恒热流加热开口腔自然对流的可视化实验和数值模拟

本文采用激光全息干涉和激光片光照射烟可视化方法获得了恒热流加热的二维开口腔自然对流问题的温度场和流场,并进行了数值分析.实验结果与数值模拟结果吻合.数值计算表明方腔内流体的流通量与Ra*和深高比B有关,当Ra*＞104时随深高比B增加流通量增加;B×Nu与深高比B呈线性关系.利用B×Nu与深高比B的线性关系,通过引入当量导热系数λc,本文还给出了加热壁面的平均温度的简单计算方法.     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals.     

开源教学平台的可用性研究——以Sakai为例

越来越多的国内外高校开始考虑使用基于开源软件的网络教学平台,在投入使用之前,开源教学平台一般需要进行二次开发过程,其中需要重点解决平台的可用性问题,因为网络教学平台的可用性是影响学习效果的重要因素.发现并解决网络教学环境中的可用性问题,是促进人机交互、提高学习效率的重要途径.开源教学平台的可用性指的是系统的有效性、效率和满意度,分析了网络教学平台的可用性诉求,并以浙江大学Sakai开放学习平台为例,进行个案研究.使用了ThinkAloud、观察法和访谈法等可用性测试方法,研究结果发现,浙江大学Sakai开放学习平台主要功能人机交互设计合理,但是由于文化差异和用户使用习惯问题,部分功能存在一定的可用性问题,值得学习平台设计者借鉴.     

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

A new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles. To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved. Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

Closed graph and open mapping theorems for normed cones

A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.     

Master equation of the reduced statistical operator of an atom in a plasma

We use the nonequilibrium Liouville equation to derive the master equation for the reduced statistical operator in a heat bath represented by a many-particle environment. Focusing on the case of a weak system-bath coupling, we consider the Born-Markov approximation of the master equation and compare the result to different approaches. The master equation is elaborated for the special case of an atom as a reduced system in a plasma background. We find that the dynamical structure factor determines the effect of the plasma on the reduced system. We consider the operator equation in the atomic eigenstate and in the phase-space representation, which yields two limiting cases: quantum mechanical behavior similar to the isolated atom for the lower strongly bound levels and a semiclassical one for highly excited Rydberg levels. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 31–62, January, 2008.     

The best quadrature formula based on Hermite information for the class KW~2[a,b]

The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.     

Quantum non-Markovian Langevin equations and transport coefficients for an inverted oscillator

Based on the non-Markovian quantum Langevin equations, we obtain time-dependent transport coefficients for an inverted oscillator coupled linearly in the coordinate to a thermostat. We comparatively analyze the diffusion coefficients for harmonic and inverted oscillators and study the role of quantum statistical effects in the passage through a parabolic barrier. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 425–443, September, 2008.