Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

We present a coupled lattice Boltzmann method (LBM) to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst–Planck equation for the ion concentration, and the Navier–Stokes equation for the flows of the electrolyte solution. In the proposed LBM, the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator, which maintains the locality of the algorithm inherent to the original LBM. Furthermore, the Neumann-type boundary condition at the solid/liquid interface is then correctly imposed. In order to validate the present LBM, we consider an electro-osmotic flow in a slit between two charged infinite parallel plates, and the results of LBM computation are compared to the analytical solutions. Good agreement is obtained in the parameter range considered herein, including the case in which the nonlinearity of the Poisson equation due to the large potential variation manifests itself. We also apply the method to a two-dimensional problem of a finite-length microchannel with an entry and an exit. The steady state, as well as the transient behavior, of the electro-osmotic flow induced in the microchannel is investigated. It is shown that, although no external pressure difference is imposed, the presence of the entry and exit results in the occurrence of the local pressure gradient that causes a flow resistance reducing the magnitude of the electro-osmotic flow.     

On MHD flow of an incompressible viscous fluid

In this paper, we apply Homotopy Perturbation Method (HPM) to find the analytical solutions of nonlinear MHD flow of an incompressible viscous fluid through convergent or divergent channels in presence of a high magnetic field. The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. The graphs are presented to reveal the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.     

Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.     

热方程的一些端点估计及其在Navier-Stokes方程中的应用——献给陆善镇教授75华诞

本文首先讨论热方程初值问题的解在Hardy、BMO（bounded mean oscillation）和Besov型空间中的估计.然后本文结合Coifmann-Lions-Meyer-Semmes在Hardy空间中的补偿紧性结果,给出Navier-Stokes方程整体弱解的二阶导数的一些端点估计.     

An immersed boundary–lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows

A combined immersed boundary–lattice Boltzmann approach is used to simulate the dynamics of elastic membrane immersed in a viscous incompressible flow. The lattice Boltzmann method is utilized to solve the flow field on a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid–membrane interaction with a Lagrangian representation of the deformable immersed boundary. The distinct feature of the method used here is to employ the combination of simple Peskin's IBM and standard LBM. In order to obtain more accurate and truthful solutions, however, a non-uniform distribution of Lagrangian points and a modified Dirac delta function are used. Two test cases are presented. In the first case, we consider a vesicle suspended in a simple shear flow commonly known as tank-treading motion. The computed results were compared with experiments, which showed reasonably good agreement. For the second test case, we consider individual healthy (soft) and sick (stiff) RBCs suspended in a shear flow. The simulation results demonstrated that elastic deformation plays an important role in overall RBC motions characterized as tank-treading and tumbling motions, in which the natural state of the elastic membrane is an essential consideration. In addition, the results confirm that the combination of the immersed boundary and lattice Boltzmann methods permits the simulation of the complex biological phenomena.     

有超车规则的交通流的元胞自动机模型

分析和评论了2014年美国大学生数学建模竞赛（MCM）A题,以及获得outstanding winner奖的6篇论文。首先对试题进行分析,并结合已有文献指出A题的主要解题思路;然后,通过评述获奖论文,指出学生论文的优点及存在的问题;最后,对今年赛题的某些问题进行讨论。     

Stability of hyperbolic manifolds with cusps under Ricci flow

We show that every finite volume hyperbolic manifold of dimension greater than or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation.     

A partially penalty immersed interface finite element method for anisotropic elliptic interface problems

In this article, we develop a partially penalty immersed interface finite element (PIFE) method for a kind of anisotropy diffusion models governed by the elliptic interface problems with discontinuous tensor‐coefficients. This method is based on linear immersed interface finite elements (IIFE) and applies the discontinuous Galerkin formulation around the interface. We add two penalty terms to the general IIFE formulation along the sides intersected with the interface. The flux jump condition is weakly enforced on the smooth interface. By proving that the piecewise linear function on an interface element is uniquely determined by its values at the three vertices under some conditions, we construct the finite element spaces. Therefore, a PIFE procedure is proposed, which is based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. Then we prove the consistency and the solvability of the procedure. Theoretical analysis and numerical experiments show that the PIFE solution possesses optimal‐order error estimates in the energy norm and norm.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1984–2028, 2014     

一种基于无监督学习的社交网络流量快速识别方法

在分析了社交网络的发展和研究现状后,结合现有的网络流量识别方法和社交网络流量特征属性,提出了一种基于KMeans聚类算法的无监督学习社交网络流量识别方法.为了提高处理的高效性、实时性,利用开源云计算平台如doop上提供的M印Reduce架构进行分布式并行处理.对比实验结果表明,提出的方法能快速、高效的识别社交网络流量,并且识别准确率有显著提高.     

金融危机后中国跨境短期资本流动与人民币汇率及资产价格波动关联研究

基于综合资产收益率平价理论构建理论模型,研究探讨了中国跨境短期资本流动规模与资产价格及人民币汇率预期变动之间的动态关系.然后在此基础上通过建立VAR模型,采用格兰杰因果检验以及脉冲响应分析等方法实证分析了2010年7月至2015年6月中国跨境短期资本流动、人民币汇率预期波动、利率、房价和股价变动之间的关联关系.实证结果表明:中国房地产市场、股票市场上涨会吸引短期跨境资本流入;美元利率上升和人民币贬值预期会引致短期跨境资本的流出;短期跨境资本流入会造成国内利率降低,但对房地产市场、股票市场的影响不显著;中国房地产市场与股票市场之间会有联动效应,人民币的贬值预期也会引致房地产价格下降.