Analytic derivation of Monin-Obukhov similarity function for open atmospheric surface layer

The Monin-Obukhov(MO) similarity function φ_m of the atmospheric surface layer(ASL) describing the deviation from the log law of the canonical turbulent boundary layer because of thermal stratification has been traditionally determined empirically.This study presents a unified analytic expression derived from a symmetry-based theory of wall turbulence,called structural ensemble dynamics(SED),which postulates a generalized dilation symmetry principle expressing the effect of the wall on turbulence,leading to an analytic multi-regimes expression for the mixing length.For ASL in unstable and stable conditions(i.e.,UC and SC),a unified two-regime formula of the mixing length is proposed,leading to a φ_m,similar to the Businger-Dyer(BD) formula;with a simplified model energy balance equation,φ_m is completely specified with no free parameter.Furthermore,the theory allows the study of the open ASL's underlying additional physical processes such as bottom-up or top-down flux due to pressure variations T_p.Assuming that T_p is decomposed into shear-like and buoyancy-like components,we propose new explanations for two important features of typical ASL:a significantly smaller Karman constant of 0.36 and a varying φ_m for SC mean speed profiles.The theory is validated by the data obtained at Kansas and also at Qingtu Lake Observation Array in Northern China for a variety of heat flux conditions.In conclusion,due to pressure variations,we assert that ASL is intrinsically open and that the current theory offers a new basis for its quantification.     

Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator

We obtain the solutions of two-dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.     

Stability and attractive basins of multiple equilibria in delayed two-neuron networks

Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r(r≥1) corner points is studied. Sufficient conditions are established for checking the existence of (2r+1)2 equilibria in delayed recurrent neural networks. Under these conditions, (r+1)2 equilibria are locally exponentially stable, and (2r+1)2-(r+1)2-r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.     

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re■320 are presented by a bifurcation diagram for Re 2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of2208 Re 2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.     

Complex dynamical behavior and chaos control in fractional-order Lorenz-like systems

In this paper, the complex dynamical behavior of a fractional-order Lorenz-like system with two quadratic terms is investigated. The existence and uniqueness of solutions for this system are proved, and the stabilities of the equilibrium points are analyzed as one of the system parameters changes. The pitchfork bifurcation is discussed for the first time, and the necessary conditions for the commensurate and incommensurate fractional-order systems to remain in chaos are derived. The largest Lyapunov exponents and phase portraits are given to check the existence of chaos. Finally, the sliding mode control law is provided to make the states of the Lorenz-like system asymptotically stable. Numerical simulation results show that the presented approach can effectively guide chaotic trajectories to the unstable equilibrium points.     

Fully Developed Convective Heat Transfer of Power Law Fluids in a Circular Tube

We present a theoretical analysis for fully developed convective beat transfer in a circular tube for power law fluids by assuming that the thermal diffusivity is a function of temperature gradient. The analytical eolution is obtained and the heat transfer behaviour is investigated under a constant heat flux boundary condition. It is shown that the Nusselt number strongly depends on the value of power law index n. The Nusselt number sharply decreases in the range of 0 〈 n 〈 0.1. However, for n 〉 0.5, the Nusselt number decreases monotonically with the increasing n, and for n 〉 20, the values of Nusselt number approach a constant.     

Generation of on-off intermittency based on RSssler chaotic system

In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Rossler chaotic system. The parameter conditions under which the on-off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of -3/2, which is a signature of on-off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on-off intermittency based on a chaotic system, which is important for application and theoretical study.     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson’s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.     

Nonparaxial propagation of Hermite-Laguerre-Gaussian beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of a Hermite-Laguerre-Gaussian （HLG） beam in uniaxial crystal orthogonal to the optical axis are derived. The intensity distribution of an HLG beam and its three components propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. Although the y and z components of an HLG beam in the incident plane are both equal to zero, they emerge upon propagation inside the uniaxial crystal. Moreover, the beam profile of the x component is relatively stable and the beam profiles of the y and z components have the same evolution law. If the ratio of the extraordinary refractive index to the ordinary refractive index is larger than unity, the beam profile of the HLG beam is elongated in the x direction and generally rotates clockwise. Otherwise, the beam profile of the HLG beam is elongated in the y direction and generally rotates anticlockwise. This research is beneficial to the optical trapping and nonlinear optics involved in the rotation of a beam profile.     

Stereodynamics study of the H′（^2S） ＋ NH（X^3∑-） 〉 N（4S） ＋ H2 reaction

The stereodynamics and reaction mechanism of the H′（^2S） ＋ NH （X^3∑^-） → N（^4S） ＋ H2 reaction are thoroughly studied at collision energies in the 0.1 eV-1.0 eV range using the quasiclassical trajectory （QCT） on the ground 4A″ potential energy surface （PES）. The distributions of vector correlations between products and reagents P（φr）, P（φr） and P（φr,φr） are presented and discussed. The results indicate that product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane; further, the product H2 presents different rotational polarization behaviors for different collision energies. Furthermore, four polarization-dependent differential cross sections （PDDCSs） of the product He are also calculated at different collision energies. The reaction mechanism is analyzed based on the stereodynamics properties. It is found that the abstraction mechanism is appropriate for the title reaction.     

Ge-Sb-Se硫系玻璃的折射率和热光系数

Ge-Sb-Se硫系玻璃被认为是极佳的红外传输材料和有潜力的非线性光学材料.在光学设计中,玻璃的线性折射率(n)及其热光系数(ζ)是关键技术参数.以预测和调控Ge-Sb-Se玻璃的n和ζ为目的,考察了玻璃的n,ζ,密度(d)和体积膨胀系数(β)与化学参数dSe和拓扑网络结构参数r的内在联系.研究发现,玻璃的n随d的增加而增大;ζ随β的增大而近似线性减小;β随dSe的减小或r的增大而减小;当Ge含量固定时, d随dSe的减小或r的增大而增大,当Sb含量固定时, d在dSe=0时具有最小值.基于实测d和n,拟合获得了Ge, Sb和Se元素在2—12μm波段的摩尔折射度(R_i),分别为R_(Ge)=10.16—10.50 cm~3/mol,RSb=16.71—17.08 cm~3/mol和RSe=11.15—11.21 cm~3/mol,根据d和R_i计算得到的n与实测值的偏差小于1%.基于实测ζ和β,拟合得到了Ge, Sb和Se元素在2—12μm波段的摩尔折射度温度系数(φ_i),分别为φ_(Ge)=21.1—22.6 ppm/K,φ_(Sb)=7.2—8.4 ppm/K和φ_(Se)=90.2—94.2 ppm/K,根据β和φ_i计算得到的ζ与实测值的偏差小于6 ppm/K.     

半干旱草原下垫面动量和感热总体输送系数参数化关系研究

本文利用锡林郭勒草原2008年春季近地层涡旋相关系统和铁塔的风、 温平均梯度观测资料, 分析了总体输送系数随梯度Richardson数的变化特征, 建立了动量总体输送系数随大气稳定度、近地层风速以及感热总体输送系数随大气稳定度和近地层气温的关系. 中性条件下, 半干旱草原植被下垫面动量总体输送系数与近地层大气动力状态之间存在明显的相互作用, 总体输送系数与近地面层风速之间满足二次曲线拟合关系; 风速较小时, 大气动力特征对地表粗糙度长度的改变不是很明显, 动量总体输送系数随气流增强而增大; 而当风速较大时, 强风速会使植被高度发生改变, 动量总体输送系数随气流增强而减小. 另外, 感热总体输送系数与近地层气温之间也存在二次曲线关系. 动量总体输送系数与近地层风速之间的关系、感热总体输送系数与近地层气温之间关系的建立为总体输送系数参数化提供了重要途径, 同时该方案避免了对动力学粗糙度长度和热力学粗糙度长度的求解. 关键词： 总体输送系数 参数化 湍流通量 相似性函数     

在线社交网络中群体互动行为的时间特征

针对在线社交网络中群体互动行为,运用有偏扩散理论,构建有偏扩散模型,从任务的间隔时间τ与执行时间θ的关系视角,系统地阐述了群体互动活动中群体发帖行为与事件行为的时间间隔分布特征.针对群体用户发帖时τ≥θ的特征,论证群体用户发帖时间间隔的幂律分布机理.针对事件时τ>>θ的特征,论证了事件时间间隔具有指数效应的幂律分布机理,实验结果与理论推导吻合.     

二维圆盘颗粒体系声学行为的数值研究

数值测量了卸载过程中二维单分散圆盘颗粒系统的横波、纵波声速、声衰减系数、非线性系数随压强的变化以及声衰减系数随频率的变化.结果表明,二维(2D)圆盘颗粒体系的横波、纵波声速均随压强呈分段幂律标度:当压强P10~(-4)时,横波、纵波声速随压强的增大而减小;当P10~(-4)时,有v_t~P~(0.202),v_l~P~(0.338).进一步得到其剪切模量和体积模量的比值G/B也随压强呈幂律标度,G/B~P~(-0.502),暗示在低压强下,与三维(3D)球形颗粒体系类似,2D圆盘颗粒体系也处于L玻璃态.水平激励和垂直激励下2D圆盘颗粒系统的衰减系数随频率变化也呈现分段行为:当频率f0.05时,衰减系数不随f变化;当f0.05时,横波纵波的衰减系数α~f;当f0.35时,横波衰减系数α_T~f~2,纵波衰减系数α_L~f~(1.5).此外,竖直水平激励下的2D圆盘颗粒系统的非线性系数和衰减系数随压强也呈现与声速类似的分段规律:当P10~(-4)时,横波非线性系数β_T~P~(-0.230),其余都不随压强变化.当P10~(-4)时,两者均随压强增大呈幂律减小:β_T~P~(-0.703),β_L~P~(-0.684),α_T~P~(-0.099),α_L~P~(-0.105).进而得到2D圆盘颗粒系统中散射相关的特征长度?~*随压强呈幂律标度,当P10~(-4)时,?~*~P~(-0.595);当P10~(-4)时,?~*~P~(0.236).     

倾斜度及温度震荡频率对三维多孔介质方腔自然对流换热的影响

对三维多孔介质倾斜方腔内非稳态自然对流换热进行数值研究.腔体右壁面(X=1)保持恒温T₀,左壁面(X=0)基于温度T₀按正弦规律变化,其他所有壁面保持绝热.采用Brinkman扩展达西模型及SIMPLE算法模拟方腔内的流动.方腔沿y轴转动倾角α1的变化范围为0°~90°,沿x轴转动倾角α2的变化范围为0°~45°,无量纲温度震荡频率f的变化范围为5π~90π.详细研究倾角和温度震荡频率对三维方腔自然对流换热的影响.计算结果表明:当倾角α1=46°,α2=45°及温度震荡频率f=45π时,方腔内的换热最强.     

182Os 核yrast带相继SU(3)–U(5)–SU(3)结构相变势能曲面的一种可能理解

基于联合实施微观相互作用玻色子模型的最大F旋方案 (sdIBM-F_max)与γ射线能量-自旋曲线 (γ-ray energy over spin curves, E-GOS)方案, 成功描述了¹⁸²Os核yrast带相继的SU(3)–U(5)–SU(3)结构相变, 由于缺少直观解释而显得抽象. 本文借助微观sdIBM-F_max的微观参数与Bohr哈密顿量的势能曲面方程之间存在的泛函关系, 几何地给出了对这种相继相变途径的另外一种可能理解; 并阐述了在完全变形核的高角动量态中, 由于量子效应在高激发态与低激发态之间生成高简并的临界区, 提供了γ振动能量会变得低于转动能量的一个可能途径, 从而实现了SU(3)–U(5)的相变. 关键词： yrast带结构演化 势能曲面 相变临界区 182Os核')" href="#">¹⁸²Os核     

γ-and α-Ce phase diagram: First-principle calculation

Controversies about the phase diagram for the isostructural γ ? α phase transition of cerium have long been standing out for several decades. To seek insight into the problems, high-precision equations of state(EOS) for γ-and α-cerium are constructed based on first-principle calculation. Versus previous works, the strong anharmonic effects of ion vibration and the variation of magnetism of γ-cerium are stressed. The new EOS generally agrees well with experimental data regarding thermodynamics, phase diagrams, and phase transitions. However, new EOS predicts that another part of phase boundary in pressure-temperature space may exist except for the commonly known boundary. In addition, the well-known critical point seems to be a critical point for γ-cerium to translate from a stable state to an unstable state.     

一端附壁高分子链的Monte Carlo研究

采用简立方格点上的Monte Carlo模拟,研究一端被无限大不可穿透平面壁吸附的高分子链的均方末端距<R²>,以及高分子链的质量中心到平面吸附壁的平均距离<Z>,与链长N、参数u(u=e^-ε/kT,ε是链骨架原子间的相互作用能量,k是玻耳兹曼常数,T是热力学温度)的关系。结果表明:<R²>和<Z>都服从标度律,<R²>=αN^γ,<Z>=βN^η,其中,γ、η、α、β都是u的函数;u从1减小到0.5,则γ从1.01增大到1.19,η从0.51增大到0.60.     

同位素效应对H+NH→N+H2反应的立体动力学性质的影响

基于翟红生和韩克利给出的势能面[Zhai H S, Han K L 2011 J. Chem. Phys. 135 104314], 运用准经典轨线方法对H+NH及其同位素取代反应的立体动力学性质进行了理论研究. 分别计算并讨论了碰撞能E_c=8和16 kcal/mol时反应的极化微分反应截面、两矢量k-j'相关分布函数P(θ_r)、 三矢量 k- k'- j'相关分布函数P(φ_r)、空间分布函数P(θ_r, φ_r). 结果表明, 对于上述的两个碰撞能, 由于同位素取代反应中质量因子的不同, 同位素效应对H+NH反应的立体动力学性质的影响很明显.