Continuous interior penalty finite element methods for Sobolev equations with convection‐dominated term

We consider implicit and semi‐implicit time‐stepping methods for continuous interior penalty (CIP) finite element approximations of Sobolev equations with convection‐dominated term. Stability is obtained by adding an interior penalty term giving L² ‐control of the jump of the gradient over element faces. Several $\cal {A}$ ‐stable time‐stepping methods are analyzed and shown to be unconditionally stable and optimally convergent. We show that the contribution from the gradient jumps leading to an extended matrix pattern may be extrapolated from previous time steps, and hence handled explicitly without loss of stability and accuracy. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

Construction of locally conservative fluxes for the SUPG method

We consider the construction of locally conservative fluxes by means of a simple postprocessing technique obtained from the finite element solutions of advection diffusion equations. It is known that a naive calculation of fluxes from these solutions yields nonconservative fluxes. We consider two finite element methods: the usual continuous Galerkin finite element method for solving nondominating advection diffusion equations and the streamline upwind/Petrov‐Galerkin method for solving advection dominated problems. We then describe the postprocessing technique for constructing conservative fluxes from the numerical solutions of the general variational formulation. The postprocessing technique requires solving an auxiliary Neumann boundary value problem on each element independently and it produces a locally conservative flux on a vertex centered dual mesh relative to the finite element mesh. We provide a convergence analysis for the postprocessing technique. Performance of the technique and the convergence behavior are demonstrated through numerical examples including a set of test problems for advection diffusion equations, advection dominated equations, and drift‐diffusion equations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1971–1994, 2015     

线性对流占优扩散方程的后验误差估计

对于线性对流占优扩散方程,采用特征线有限元方法离散时间导数项和对流项,用分片线性有限元离散空间扩散项,并给出了一致的后验误差估计,其中估计常数不依赖与扩散项系数。     

A two‐grid characteristic finite volume element method for semilinear advection‐dominated diffusion equations

A two‐grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time‐dependent advection‐dominated diffusion equations in two space dimensions. The solution of a nonlinear system on the fine‐grid space (with grid size h) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse‐grid space (with grid size H) and a linear system on the fine‐grid space. An optimal error estimate in H¹ ‐norm is obtained for the two‐grid method. It shows that the two‐grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O(H²). Numerical example is presented to validate the usefulness and efficiency of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Ultrasound assisted deposition of highly stable self-assembled Bi2MoO6 nanoplates with selective crystal facet engineering as photoanode

The use of crystal facets of photocatalysts is well known as a promising strategy for the design of new photocatalysts with interesting physicochemical features for energy production applications. In this work, Bi₂MoO₆ thin films were synthesized by two methods, electrodeposition and sonoelectrodeposition. Preferential growth orientation depended on synthesis method. Results suggested that sonoelectrodeposition led to dominate the crystal facet {1 0 0} growth with self-assembled nanoplate morphologies while growth orientation in the {0 1 0} facet was dominant in electrodeposition in the absence of ultrasonic waves. As a highlight result, the {1 0 0} facet shows a smaller band gap, higher photocatalytic water splitting than the {0 1 0} facet. Efficient separation of charge pairs and long life time of photogenerated electrons was observed to be intrinsic features of the {1 0 0} facets. The higher charge transfer was confirmed by a higher photocurrent from linear sweep voltammetry and a smaller Nyquist radius arc. Ultrasound plays a key role in growth orientation and led to a production of homogeneous films with nanoplates which self-assembled together to form a flower-like structure. While in the absence of ultrasound the film has coral-like structure. Highly stable sonoelectrodeposited films exhibited incident photon-to-electron conversion efficiency (IPCE) of 22.4% at the specific wavelength of 500 nm. The sonoelectrodeposition method could act as a promising method for forming new films with specific crystal facet selection and developing as highly efficient photoanodes for PEC water splitting.     

碳纸负载高指数晶面铂纳米粒子的制备及其在直接甲酸燃料电池中的催化性能研究

直接甲酸燃料电池(DFAFCs)是一种很有前景的可用于移动电子设备的电源. 钯对甲酸电催化氧化有很高的活性,但稳定性较差,容易失活;铂对甲酸电催化氧化的活性低于钯,但稳定性好. 前期研究表明,高指数晶面铂纳米粒子对甲酸的电催化氧化活性显著高于低指数晶面铂纳米粒子. 本文以碳纸为载体,应用方波电位法生长高指数晶面铂纳米粒子（HIF-Pt/C-paper）,通过改变方波上下限电位,合成出不同粒径的二十四面体和偏方三八面体铂纳米粒子. 进一步在碳纸上修饰一层碳黑微孔层并优化电沉积条件,制备出粒径约10 nm,载量0.069 mg•cm^-2的HIF-Pt/C-paper作为DFAFCs的阳极催化剂.在甲酸浓度为3M时,测得30℃下单电池最大功率密度10.6 mW•cm^-2,最大质量功率密度153.5 mW•mg^-1_Pt,是以1mg•cm^-2 载量的商业60 wt% Pt/C为阳极催化剂的电池的8.4倍. HIF-Pt/C-paper阳极DFAFCs在20 mA•cm^-2条件下运行50 h,电压保持率为95%,显示出很好的稳定性.     

基于模糊聚类的构件检索方法

在构件的检索过程中,由于用户对于构件的描述形式或者机制不是很理解,因此很难把自己的需求以专业的术语或者表达形式表示出来,从而影响了检索的效率。引入了刻面权重的定义,将用户的需求有效的具象化,并提出了基于模糊聚类分析的构件检索方法,利用一定的聚类准则将构件库里的构件集合划分为不同的类别,降低构件检索的规模,提高构件检索的效率,同时具有较好的查全率和查准率。实验结果证明了该方法的可行性与有效性。     

任意随机序列关于二重非齐次马氏链的随机和的一类随机选择系统的随机逼近定理

本文引进任意随机变量序列随机极限对数似然比的概念,通过测度$\pr$下任意相依随机序列联合分布与测度$\qr$下二重非齐次马氏分布相比较,利用母函数与尾概率母函数工具研究任意受控随机序列之随机和在随机选择系统中的一类随机逼近定理.     

When almost all sets are difference dominated

We investigate the relationship between the sizes of the sum and difference sets attached to a subset of {0,1,…,N}, chosen randomly according to a binomial model with parameter p(N), with N^?1 = o(p(N)). We show that the random subset is almost surely difference dominated, as N → ∞, for any choice of p(N) tending to zero, thus confirming a conjecture of Martin and O'Bryant. The proofs use recent strong concentration results. Furthermore, we exhibit a threshold phenomenon regarding the ratio of the size of the difference to the sumset. If p(N) = o(N^?1/2) then almost all sums and differences in the random subset are almost surely distinct and, in particular, the difference set is almost surely about twice as large as the sumset. If N^?1/2 = o(p(N)) then both the sum and difference sets almost surely have size (2N + 1) ? O(p(N)^?2), and so the ratio in question is almost surely very close to one. If p(N) = c · N^?1/2 then as c increases from zero to infinity (i.e., as the threshold is crossed), the same ratio almost surely decreases continuously from two to one according to an explicitly given function of c. We also extend our results to the comparison of the generalized difference sets attached to an arbitrary pair of binary linear forms. For certain pairs of forms f and g, we show that there in fact exists a sharp threshold at c_f,g · N^?1/2, for some computable constant c_f,g, such that one form almost surely dominates below the threshold and the other almost surely above it. The heart of our approach involves using different tools to obtain strong concentration of the sizes of the sum and difference sets about their mean values, for various ranges of the parameter p. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009