An algebraic variational multiscale–multigrid method for large-eddy simulation of turbulent variable-density flow at low Mach number

An algebraic variational multiscale–multigrid method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. Scale-separating operators generated by level-transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups (here, the smaller of the resolved scales) in a purely algebraic way. Thus, for scale separation, no additional discretization besides the basic one is required, in contrast to earlier approaches based on geometric multigrid methods. The proposed method is thoroughly validated via three numerical test cases of increasing complexity: a Rayleigh–Taylor instability, turbulent channel flow with a heated and a cooled wall, and turbulent flow past a backward-facing step with heating. Results obtained with the algebraic variational multiscale–multigrid method are compared to results obtained with residual-based variational multiscale methods as well as reference results from direct numerical simulation, experiments and LES published elsewhere. Particularly, mean and various second-order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small-scale subgrid-viscosity term within the algebraic multigrid framework instead of residual-based terms accounting for the subgrid-scale part of the non-linear convective term.     

网络体验式广告探析

网络体验式广告主要采用游戏策略、虚拟体验策略、鼓励策略和悬疑策略等,成功的网络体验式广告运营模式具有平台广阔、互动性强、技术完善、成本低廉以及良好的广告效果测定手段等投放优势.我国网络体验式广告起步较晚,存在着互动性不强、运营模式单一、广告投放效果不佳等问题,应综合运用多种广告表现策略,并与其它营销策略与媒体整合运用,以期得到良好的发展.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.     

聚苯并双噁唑酰亚胺的热分解动力学研究

采用二步法合成了以2,6-二(对-氨基苯)苯[1,2-d;5,4-d’]二噁唑和1,4-二(3,4-二苯氧基)苯四甲酸二酐(HQDPA)为单体的聚苯并双噁唑酰亚胺.该聚酰亚胺的预聚体聚酰胺酸的黏度为1.70 dL/g,经过热环化后能够生成浅黄色的聚酰亚胺薄膜.通过热重分析法研究了聚苯并双噁唑酰亚胺在N2气氛中的热降解机理.采用Flynn-Wall-Ozawa和Friedman法计算了聚苯并双噁唑酰亚胺热降解表观活化能,分别为356.36kJ/mol和370.54 kJ/mol,平均值为363.45 kJ/mol;反应级数为4.22,指前因子为6.44×1016s-1.采用Coast-Redfern法和Phadnis-Deshpande法研究了聚苯并双噁唑酰亚胺的热降解固相反应机理,认为该聚酰亚胺的热降解机理属于反曲线(A3)机理,是成核和增长模式(Avrami equation 2方程)控制的热降解反应,积分形式为g(X)=[-ln(1-X)]3.     

联吡啶[3,2-a：2’,3-c]-7-氮杂-吩嗪铜(I)配合物的合成、表征及其与DNA的相互作用

合成了邻菲罗啉衍生物联吡啶[3,2-a:2',3'-c]-7-氮杂-吩嗪(dpapz)及其铜(I)配合物[Cu(dpapz)₂]PF₆, 利用核磁共振氢谱(¹H NMR), 傅里叶变换红外(FTIR)光谱, 高分辨质谱(HR ESI-MS)等对合成的化合物进行了表征.采用紫外-可见吸收光谱,荧光光谱, DNA熔解温度实验和循环伏安方法研究了dpapz和[Cu(dpapz)₂]PF₆与小牛胸腺DNA(CT DNA)的相互作用. 配体dpapz与小牛胸腺DNA(CT DNA)作用时未观察到吸收峰红移并且减色效应较小(<30%), 且DNA熔解温度也上升较小(ΔT_m=7.8 ℃), 说明dpapz以沟槽结合的方式与CT DNA相互作用. 而[Cu(dpapz)₂]PF₆与CT DNA作用时, 可观测到较小的吸收峰红移(2-3 nm)和较大的减色效应(>50%), 同时DNA熔解温度上升较大(ΔT_m=11.1 ℃), 表明[Cu(dpapz)₂]PF₆以静电相互作用和部分扦插的方式与DNA结合. 溴乙锭(EB)荧光竞争实验和循环伏安实验进一步证实了这一结论. 配体dpapz和[Cu(dpapz)₂]PF₆与DNA的结合常数分别为2.88×10⁵和5.32×10⁵ mol·L^-1. 光照条件下, [Cu(dpapz)₂]PF₆产生单重态氧的能力与dpapz相当, 但产生超氧负离子自由基的能力要弱于dpapz. 活性氧猝灭实验表明, 超氧负离子自由基、单重态氧和羟基自由基均参与了dpapz和[Cu(dpapz)₂]PF₆对DNA的光损伤作用. [Cu(dpapz)₂]PF₆对DNA的亲和性要高于对dpapz的, 使得[Cu(dpapz)₂]PF₆对质粒DNA的光损伤效率明显强于dpapz.     

NO2在Ag/Pt(110)双金属表面上的吸附和分解

利用俄歇电子能谱(AES)和程序升温脱附谱(TDS)研究了NO₂在Ag/Pt(110)双金属表面的吸附和分解.室温下NO₂ 在Ag/Pt(110)双金属表面发生解离吸附, 生成NO(ads)和O(ads)表面吸附物种. 在升温过程中NO(ads)物种发生脱附或者进一步分解. 500 K时NO₂在Ag/Pt(110)双金属表面发生解离吸附生成O(ads)表面吸附物种. Pt 向Ag传递电子, 从而削弱Pt－O键的强度, 降低O(ads)从Pt 表面的并合脱附温度. 发现能够形成具有稳定组成的Ag/Pt(110)合金结构, 其表现出与Pt(110)-(1×2)相似的解离吸附NO₂能力, 但与O(ads)的结合明显弱于Pt(110)-(1×2). 该AgPt(110)合金结构是可能的低温催化直接分解氮氧化物活性结构.     

A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. Löhne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a “lattice difference quotient.” A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs. The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions.     

Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.