Mode-detailed analysis of transmission based directly on Green’s functions

Fisher-Lee relation\hbox{$\bm{t}= {i}\bm{\Gamma}_L^{1/2}\bm{G}\bm{\Gamma}^{1/2}_R$}t=iΓL1/2GΓR1/2is a well-established tool to decode the modeinformation from Green’s function and coupling parameters. Using the Bloch eigen-modes ofthe leads, we show that the\hbox{$\bm{\Gamma}^{1/2}_{L/R}$}ΓL/R1/2term can be expressed by the Bloch eigen-mode vectorsand the wave velocities which give unambiguous algorithm of\hbox{$\bm{\Gamma}^{1/2}_{L/R}$}ΓL/R1/2in the Fish-Lee relation. Using this approach, wepresent an accurate and convenient technique to analyze all transport modes and also thedominant channels of an electronic transport system in tight-binding model. We studygraphene nanoribbon structures to demonstrate the typical application of our technique.     

Transition parameters of Li-like ions(Z = 7–11) in dense plasmas

The energy levels, transition energies, transition probabilities, weighted oscillator strengths, and line strengths of Lilike ions(Z = 7–11) in dense plasmas are investigated in this work. The relativistic effects and electron correlation effects are described by the MCDHF method. The ion sphere model is applied to include the dense plasma screening effect. The ground configuration 1 s~22 s and the excited 1 s~22 p, 1 s~23 l(l = 0–2) are considered. The configuration sets are enlarged until n = 7 where the calculated energy levels have converged. The critical free electron densities of 1 s~23 d states are estimated.Except for 1 s~23 s–1 s~23 p transitions, the transition energies for Δn = 0 increase, and for Δn ≠ 0 decrease with increasing free electron densities. For 1 s~23 s–1 s~23 p transitions, the spectra show blue-shift at lower free electron densities and red-shift at higher free electron densities, and the energy level crossing phenomens are observed at higher free electron densities.     

Constraints on $H_0$ from WMAP and BAO Measurements *

We report the constraints of $H_0$ obtained from Wilkinson Microwave Anisotropy Probe (WMAP) 9-year data combined with the latest baryonic acoustic oscillations (BAO) measurements. We use the BAO measurements from 6dF Galaxy Survey (6dFGS), the SDSS DR7 main galaxies sample (MGS), the BOSS DR12 galaxies, and the eBOSS DR14 quasars. Adding the recent BAO measurements to the cosmic microwave background (CMB) data from WMAP, we constrain cosmological parameters $\Omega_m=0.298\pm0.005$, $H_0=68.36^{+0.53}_{-0.52} {\rm km}\cdot {\rm s}^{-1}\cdot {\rm Mpc}^{-1}$, $\sigma_8=0.8170^{+0.0159}_{-0.0175}$ in a spatially flat $\Lambda$ cold dark matter ($\Lambda$CDM) model, and $\Omega_m=0.302\pm0.008$, $H_0=67.63\pm1.30 {\rm km}\cdot{\rm s}^{-1}\cdot {\rm Mpc}^{-1}$, $\sigma_8=0.7988^{+0.0345}_{-0.0338}$ in a spatially flat $w$CDM model, respectively. Our measured $H_0$ results prefer a value lower than 70 ${\rm km}\cdot {\rm s}^{-1}\cdot{\rm Mpc}^{-1}$, consistent with the recent data on CMB constraints from Planck (2018), but in $3.1$ and $3.5\sigma$ tension with local measurements of SH0ES (2018) in $\Lambda$CDM and $w$CDM framework, respectively. Our results indicate that there is a systematic tension on the Hubble constant between SH0ES and the combination of CMB and BAO datasets.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

Enhanced interface properties of diamond MOSFETs with Al_2O_3 gate dielectric deposited via ALD at a high temperature

The interface state of hydrogen-terminated(C–H) diamond metal–oxide–semiconductor field-effect transistor(MOSFET) is critical for device performance. In this paper, we investigate the fixed charges and interface trap states in C–H diamond MOSFETs by using different gate dielectric processes. The devices use Al_2O_3 as gate dielectrics that are deposited via atomic layer deposition(ALD) at 80℃ and 300℃, respectively, and their C–V and I–V characteristics are comparatively investigated. Mott–Schottky plots(1/C~2–VG) suggest that positive and negative fixed charges with low density of about 1011 cm~(-2) are located in the 80-℃-and 300-℃ deposition Al_2O_3 films, respectively. The analyses of direct current(DC)/pulsed I–V and frequency-dependent conductance show that the shallow interface traps(0.46 e V–0.52 e V and0.53 e V–0.56 e V above the valence band of diamond for the 80-℃ and 300-℃ deposition conditions, respectively) with distinct density(7.8 × 10~(13) e V~(-1)·cm~(-2)–8.5 × 10~(13) e V-1·cm~(-2) and 2.2 × 1013 e V~(-1)·cm~(-2)–5.1 × 10~(13) e V~(-1)·cm~(-2) for the80-℃-and 300-℃-deposition conditions, respectively) are present at the Al_2O_3/C–H diamond interface. Dynamic pulsed I–V and capacitance dispersion results indicate that the ALD Al_2O_3 technique with 300-℃ deposition temperature has higher stability for C–H diamond MOSFETs.     

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method (ATMM) is applied to calculating the critical radius $r_{\rm c}$ and the dipole polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen atom and the Hulth\'{e}n potential. We find that there exists a linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$ for a fixed angular quantum number $l$, moreover, the three bounds of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$, $\alpha_{\rm d}^{U}$) satisfy an inequality: $\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.     

Theory of nine elastic constants of biaxial nematics

In this paper, a rotational invariant of interaction energy between two biaxial-shaped molecules is assumed and in the mean field approximation, nine elastic constants for simple distortion patterns in biaxial nematics are derived in terms of the thermal average （Dmn^（l）） （Dm＇n＇^（l＇））, where Dmn^（l） is the Wigner rotation matrix. In the lowest order terms, the elastic constants depend on coefficients Γ,Γ＇, λ, order parameters Q0 = Q0（D00^（2）） ＋Q2（D02^（2）＋D0-2^（2）） and Q2 = Q0（D20^（2）） ＋ Q2（D22^（2）＋D2-2^（2））. Here Γ and Γ＇ depend on the function form of molecular interaction energy vj′j″j （τ12） and probability function fk′k″k （τ12）, where r12 is the distance between two molecules, and λ is proportional to temperature. Q0 and Q2 are parameters related to multiple moments of molecules. Comparing these results with those obtained from Landau-de Gennes theory, we have obtained relationships between coefficients, order parameters used in both theories. In the special case of uniaxial nematics, both results are reduced to a degenerate case where K11=K33.     

Integrated silicon-based suspended racetrack micro-resonator for biological solution sensing with high-order mode

A biological sensing structure with a high-order mode ($\mathrm{E}_{21}^{y}$) is designed, which is composed of a suspended racetrack micro-resonator (SRTMR) and a microfluidic channel. The mode characteristics, coupling properties, and sensing performances are simulated by using the finite element method (FEM). To analyze the mode confinement property, the confinement factors in the core and cladding of the suspended waveguide for the $\mathrm{E}_{11}^{x}$, $\mathrm{E}_{11}^{y}$, and $\mathrm{E}_{21}^{y}$ are calculated. The simulation results show that the refractive index (RI) sensitivity of the proposed sensing structure can be improved by using the high-order mode ($\mathrm{E}_{21}^{y}$). The RI sensitivity for the $\mathrm{E}_{21}^{y}$ mode is ～ 201 nm/RIU, which is twice to thrice higher than those for the $\mathrm{E}_{11}^{x}$ mode and the $\mathrm{E}_{11}^{y}$ mode. Considering a commercial spectrometer, the proposed sensing structure based on the SRTMR achieves a limit of detection (LOD) of ～ 4.7×10^-6 RIU. Combined with the microfluidic channel, the SRTMR can possess wide applications in the clinical diagnostic assays and biochemical detections.     

Chirality-asymmetry force between ɑ-quartz and copper block

The chirality-asymmetry macroscopic force mediated by light pseudoscalar particles between α -quartz and some achiral matter is studied. If this force between achiral source mass and α -quartz with some chirality is attractive, it will become repulsive when the chirality of the α -quartz crystal is changed. According to the tested limits of the coupling constant g_s g_p /\hbar c< 1.5× 10^-24 at the Compton wavelength λ = 10^-3 m, the force (F) between a 0.08× 0.08× 0.002 m³ block of α -quartz and a 0.08× 0.08× 0.01 m³ copper block with a separation being 0.5× 10^-3 \mbox{m} in between, is estimated from the published data at less than 4.64× 10^-24 N, i.e. F < 4.64× 10^-24 N.     

Ground state for CH2 and symmetry for methane decomposition

Using the different level of methods B3P86, BLYP, B3PW91, HF, QCISD、 CASSCF （4,4） and MP2 with the various basis functions 6-311G^＊＊, D95, cc-pVTZ and DGDZVP, the calculations of this paper confirm that the ground state is X^-3B1 with C2v group for CH2. Furthermore, the three kinds of theoretical methods, i.e. B3P86、 CCSD（T, MP4） and G2 with the same basis set cc-pVTZ only are used to recalculate the zero-point energy revision which are modified by scaling factor 0.989 for the high level based on the virial theorem, and also with the correction for basis set superposition error. These results are also contrary to X^-3∑^-g for the ground state of CH2 in reference. Based on the atomic and molecular reaction statics, this paper proves that the decomposition type （1） i.e. CH4 →CH2＋H2, is forbidden and the decomposition type （2） i.e. CH4→CHa＋H is allowed for CH4. This is similar to the decomposition of SiH4.     

激光冷却SH~–阴离子的理论研究

本文采用多组态相互作用及Davidson修正方法和全电子基组计算了SH~-阴离子的X~1∑~+,a~3∏和A~1∏态的势能曲线、电偶极矩和跃迁偶极矩.计算的光谱常数与实验值及已有的理论值符合得很好.在计算中考虑了自旋-轨道耦合效应.计算得到a~3∏_1(v'=0)?X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)?X~1Σ_(0+)~+(v"=0)跃迁具有高对角分布的弗兰克-康登因子,分别为0.9990和0.9999;计算得到a~3∏_1和A~1∏_1态的自发辐射寿命分别为1.472和0.188 ms.A~1∏_1?X~1∑_(0+)~+跃迁存在中间态a~3∏_(0+)和a~3∏_1,但中间态对激光冷却SH~-阴离子的影响可以忽略.分别利用a~3∏_1(v'=0)? X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)? X~1∑_(0+)~+(v"=0)跃迁构建了准闭合的能级系统,冷却所需的激光波长分别为492.27和478.57 nm.最后预测了激光冷却SH~-阴离子能达到的多普勒温度和反冲温度.这些结果为进一步实验提供了理论参数.     

The dissociation pathways of N2+ in intense femtosecond laser fields

Using a neutral N2 beam as target,this paper studies the dissociation of N2+ in intense femtosecond laser fields(45 fs,～1×10 16 W/cm 2) at the laser wavelength of 800 nm based on the time-of-flight mass spectra of N + fragment ions.The angular distributions of N+ and the laser power dependence of N + yielded from different dissociation pathways show that the dissociation mechanisms mainly proceed through the couplings between the metastable states(A,B and C) and the upper excited states of N2+.A coupling model of light-dressed potential energy curves of N+2 is used to interpret the kinetic energy release of N+.     

Three-party quantum secret sharing of secure direct communication based on χ-type entangled states

Based on χ-type entangled states and the two-step protocol [Deng F G,Long G L and Liu X S 2003 Phys.Rev.A 68 042317],a quantum secret sharing protocol of secure direct communication based on χ-type entangled states |χ00 3214 is proposed.Using some interesting entanglement properties of this state,the agent entirety can directly obtain the secret message from the message sender only if they collaborate together.The security of the scheme is also discussed.     

Dynamics of exact soliton solutions to the coupled nonlinear system using reliable analytical mathematical approaches

Nonlinear Schrödinger-type equations are important models that have emerged from a wide variety of fields, such as fluids, nonlinear optics, the theory of deep-water waves, plasma physics, and so on. In this work, we obtain different soliton solutions to coupled nonlinear Schrödinger-type (CNLST) equations by applying three integration tools known as the $\left(\tfrac{{G}^{{\prime} }}{{G}^{2}}\right)$-expansion function method, the modified direct algebraic method (MDAM), and the generalized Kudryashov method. The soliton and other solutions obtained by these methods can be categorized as single (dark, singular), complex, and combined soliton solutions, as well as hyperbolic, plane wave, and trigonometric solutions with arbitrary parameters. The spectrum of the solitons is enumerated along with their existence criteria. Moreover, 2D, 3D, and contour profiles of the reported results are also plotted by choosing suitable values of the parameters involved, which makes it easier for researchers to comprehend the physical phenomena of the governing equation. The solutions acquired demonstrate that the proposed techniques are efficient, valuable, and straightforward when constructing new solutions for various types of nonlinear partial differential equation that have important applications in applied sciences and engineering. All the reported solutions are verified by substitution back into the original equation through the software package Mathematica.     

A new transition metal diphosphide α-MoP2 synthesized by a high-temperature and high-pressure technique

Monoclinic $\alpha $-MoP$_{2}$, with the OsGe$_{2}$-type structure (space group $C2/m$, $Z = 4$) and lattice parameters $a = 8.7248(11) $ Å, $b = 3.2322(4) $ Å, $c = 7.4724(9) $ Å, and $\beta =119.263^\circ $, was synthesized under a pressure of 4 GPa at a temperature between 1100 ${^\circ}$C and 1200 ${^\circ}$C. The structure of $\alpha $-MoP$_{2}$ and its relationship to other transition metal diphosphides are discussed. Surprisingly, the ambient pressure phase orthorhombic $\beta $-MoP$_{2}$ (space group Cmc2$_{1}$) is denser in structure than $\alpha $-MoP$_{2}$. Room-temperature high-pressure x-ray diffraction studies exclude the possibility of phase transition from $\beta $-MoP$_{2}$ to $\alpha $-MoP$_{2}$, suggesting that $\alpha $-MoP$_{2}$ is a stable phase at ambient conditions; this is also supported by the total energy and phonon calculations.     

Relativistic calculations on the transition electric dipole moments and radiative lifetimes of the spin-forbidden transitions in the antimony hydride molecule

Calculations on the spectroscopic constants and transition properties of the first three states (${\rm a}^{1}\Delta $, ${\rm b}^{1}\Sigma^{+}$, and X$^{3}\Sigma^-$) of the SbH molecule were performed under the relativistic framework using the exact two-component Hamiltonian (X2C). The potential energy curves in the Franck-Condon region were computed and compared with the previous values. Furthermore, the transition dipole moments for the weak spin-forbidden transitions (${\rm b}0^{+}$-X$_{1}0^{+}$, ${\rm b}0^{+}$-X$_{2}$1, X$_{1}0^{+}$-X$_{2}$1, and X$_{2}$1-${\rm a}$2) were reported. The spontaneous radiative lifetime of the ${\rm b}^{1}\Sigma^{+}$ ($\upsilon '=0$) state was calculated as 163.5 $\pm$ 7.5 μs, which is in reasonable agreement with the latest experimental value of 173 $\pm$ 3 μs. The spontaneous radiative lifetimes of the X$_{2}$1 ($\upsilon '=0$) state and the ${\rm a}$2 ($\upsilon '=0$) state were calculated to be 48.6 s and $\sim 8 $ ms, respectively. Our study is expected to be a benchmark transition property computation for comparison with other theoretical and experimental results. The datasets presented in this paper, including the transition dipole moments, are openly available at https://dx.doi.org/10.11922/sciencedb.j00113.00018.     

Central black hole mass determination for blazars

In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of In this paper, we use a method to determine some basic parameters for the $\gamma$-ray loud blazars. The parameters include the central black mass ($M$), the boosting factor ($\delta$), the propagation angle (${\it {\it\Phi}}$), the distance along the axis to the site of the $\gamma$-ray production ($d$). A sample including 32 $\gamma$-ray loud blazars with available variability time scales has been used to discuss the above properties. In this method, the $\gamma$-ray energy, the emission size and the property of the accretion disc determine the absorption effect. If we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, i.e. $L_{\gamma}^{\rm in}=\lambda{L_{\rm Edd}}$, then we have the following results: the mass of the black hole is in the range of $(0.59-67.99)\times10^{7}M_{\odot} \ (\lambda=1.0)$ or $(0.90-104.13)\times10^{7}M_{\odot} \ (\lambda=0.1)$; the boosting factor ($\delta$) in the range of $0.16-2.09(\lambda=1.0)$ or $0.24-2.86\ (\lambda=0.1)$; the angle (${\it\Phi}$) in the range of $9.53^{\circ}-73.85^{\circ}\ (\lambda=1.0)$ or $7.36^{\circ}-68.89^{\circ}\ (\lambda=0.1)$; and the distance ($d/R_{\rm g}$) in the range of $22.39-609.36\ (\lambda=1.0)$ or $17.54-541.88\ (\lambda=0.1)$.     

The structures and properties of FeSin/FeSi\hbox{$_{\mathsf{n}}^{+}$}+n/FeSi\hbox{$_{\mathsf{n}}^{-}$}−n (n = 1 ~ 8) clusters

The geometry, stability, and electronic properties of iron-doped silicon clusters FeSi _n /FeSi\hbox{$_{n}^{+}$}+n/FeSi\hbox{$_{n}^{-}$}?n (n = 1 ~ 8) have been systematically investigated using the density functional theory (DFT) approach at the B3LYP/6-311+G* level. Our results show that the ground state structures of FeSi _n /FeSi\hbox{$_{n}^{+}$}+n/FeSi\hbox{$_{n}^{-}$}?n change from planar to three-dimensional for n > 3. Bipyramidal structures, or their face-capped isomers, are favored for the larger clusters. For neutral FeSi _n clusters, their ground state structures are the trigonal, tetragonal, capped tetragonal, capped pentagonal, and combined tetragonal bipyramids for n = 4 ~ 8, respectively. The lowest-energy structures of the anionic FeSi\hbox{$_{n}^{-}$}?n clusters essentially retain similar frameworks to their neutral counterparts, while those of the cationic FeSi\hbox{$_{n}^{+}$}+n clusters are significantly deformed; this is confirmed by their calculated ionization potential and electronic affinity values. For most of the stable structures, the spin electronic configurations are s = 1 or 2 for neutral FeSi _n , s = 3/2 or 5/2 for ionic FeSi\hbox{$_{n}^{+}$}+n/FeSi\hbox{$_{n}^{-}$}?n. The average binding energy values generally increase with increasing cluster size, indicating the clusters can continue to gain energy during the growth process. Fragmentation and second-order energy peaks (maxima) are found at n = 2, 5, and 7 for FeSi _n /FeSi\hbox{$_{n}^{-}$}?n, n = 4 and 6 for FeSi\hbox{$_{n}^{+}$}+n, suggesting that these clusters possess higher relative stability. Furthermore, the HOMO-LUMO gap values show that anionic FeSi\hbox{$_{n}^{-}$}?n have greater chemical reactivity than cationic FeSi\hbox{$_{n}^{+}$}+n and neutral FeSi _n , except when n = 7.     

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in′a square cavity by direct numerical simulations.The Rayleigh number range is 1×10⁸≤Ra≤1×10¹³,and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max～(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10⁹,the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10¹⁰,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV～Ra?0.14±0.01.     

Accurate calculation of the elastic scattering properties of ^7Li atoms at ultralow temperatures

The elastic scattering properties for collisions between two ^7Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X^1 ∑g^＋ and triplet a^3 ∑u^＋ ground states of the Li2, Our calculated values for the scattering lengths α and the effective ranges re are compared with previous ones, and found them to be in good agreement. The scattering lengths are 34.6α0 for the singlet state and -27.6α0 for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X^1 ∑g^＋ and a^3 ∑u^＋ states.