A new pinning control scheme of complex networks based on data flow

In this paper, a new pinning control scheme called DF (data flow)-based pinning scheme is proposed. The new scheme can obtain the similar pinning efficiency with BC-based pinning scheme in real-world networks. Comparing with BC-based pinning scheme, DF-based pinning scheme has two main advantages. First, it just needs local information of network. Second, the new pinning scheme has a much lower time complexity than BC-based pinning scheme. In this paper, we have pinned two real-world networks (the US airline routing map network and the protein–protein network in yeast) to compare the new pinning scheme with degree-based, BC-based, LBC-based pinning schemes and we also pin a small-world network, a scale-free network to analyze DF-based pinning scheme in detail. Based on the Lyapunov stability theory, the validity of the scheme is proved. Finally, the numerical simulations are verified the effectiveness of the proposed method.     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

Convergence of Discrete-Velocity Schemes for the Boltzmann Equation

In this paper we prove the convergence of two discrete-velocity deterministic schemes for the Boltzmann equation, namely, Buet's scheme and a new finite-volume scheme that we introduce here. We write the discretized equation in the form of a Boltzmann continuous equation in order to be in the framework of the DiPerna-Lions theory of renormalized solutions. In order to prove convergence we have to overcome two difficulties: the convergence of the discretized collision kernel is very weak and the lemma on the compactness of velocity averages can be recovered only asymptotically when the parameter of discretization tends to zero. (Accepted February 6, 1996)     

On numerical solutions of the time-dependent Euler equations for incompressible flow

This paper presents finite element methods for the non-stationary Euler equations of a two dimensional inviscid and incompressible flow. For the time discretization, we compare numerical results obtained by the use of a leap-frog scheme and a semi-implicit scheme of order two.     

Part II. Comparison of Numerical Solvers for a Multicomponent Turbulent Flow

We focus on the computation of a hyperbolic system describing a multicomponent turbulent flow for isentropic gases, using an exact Riemann solver. This method is very robust, but costly. Thus, we introduce two approximate upwinding schemes: a Godunov scheme called VFRoe and a Rusanov scheme. The Rusanov scheme always ensures positive values for mass, concentration and turbulent kinetic energy, but generates less accurate results. We show some one- and two-dimensional computations and compare these three resolution methods.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method (DEM) when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

非线性双曲型守恒律的两步二阶TVD差分格式

通过Mac Cormack格式和Warming-Beam的结合,构造了一种非常简单的两步二阶TVD差分格式,该差分格式更适合于使用分量形式差分计算而无须对欧拉方程组进行特征解耦。通过对流体力学方程组的大量数值试验,并与二阶ENO格式进行了比较,充分显示了该格式高精度、高分辨并且极其简单的优良特性。     

Entropy dissipation scheme and minimums‐increase‐and‐maximums‐decrease slope limiter

In this paper, we continue to study the entropy dissipation scheme developed in former. We start with a numerical study of the scheme without the entropy dissipation term on the linear advection equation, which shows that the scheme is stable and numerical dissipation and numerical dispersion free for smooth solutions. However, the numerical results for discontinuous solutions show nonlinear instabilities near jump discontinuities. This is because the scheme enforces two related conservation properties in the computation. With this study, we design a so‐called ‘minimums‐increase‐and‐maximums‐decrease’ slope limiter in the reconstruction step of the scheme and delete the entropy dissipation in the linear fields and reduce the entropy dissipation terms in the nonlinear fields. Numerical experiments show improvements of the designed scheme compared with the results presented in former. However, the minimums‐increase‐and‐maximums‐decrease limiter is still not perfect yet, and better slope limiters are still sought. Copyright © 2011 John Wiley & Sons, Ltd.     

Cryptanalysis of image scrambling based on chaotic sequences and Vigenère cipher

Recently, an image scrambling scheme based on chaos theory and Vigenère cipher was proposed. The scrambling process is firstly to shift each pixel by sorting a chaotic sequence as Vigenère cipher, and then the pixel positions are shuffled by sorting another chaotic sequence. In this study, we analyze the security weakness of this scheme. By applying the combination of chosen-plaintext attack and differential attack, we propose two efficient cryptanalysis methods. Results show that all the keystream can be revealed. The original image scrambling scheme can be remedied by leveraging the MD5 hash value of the plain image as the initial condition of the chaotic system.     

Numerical solutions for singularly perturbed semi-linear parabolic equation

In this paper,we discuss singularly perturbed semi-linear parabolic equations for one dimension and two dimension,we find numerical solutions by using both the line-method and the exact difference scheme on a special non-uniform discretization mesh.The uniform convergence in e of the first order accuracy is obtained.     

On stability of some solutions for equations of locked lasing of optically coupled lasers with periodic pumping

Based on a numerical-analytic scheme of investigation of periodic solutions, we propose a method for the construction of a matrix-valued Lyapunov function for the linear approximation of a system of equations of locked lasing of two optically coupled lasers with periodic pumping.     

A Roe scheme for a compressible six‐equation two‐fluid model

We derive a partially analytical Roe scheme with wave limiters for the compressible six‐equation two‐fluid model. Specifically, we derive the Roe averages for the relevant variables. First, the fluxes are split into convective and pressure parts. Then, independent Roe conditions are stated for these two parts. These conditions are successively reduced while defining acceptable Roe averages. For the convective part, all the averages are analytical. For the pressure part, most of the averages are analytical, whereas the remaining averages are dependent on the thermodynamic equation of state. This gives a large flexibility to the scheme with respect to the choice of equation of state. Furthermore, this model contains nonconservative terms. They are a challenge to handle right, and it is not the object of this paper to discuss this issue. However, the Roe averages presented in this paper are fully independent from how those terms are handled, which makes this framework compatible with any treatment of nonconservative terms. Finally, we point out that the eigenspace of this model may collapse, making the Roe scheme inapplicable. This is called resonance. We propose a fix to handle this particular case. Numerical tests show that the scheme performs well. Copyright © 2012 John Wiley & Sons, Ltd.     

Spatial accuracy and performance of a mixed‐order,explicit multi‐stage method for unsteady flows

We assess the spatial accuracy and performance of a mixed‐order, explicit multi‐stage method in which an inexpensive low‐order scheme is used for the initial stages, and a more expensive high‐order scheme is used for the final stage only. Compared with the use of a high‐order scheme for all stages, we observe that the mixed‐order scheme achieves comparable accuracy and convergence while providing a speed‐up of a factor of two on mesh sizes of O(10⁶ ? 10⁷) tetrahedron. For calculations with significant adaptive mesh refinement, a more modest speed‐up of 30% is obtained. Published 2012. This article is a US Government work and is in the public domain in the USA.     

A semi‐discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow

In this paper, we develop a new Godunov‐type semi‐discrete central scheme for a scalar conservation law on the basis of a generalization of the Kurganov and Tadmor scheme, which allows for spatial variability of the storage coefficient (e.g. porosity in multiphase flow in porous media) approximated by piecewise constant interpolation. We construct a generalized numerical flux at element edges on the basis of a nonstaggered inhomogeneous dual mesh, which reproduces the one postulated by Kurganov and Tadmor under the assumption of homogeneous storage coefficient. Numerical simulations of two‐phase flow in strongly heterogeneous porous media illustrate the performance of the proposed scheme and highlight the important rule of the permeability–porosity correlation on finger growth and breakthrough curves. Copyright © 2013 John Wiley & Sons, Ltd.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.     

加权型紧致格式与加权本质无波动格式的比较

线性紧致格式和加权本质无波动格式是两种典型的高阶精度数值格式,它们各有优缺点.线性紧致格式在具有高阶精度的同时,格式的分辨率也比较高,耗散低,是计算多尺度流场结构的较好格式,但是不能计算具有强激波的流场.加权本质无波动格式是一种高阶精度捕捉激波格式,鲁棒性好,但耗散比较高,分辨率也不理想.近年来,在莱勒的线性紧致格式基础上,采用加权本质无波动格式捕捉激波思想,发展了一系列加权型紧致格式.本文较全面地比较了加权型紧致格式和加权本质无波动格式,包括构造方法、鲁棒性、分辨率、耗散特性、收敛特性以及并行计算效率.结果表明,现有的加权型紧致格式基本保持了加权本质无波动格式的性质,对于气动力等宏观量的计算,比加权本质无波动格式没有明显的优势.      

The multi‐stage centred‐scheme approach applied to a drift‐flux two‐phase flow model

For two‐phase flow models, upwind schemes are most often difficult do derive, and expensive to use. Centred schemes, on the other hand, are simple, but more dissipative. The recently proposed multi‐stage (MUSTA ) method is aimed at coming close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. So far, the MUSTA approach has been shown to work well for the Euler equations of inviscid, compressible single‐phase flow. In this work, we explore the MUSTA scheme for a more complex system of equations: the drift‐flux model, which describes one‐dimensional two‐phase flow where the motions of the phases are strongly coupled. As the number of stages is increased, the results of the MUSTA scheme approach those of the Roe method. The good results of the MUSTA scheme are dependent on the use of a large‐enough local grid. Hence, the main benefit of the MUSTA scheme is its simplicity, rather than CPU ‐time savings. Copyright © 2006 John Wiley & Sons, Ltd.