A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

Iterative and adjusting method for computing stream function and velocity potential in limited domains and convergence analysis

The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.

RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (NAVIER-STOKES) EQUATION WITH STREAM FUNCTION FORM

Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

Stream Function Wave Derived by Unified Variational Principle of Water Gravity Wave

Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.

TWO-LEVEL METHOD FOR UNSTEADY NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM

Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.

The Classical Hall Effect in Multiply-Connected Plane Regions Part I: Topologies with Stream Function

Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.

Finite Element Solution of a Stream Function-Vorticity System and Its Application to the Navier Stokes Equations

The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.

Sea surface height and transport stream function of the South China Sea from a variable-grid global ocean circulation model

A fine-grid model (1/6) covering the South China Sea (SCS), East China Sea and Ja-pan/East Sea, which is embedded into a coarse-grid (3) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Com-parison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water in-trudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS South-ern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.

Artificial viscosity in the transonic stream function formulation

The artificial density method which has been applied widely in the transonic potential calculation and the current transonic stream function calculation is investigated theoretically. The analysis shows that in the stream function formulation the artificial density is not equivalent to the artificial viscosity and cannot be used, and a correct expression of the artificial viscosity in the stream function method is then derived. The principal equation of the stream function, the density equation converted from one of the momentum equations and the present artificial viscosity scheme constitute the complete transonic stream function formulation. The numerical practice demonstrates that the range of Mach number computed by this approach is extended and the shock location is close to the experimental result.

STUDY ON STREAM CIPHERS USING GENERATING FUNCTIONS

Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.

The Nonlinear Filter Boolean Function of LILI-128 Stream Cipher Generator Is Successfully Broken Based on the Complexity of Nonlinear 0 1 Symbol Sequence

The nonlinear filter Boolean function of LILI-128 stream cipher generator is studied in this paper. First we measure the complexity of the stream ciphers sequence of LILI-128 stream cipher generator and obtain the shortest bit stream sequence reconstructed Boolean function of nonlinear filter in LILI-128 stream cipher generator. Then the least nonlinear Boolean function of generating stream cipher sequence is reconstructed by clusterig, nonlinear predictive and nonlinear synchronization from shortest bit stream sequence. We have verified the correctness of our reconstruction result by simulating the block diagram of Lili-128 keystream generator using our getting Boolean function and implement designers’ reference module of Lili-128 stream cipher public online, and two methods produce the same synchronous keystream sequence under same initial state, so that our research work proves that the nonlinear Boolean function of LILI-128 stream cipher generator is successfully broken.

新形态对称密码算法研究

安全多方计算、全同态加密和零知识证明是解决数据安全问题的重要密码技术,其快速发展和应用需求驱动,引发了新形态对称密码的设计与安全性分析.本文系统介绍适宜安全多方计算、全同态加密和零知识证明的新形态对称密码算法.首先梳理新形态对称密码算法的应用需求和设计目标;然后归类介绍新形态对称密码算法的设计理念和最新的安全性评估结果;最后总结探讨新形态对称密码算法的设计特点以及面临的问题.

The Upstream ＂Strong Signals＂ of the Water Vapor Transport over the Tibetan Plateau during a Heavy Rainfall Event in the Yangtze River Basin

A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream ＂strong signals＂ of the water vapor transport in the Tibetan Plateau （TP）. The studied time period covers from 2000 LST 5 July to 2000 LST 15 July （temporal resolution： 6 hours）. By analyzing the three-dimensional structure of the water vapor flux, vorticity and divergence prior to and during the heavy rainfall event, the upstream ＂strong signals＂ related to this heavy rainfall event are revealed. A strong correlation exists between the heavy rainfall event in the YRB and the convective clouds over the TE The ＂convergence zone＂ of the water vapor transport is also identified, based on correlation analysis of the water vapor flux two days and one day prior to, and on the day of, the heavy rainfall. And this ＂convergence zone＂ coincides with the migration of the maximum rainfall over the YRB. This specific coupled structure actually plays a key role in generating heavy rainfall over the YRB. The eastward movement of the coupled system with a divergence]convergence center of the potential function at the upper/lower level resembles the spatiotemporal evolution of the heavy rainfall event over the YRB. These upstream ＂strong signals＂ are clearly traced in this study through analyzing the three-dimensional structure of the potential/stream function of upstream water vapor transport.

基于交互基函数的数据流聚类算法研究

聚类是数据挖掘的有效工具,数据流聚类成为当前研究热点,目前很多数据流聚类算法已经被提出,但大部分算法将距离作为相似度度量标准,存在对噪点敏感问题,且聚类效果不理想。为了增强数据流聚类算法的灵活性并提升聚类质量,该文将分数阶交互基函数(IBFs)引入数据流聚类,结合模糊ART算法对其进行了扩展,生成柔性决策边策略,提出了新颖的数据流聚类算法IBFs_ART。该算法首先对到达的数据点根据特征之间的相关性通过预计算函数特征扩展,并对原有特征进行分数阶变换,之后再基于交互基函数进行数据流聚类。交互基函数可生成灵活的决策边界且不需要指定软件,预计算函数可以在任何算法中实现,其可用于数据流聚类算法的任何扩展。经过实验表明,使用IBFs实现了较低计算成本生成灵活决策边界来找到最优聚簇,在相同警戒参数下实现了更高聚类质量和纯度,较传统聚类算法拥有更高的聚类精度、对称度量和更小的错误率。

双金属板材异步轧制复合轧后层厚建模与分析

根据双层金属复合板材同径异速异步轧制复合问题,利用流函数法和上界法建立了异步轧制轧后层厚的数学计算模型。进行异步轧制有限元模拟,将有限元模拟结果与理论结果进行对比,所建立的理论模型误差范围为2.55%~4.17%。该模型不仅可以快速计算轧后复合板的层厚比,在单一工况下,还能快速掌握不同工艺参数(压下量、初始板厚、异速比、层厚比)对轧后层厚比的影响规律,对设置和优化生产工艺提供了重要参考。

NONLINEAR GALERKIN METHOD FOR NAVIER-STOKES EQUATIONS WITH STREAM-VORTICITY FORM

A nonlinear Galerkin finite element method is presented for the two dimensional incom- pressible Navier-Stokes equations with stream-vorticity form.the scheme is based on two finite ele- ment spaces XH and XH for the approximation of the stream and vorticity function ,defined respec- tively on a coarse grid with grid size H and a fine grid with grid size h<<H.We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin method is of the order H2both in stream function and vorticity.

ENUMERATING CORRELATION-IMMUNE BOOLEAN FUNCTIONS OF ORDER ONE

A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.

The Classical Hall Effect in Multiply-Connected Plane Regions Part II: Spiral Current Streamlines

Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.

Algebraic Attack on Filter-Combiner Model Keystream Generators

Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].

Comparing Freshwater Benthic Macroinvertebrate Communities in Forest and Urban Streams of the Coastal Ecological Region of Cameroon

In this study conducted in the coastal zone of Cameroon, biological indices and functional feeding groups of benthic macroinvertebrates were used to assess the health status of two urban streams. For a better diagnosis, two streams located in coastal forest zone were used as a reference. Benthic macroinvertebrates were sampled monthly over a 3-month period (from May to July 2017) in six urban stations and six forest stations. Measurements of the physicochemical variables were done simultaneously. Physicochemical analysis revealed that urban streams are strongly polluted with high content of decaying organic matters, while forest streams are slightly polluted as indicated by the Principal Component Analysis. Concerning benthic macroinvertebrates, urban streams are poorly diversified with the proliferation of taxa tolerant to water pollution and belonging to the functional feeding groups of collectors-gatherers. Inversely, forest streams are more diversified and dominated by sensitive taxa, most belonging to the functional feeding groups of predators and shredders. These marked differences between biological indices and feeding mode of benthic macroinvertebrates in forest and urban rivers confirm the reliability of benthic macroinvertebrates as good indicators of freshwater ecosystem in the coastal zone of Cameroon.