems

In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations.     

Kirkwood–Buff integrals of finite systems: shape effects

The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.     

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently ‘simple’ numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4?2ε dimensions. One method uses Mellin–Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A.V. Smirnov and V.A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop ε-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sector_decomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin–Barnes representations and sector decompositions, is compared. The computational packages are publicly available.     

Experimental study of the acoustic characteristics of micro-perforated functional absorbers

Micro-perforated panels have been widely used as fiber-free acoustical material for decades in the form of wall or ceiling covering with some air space behind. This paper presents the test study on the acoustical characteristics of two different types of functional absorbers, panel type and tube type, constructed with micro-perforated metal or PVC (polyvinyl chloride) sheets. Acoustical measurements of such functional absorbers in reverberation chamber demonstrate the merit of good absorption as expected. They are not only cost effective in construction and installation, but also appealing esthetically for architectural interior design.     

First evidence of ψ(2S)→Ω-Ω+

The decay ψ(2S)→Ω^-Ω⁺ is analyzed using 14×10⁶ ψ(2S) events recorded by the Beijing Spectrometer Ⅱ (BESⅡ) at the Beijing Electron Positron Collider (BEPC). Based upon events with no missing charged tracks and a satisfactory four-constraint kinematic t, we determine the upper limit for the branching fraction of ψ(2S)→Ω^-Ω⁺ to be 1.5×10⁴ at a 90% confidence level. By including events with one missing charged track, we are able to report the first evidence of an Ω⁺ signal with a statistical signi cance of 3.1|σ. The branching fraction of ψ(2S)Ω⁺ is determined to be (4.80±1.56(stat)±1.30(sys))10⁵.     

The discrete variational principle and the first integrals of Birkhoff systems＊

This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.     

H→γγ: a comment on the indeterminacy of non-gauge-invariant integrals

We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al. [1, 2]. The reasons for why this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon Rξ-gauge calculations with four-dimensional gauge-breaking regulators, allows us to recover the well known H→γγ result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in the same way. The combination of the unitary gauge with a cutoff regularization scheme turns out to be non-predictive.     

Mn-based antiperovskite functional materials： Review of research

Our recent research on the Mn-based antiperovskite functional materials AXMn 3(A:metal or semiconducting elements;X:C or N) is outlined.Antiperovskite carbides(e.g.,AlCMn 3) show large magnetocaloric effect comparable to those of typical magnetic refrigerant materials.Enhanced giant magnetoresistance up to 70% at 50 kOe(1 Oe = 79.5775 A.m-1) over a wide temperature span was obtained in Ga1-xZnxCMn3 and GaCMn3-xNix.In Cu0.3Sn0.5NMn3.2,negative thermal expansion(NTE) was achieved in a wide temperature region covering room temperature(α =-6.8 ppm/K,150 K-400 K).Neutron pair distribution function analysis suggests the Cu/Sn-Mn bond fluctuation is the driving force for the NTE in Cu1-xSnxNMn3.In CuN1-xCx Mn3 and CuNMn3-yCoy,the temperature coefficient of resistivity(TCR) decreases monotonically from positive to negative as Co or C content increases.TCR is extremely low when the composition approaches the critical points.For example,TCR is ～ 1.29 ppm/K between 240K and 320K in CuN0.95C0.05Mn3,which is one twentieth of that in the typical low-TCR materials(～ 25 ppm/K).By studying the critical scaling behavior and X deficiency effect,some clues of localized-electron magnetism have been found against the background of electronic itinerant magnetism.     

Transition metal catalyzed borylation of functional π-systems

Borylated functional π-systems are useful building blocks to enable efficient synthesis of novel molecular architectures with beautiful structures, intriguing properties and unique functions. Introduction of boronic ester substituents to a variety of extended π-systems can be achieved through either iridium-catalyzed direct C–H borylation or the two-step procedure via electrophilic halogenation followed by palladium-catalyzed borylation. This review article focuses on our recent progress on borylation of large π-conjugated systems such as porphyrins, perylene bisimides, hexabenzocoronenes and dipyrrins.     

Calculation of the transfer integrals in Wannier representation for a planar trans-polyacetylene chain

In this paper,the electronic transfer integrals,the energy gap,and the bandwidth of a planar trans-polyacetylene chain are calculated in Wannier representation,in which a combination of the wave function of hydrogen-like atoms is used to stand for the Wannier function.When the effective nuclear charge number Z=2.125 and the distortion amplitude of the carbon sites u=0.0038 nm,the nearest,next,and third neighborhopping energies obtained are -3.224 78 eV,-2.388 61 eV,0.148 14 eV,0.006 65 eV,and 0.00650 eV,respectively.The energy bandwidth and gap corresponding to these values are Wd=11.19 eV and Eg=1.70 eV,respectively.These results coincide with the experimental values.     

First evidence of ψ(2S)→Ω-Ω+

The decay ψ(2S)→Ω^-Ω⁺ is analyzed using 14×10⁶ ψ(2S) events recorded by the Beijing Spectrometer Ⅱ (BESⅡ) at the Beijing Electron Positron Collider (BEPC). Based upon events with no missing charged tracks and a satisfactory four-constraint kinematic t, we determine the upper limit for the branching fraction of ψ(2S)→Ω^-Ω⁺ to be 1.5×10⁴ at a 90% confidence level. By including events with one missing charged track, we are able to report the first evidence of an Ω⁺ signal with a statistical signi cance of 3.1|σ. The branching fraction of ψ(2S)Ω⁺ is determined to be (4.80±1.56(stat)±1.30(sys))10⁵.     

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.