B2C(1A1)和BC2(2A′)的结构与解析势能函数

采用单双取代的二次组态相互作用方法，分别选用6-311++G(d,p)和6-311G(df,pd)基组，对B₂C和BC₂分子的结构进行了优化，得到这两个分子的基态结构为C_2v和C_s，基态电子状态为¹A₁和²A′，同时还得到了它们的平衡几何结构、离解能、谐振频率和力常数. 关键词： 碳化硼 Murrell-Sorbie函数 谐振频率 势能函数     

Improved search for $B_{s}^{0} - \overline{B}_{s}^{0}$ oscillations

An improved search for B _s ⁰ oscillations is performed in the ALEPH data sample collected during the first phase of LEP, and reprocessed in 1998. Three analyses based on complementary event selections are presented. First, decays of B _s ⁰ mesons into hadronic flavour eigenstates are fully reconstructed. This selection yields a small sample of candidates with excellent decay length and momentum resolution and hi gh average B _s ⁰ purity. Semileptonic decays with a reconstructed D _s ^- meson provide a second sample with larger statistics, high average B _s ⁰ purity, but a poorer momentum and decay length resolution due to the partial decay reconstruction. Finally, semileptonic b-hadron decays are inclusively selected and yield the data sample with the highest sensitivity to B _s ⁰ oscillations, as the much higher statistics compensate for the low average B _s ⁰ purity and poorer time resolution. A lower limit is set atps^-1 at 95% C.L., significantly lower than the expected limit of 15.2 ps^-1. Received: 21 February 2003 / Published online: 11 June 2003     

Dynamos at extreme magnetic Prandtl numbers: insights from shell models

We present a magnetohydrodynamic (MHD) shell model suitable for computation of various energy fluxes of MHD turbulence for very small and very large magnetic Prandtl numbers Pm; such computations are inaccessible to direct numerical simulations. For small Pm, we observe that both kinetic and magnetic energy spectra scale as k^?5/3 in the inertial range, but the dissipative magnetic energy scales as k^?11/3exp?(? k/k_η). Here the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated by Joule heating. The large-Pm dynamo has a similar behaviour except that the dissipative kinetic energy scales as k^?13/3. For this case, the large-scale velocity field transfers energy to the large-scale magnetic field, which gets transferred to small-scale velocity and magnetic fields; the energy of the small-scale magnetic field also gets transferred to the small-scale velocity field, and the energy thus accumulated is dissipated by the viscous force.     

Revisiting generalized Chaplygin gas as a unified dark matter and dark energy model

In this paper, we revisit the generalized Chaplygin gas (GCG) model as a unified dark matter and dark energy model. The energy density of GCG model is given as ρ _GCG/ρ _GCG0=[B _s +(1−B _s )a ^−3(1+α)]^1/(1+α), where α and B _s are two model parameters which will be constrained by type Ia supernova as standard candles, baryon acoustic oscillation as standard rulers and the seventh year full WMAP data points. In this paper, we will not separate GCG into dark matter and dark energy parts any more as adopted in the literature. By using the Markov Chain Monte Carlo method, we find the results a = 0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268}\alpha=0.00126_{-0.00126- 0.00126}^{+ 0.000970+ 0.00268} and B_s = 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}B_{s}= 0.775_{-0.0161- 0.0338}^{+ 0.0161+ 0.0307}.     

Besov spaces and the multifractal hypothesis

Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h _min,h _max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz _p ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL ^p -mean Hölder indexs, i.e., if it lies in the Besov spaceB _p ^s, , then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz _p , and, more generally, the maximal Besov index of order,p, ass _p =z _p /p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence.     

Non-Uniform Dependence on Initial Data of Solutions to the Euler Equations of Hydrodynamics

We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove that the data-to-solution map is not uniformly continuous in Sobolev H ^s (Ω) topology for any ${s \in \mathbb{R}}We show that continuous dependence on initial data of solutions to the Euler equations of incompressible hydrodynamics is optimal. More precisely, we prove that the data-to-solution map is not uniformly continuous in Sobolev H ^s (Ω) topology for any s ? \mathbbR{s \in \mathbb{R}} if the domain Ω is the (flat) torus \mathbbTⁿ=\mathbbRⁿ/2p\mathbbZⁿ{\mathbb{T}^n=\mathbb{R}^n/2\pi\mathbb{Z}^n} and for any s > 0 if the domain is the whole space \mathbbRⁿ{\mathbb{R}^n}.     

Eikonal equation of the Lorentz-violating Maxwell theory

We derive the eikonal equation of light wavefront in the presence of Lorentz invariance violation (LIV) from the photon sector of the standard model extension (SME). The results obtained from the equations of the E and B fields, respectively, are the same. This guarantees the self-consistency of our derivation. We adopt a simple case with only one non-zero LIV parameter as an illustration, from which we find two points. One is that, in analogy with the Hamilton–Jacobi equation, from the eikonal equation, we can derive dispersion relations which are compatible with results obtained from other approaches. The other is that the wavefront velocity is the same as the group velocity, as well as the energy flow velocity. If further we define the signal velocity v _s as the front velocity, there always exists a mode with v _s >1; hence causality is violated classically. Thus, our method might be useful in the analysis of Lorentz violation in QED in terms of classical causality.     

Discontinuity of Plasma Flow Parameters

This paper is concerned with the study of the dynamics of the expanded dense plasma from a coaxial electrodes discharge device. Experimental investigations were carried out with hydrogen gas at 0.8 Torr base pressure. The condenser bank voltage was 12 KV, which corresponds to a capacitor bank energy of 4.5 KJ. The experimental results show that a shock wave is generated near the muzzle, and is separated from the plasma shell. The shock front velocity (V_s) and the plasma shell velocity (V₁) decay within propagation up to 14 cm according to the relations, V_s ∞ Z^?1 and V₁ ∞ Z^?2. At Z = 14 cm a discontinuity in the velocity curves occurs, where velocities of both the shock front and the plasma shell are increased. The distribution of the self-induced axial magnetic field along the expansion chamber axis shows that at Z = 14 cm the magnetic field lines have a solitary form. Its value is decreased before Z = 14 cm according to B_z ∞ Z^?1, but after Z = 14 cm as the relation B_z ∞ Z^?3. The time evaluation of soft X-ray consists of two different spikes.     

Photon electrodynamics and photon structure as a bunch of one of many possible states of electromagnetic field

Fundamental laws of conservation are used to show that electromagnetic field is generally represented (even in vacuum at ρ = 0 and j = 0) using four vectors D, E, B, and H with different equations of state (material equations) that are linear for electromagnetic waves and nonlinear for photons and particles. An equation that describes different states of electromagnetic field (i.e., different but not arbitrary relationships of field vectors E, H, D, and B) is derived. It is shown that electromagnetic wave and photon are different states of electromagnetic field that exhibit different dependences of energy density on field vectors. Partial analytical solutions are obtained for a photon (spatially localized bunch of electromagnetic field energy) that propagates at a velocity of light along a single (as distinct from electromagnetic wave) direction.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

A new class of interior solutions for a stress-energy tensor of Segré characteristic [111, 1]

The interior solutions of (the tetrad versions of) Einstein's field equations withT _AB having Segré characteristic [111, 1] (which has all four eigenvalues distinct), are investigated. For this purpose amixed method, which combines Synge'sg method andT method, is introduced. Some of the tetrad equations are solved for the metric functions while the remaining equations are used to define the corresponding components ofT _AB . As necessary conditions of the consistency of the mixed method the conservation equationsT ^AB _B =0 are explicitly verified. Several simplifications and analysis of some differential inequalities show the existence of a new class of solutions which, in addition to having Segré characteristic [111, 1], also satisfy the strong energy conditions of Hawking and Ellis.This Author is a member of the Theoretical Sciences Institute, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada.     

NMR方法监测季铵型双子表面活性剂的胶束交换动力学

The dynamic NMR (DNMR) method was used to detect kinetic parameters of the molecular exchange process between monomers in bulk solution and those in the micelle for Gemini surfactants,12-s-12 and 14-s-14(s=2,3 and 4).The escape rate constant,k^-,was derived based on the simplified equations of DNMR theory,and the apparent activation energy of escape,E_a^-,was obtained based on the Arrhenius equation through temperature variation experiments.Results show that the orders of magnitude of k^- for 14-s-14 and 12-s-12 are respectively 10 and 10³ s^-1,E_a^- of 14-s-14 and 12-s-12 are respectively 54.04-73.64 and 33.42-47.09 kJ/mol.Furthermore, increases and E_a^- decreases with the spacer length growing.In combination with the micro-polarity measurements,it was revealed that molecules of 14-s-14 and 12-s-12 have to experience conformation changes when escaping from the micelles.The two-step molecular exchange mechanism for Gemini surfactants was therefore supported.     

Exploring CP violation and penguin effects through B0d→D+D- and B0s→D+sD-s

The decay B⁰ _d→D⁺D^- offers an interesting probe of CP violation, but it requires control of penguin effects, which can be done through B⁰ _s→D⁺ _sD^- _s by means of the U-spin flavour symmetry of strong interactions. Recently, the Belle collaboration reported indications of large CP violation in the B⁰ _d decay, which were, however, not confirmed by BaBar, and first signals of the B⁰ _s channel were observed at the Tevatron. In view of these developments and the quickly approaching start of the LHC, we explore the allowed region in observable space for CP violation in B⁰ _d→D⁺D^-, perform theoretical estimates of the relevant hadronic penguin parameters and observables, and we address questions both about the most promising strategies for the extraction of CP-violating phases and about the interplay with other measurements of CP violation and the search for new physics. As far as the latter aspect is concerned, we point out that the B⁰ _q→D_q ⁺D^- _q system provides a setting for the determination of the B⁰ _q–B̄⁰ _q mixing phases (q∈{d,s}) that is complementary to the conventional B⁰ _d→J/ψK_S and B⁰ _s→J/ψφ modes with respect to possible new-physics effects in the electroweak penguin sector.     

Universal rise of hadronic total cross sections based on forward πp and scatterings

Recently there are several evidences of the increase of the total cross section σ_tot to be log²s consistent with the Froissart unitarity bound, and the COMPETE collaborations in the PDG have further assumed σ_totBlog²(s/s₀) to extend its universal rise with a common value of B for all the hadronic scatterings. However, there is no rigorous proof yet based only on QCD. Therefore, it is worthwhile to prove this universal rise of σ_tot even empirically. In this Letter we attempt to obtain the value of B for πp scattering, B_πp, with reasonable accuracy by taking into account the rich πp data in all the energy regions. We use the finite-energy sum rule (FESR) expressed in terms of the πp scattering data in the low and intermediate energies as a constraint between high-energy parameters. We then have searched for the simultaneous best fit to the σ_tot and ρ ratios, the ratios of the real to imaginary parts of the forward scattering amplitudes. The lower energy data are included in the integral of FESR, the more precisely determined is the non-leading term such as logs, and then helps to determine the leading terms like log²s. We have derived the value of B_πp as B_πp=0.311±0.044 mb. This value is to be compared with the value of B for scattering, B_pp, in our previous analysis [M. Ishida, K. Igi, Eur. Phys. J. C 52 (2007) 357], B_pp=0.289±0.023 mb. Thus, our result appears to support the universality hypothesis.     

Classical and quantum turbulence

The reconnection of two singularities in 2D, 3D, and 4D classical and quantum turbulence is examined. Singularity reconnection plays an essential role in the dissipation of the incompressible part of kinetic energy. A reconnection condition 2(d_s+1)≥d+1 is derived, which crucially depends on the dimension d_s of the singular structure in relation to the spatial dimension d of the system. The feasibility of this condition is examined using direct numerical simulations of the Navier-Stokes and Gross-Pitaevskii equations for the classical and quantum turbulence, respectively. We observed that the condition was satisfied for d=3 and 4, in agreement with the occurrence of energy cascades in both classical and quantum turbulence in those dimensions.     

Integrable Euler equations on SO(4) and their physical applications

For the Lie algebra SO(4) (and other six dimensional Lie algebras) we find some Euler's equations which have an additional fourth order integral and are algebraically integrable (in terms of elliptic functions) in a one parameter set of orbits. Integrable Euler's equations having an additional second order integral and generalizing Steklov's case are presented. Equations for rotation of a rigid body havingn ellipsoid cavities filled with the ideal incompressible fluid being in a state of homogeneous vortex motion are derived. It is shown that the obtained equations are Euler's equations for the Lie algebra of the groupG _n+1=SO(3) × ... × SO(3). New physical applications of Euler's equations on SO(4) are discussed.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents

The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio r _s = a/a _B ^*. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r _s ^* below which the lattice spacing s becomes a relevant scale and r _s ceases to be the scaling parameter. For systems of small ratios s/a _B ^*, s becomes only relevant at small r _s (large densities) where one has a quantum fluid with a deformed Fermi surface. For systems of large s/a _B ^*, s plays also a role at large r _s (small densities) where one has a Wigner solid, the lattice limiting its harmonic vibrations. The thermodynamic limit of physical systems of different a _B ^* is qualitatively discussed, before quantitatively studying the lattice effects occurring at large r _s . Using a few particle system, we compare exact numerical results obtained with a lattice and analytical perturbative expansions obtained in the continuum limit. Three criteria giving similar values for the lattice threshold r _s ^* are proposed. The first one is a delocalization criterion in the Fock basis of lattice site orbitals. The second one uses the persistent current which can depend on the interaction in a lattice, while it becomes independent of the interaction in the continuum limit. The third one takes into account the limit imposed by the lattice to the harmonic vibrations of the electron solid.Received: 20 January 2004, Published online: 18 June 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 73.20.Qt Electron solids     

Radial excitations of heavy-light mesons

The recent discovery of D_s states suggests the existence of radial excitations. Our semirelativistic quark potential model succeeds in reproducing these states within one to two percent of accuracy compared with the experiments, D _s0(2860) and D _s ^*(2715), which are identified as 0⁺ and 1^- radial excitations (n = 2). We also present calculations of radial excitations for B/B _s heavy mesons. The relation between our formulation and the modified Goldberger-Treiman relation is also described.