Variational Operators,Symplectic Operators,and the Cohomology of Scalar Evolution Equations

For a scalar evolution equation u_t = K(t, x, u, u_x, . . . , u_2m+1) with m ≥ 1, the cohomology space H^1,2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for u_t = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H^1,2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest.     

Dew Points of Binary Methane + Water: Measurement and Correlation

Experimental measurements of dew points for four methane + water mixtures between 2.6 2 10 5 Pa and 100.4 2 10 5 Pa and the temperature range from 225.5 K to 272.7 K were carried out. The experimental results were analysed in terms of both an equation of state model and an excess function-equation of state method, which reproduced the experimental data within AAD from 1.8 to 3.1 K and from 0.9 to 1.8 K, respectively.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

低温液体无损贮存压力升高的实验与计算

准确、简单地预测低温液体无损贮存时的压力升高具有重要的实用价值。对一低温容器利用液氮为介质进行了多次无损贮存实验,利用多元线性回归方法对实验数据进行分析和检验。分析表明无损贮存时间、初始充满率对压力升高的影响较大,而环境温度的影响可以忽略,并拟合出了压力升高的计算公式。计算结果和实验结果在很大范围内能够较好地吻合。该种计算方法在预测低温液体无损贮存压力升高时有较高的准确性与可靠性。     

MgSiO3状态方程的分子动力学模拟

The equation of state of MgSiO3 perovskite under high pressure and high temperature is simulated using the molecular dynamics method. It was found that the molecular dynamics simulation is very successful in accurately reproducing the measured molar volumes of MgSiO3 perovskite over a wide range of temperatures and pressures. The simulated equation of state of MgSiO3 perovskite matched experimental data at up to 140GPa at 300 K, as well as the fitting data of others and results from the first-principles simulation based on the local density approximation. The simulated equations of state of MgSiO3 perovskite at higher temperatures and higher pressures also correspond to the other calculations. In addition, the volume compression data of MgSiO3 perovskite is simulated up to 120 GPa at 300, 900, 2000 and 3000 K, respectively.     

Predicting ion selectivity in water purification by capacitive deionization: Electric double layer models

Ion-selective water treatment is needed to address emerging problems in an energy- and cost-efficient manner. Capacitive deionization (CDI) is a membraneless water treatment technology, which relies on storing ions in charged electric double layers (EDLs) of micropores. CDI has shown remarkable selectivity, with local density approximations (LDAs) showing some success in guiding selective separations. However, many underlying processes are represented by lumped fitting parameters in LDA models, hindering further progress. Atomistic models help unravel selectivity mechanisms, but are difficult to integrate with cell-level CDI theory. Here, we review and extend LDA models for CDI, highlight a knowledge gap in connecting between LDA and atomistic models for CDI, and emphasize and build upon analogies between micropore EDLs and nanofiltration membranes.     

解非定常不可压缩N-S方程的迭代压力Poisson方程法

１．引 言 数值求解不可压缩流体流动问题可以采用原始变量的方程作为控制方程,也可以用涡量一流函数方程作为控制方程．直接求解原始变量的不可压缩 Ｎａｖｉｅｒ—Ｓｔｏｋｅｓ方程存在一个主要困难：速度向量在每一时刻都必须满足零散度约束条件,即不可压缩性连续方程．用涡量一流函数方程求解时,连续方程自动满足,所以不存在约束条件的问题,但涡量的边界条件比较难处理,且不易应用于三维问题和带有自由表面或其它流体交界面的问题． 解决上述速度向量必须满足零散度约束条件的困难的方法有：人工压缩法［３,１７］;压力Ｐｏｉｓ…