原图边与线图边扰动的相继故障仿真研究

本文将ER随机网络与BA无标度网络转化为线图结构,并将线图与原图的故障规模做归一化计算,提出基于BA无标度网络和ER随机网络拓扑结构的线图结构,继而进行线图边扰动的仿真实验,进行蓄意和随机两种方式的攻击,模拟相继故障的发生,并将其与原图边扰动的相继故障进行比较.通过对仿真结果中线图与原图间的阈值关系进行比较,实验结果表明:不论蓄意攻击还是随机攻击,在相同的扰动值下,原图引起的故障规模总是比线图大.

概率网络中星形2-hub放置问题的边扰动算法

在交通运输、邮政和电信网络中,hub作为特殊的设备起着交换、转载和整理的重要作用。该文研究概率网络中的星形2-hub放置问题,网络中的每条边上都有独立的工作概率,给出基于最大概率路图的边扰动算法并在多项式时间内获得最优2-hub树。

STABILITY OF 3-D DISTURBANCE WAVES ON BOUNDARY LAYER WITH DISTRIBUTED LOCAL ROUGHNESS

The numerical solution of the stable basic flow on a 3-D boundary layer is obtained by using local ejection, local suction, and combination of local ejection and suction to simulate the local rough wall. The evolution of 3-D disturbance T-S wave is studied in the spatial processes, and the effects of form and distribution structure of local roughness on the growth rate of the 3-D disturbance wave and the flow stability are discussed. Numerical results show that the growth of the disturbance wave and the form of vortices are accelerated by the 3-D local roughness. The modification of basic flow owing to the evolvement of the finite amplitude disturbance wave and the existence of spanwise velocity induced by the 3-D local roughness affects the stability of boundary layer. Propagation direction and phase of the disturbance wave shift obviously for the 3-D local roughness of the wall. The flow stability characteristics change if the form of the 2-D local roughness varies.

SOLVABILITY RESULTS OF A CONDITIONAL INPUT-OUTPUT EQUATION BASED ON A TYPE OF NONLINEAR LEONTIEF MODEL

A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.

DIRECT NUMERICAL SIMULATION OF VIBRATIONINDUCED T-S WAVE ON BOUNDARY LAYER WALL

The spatial growth of the disturbance in the boundary layer is directly numerically simulated, and the receptivity of the Blasius basic flow to the local two-dimensional （2-D） sustainable micro-vibration is investigated. Results show that the disturbance velocity presents the sine vibration features with the change of time, and the vibration period is identical to the vibration of the local wall. The disturbance velocity presents the fluctuation feature downstream, and the streamwise wave length approximates to the results from the Orr-Sommerfeld equation （OSE）. The growth rate from direct numerical simulation（DNS） is a little greater than that from OSE, and their trends are almost consistent. Under the condition of Re= 2 800, the disturbance amplitude gradually grows in the given computational region with the period T=30. However, it firstly increases and then decreases with the period T= 20. The disturbance harmonic of the former is obviously larger than that of the latter. The maximum streamwise and vertical disturbance velocities from DNS do not fully coincide with those from OSE at the vicinity of the local vibration wall, but coincide well with the former when they travel downstream. The 2-D disturbance induced by the local micro-vibration represents the form of Tollmien-Schlichting （T-S） wave on the boundary layer.

Quasilinear singularly perturbed problem with boundary perturbation

A class of quasilinear singularly perturbed problems with boundary perturbation is considered. Under suitable conditions, using theory of differential inequalities we studied the asymptotic behavior of the solution for the boundary value problem.

Homotopic Mapping Solving Method for Perturbed Mechanism of Western Boundary Undercurrents in Equator Pacific

The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.

Quasilinear Robin Problem with Boundary Perturbation

A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.

A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems

A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.

Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation

Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky （KS） equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure. The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions. Furthermore, when the distance from bifurcation is of comparable order ε2 （｜ε｜≤1）, the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method. Such information is useful to the bifurcation control.

Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems

The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L^1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.

Research on Locating the Source of Abnormal Disturbances in the Border Region of Shaanxi and Gansu

Abnormal disturbances, s uch as sharp pulses, w ere observed by vertical pendulum tiltmeters in Wudu, Hanzhong and Ningshaan seismic stations on August 6, 2008.According to the time and spatial location of the anomalies,we build a"source precursor"propagator to calculate possible focal region by aid of quasi-Newton least squares and grid search methods. The calculated focal region is located at the aftershock area of the Wenchuan earthquake on the northern section of Longmenshan fault zone,which may be related to the 54km-away M S5. 0 Pingwu-Beichuan earthquake,with starting time of about thirty three hours before the earthquake.

Hypersonic flow control of shock wave/turbulent boundary layer interactions using magnetohydrodynamic plasma actuators

The effect of magnetohydrodynamic(MHD)plasma actuators on the control of hypersonic shock wave/turbulent boundary layer interactions is investigated here using Reynolds-averaged Navier-Stokes calculations with low magnetic Reynolds number approximation.A Mach 5 oblique shock/turbulent boundary layer interaction was adopted as the basic configuration in this numerical study in order to assess the effects of flow control using different combinations of magnetic field and plasma.Results show that just the thermal effect of plasma under experimental actuator parameters has no significant impact on the flow field and can therefore be neglected.On the basis of the relative position of control area and separation point,MHD control can be divided into four types and so effects and mechanisms might be different.Amongst these,D-type control leads to the largest reduction in separation length using magnetically-accelerated plasma inside an isobaric dead-air region.A novel parameter for predicting the shock wave/turbulent boundary layer interaction control based on Lorentz force acceleration is then proposed and the controllability of MHD plasma actuators under different MHD interaction parameters is studied.The results of this study will be insightful for the further design of MHD control in hypersonic vehicle inlets.

Competition of the multiple Grtler modes in hypersonic boundary layer flows

Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode （mode W） and the trapped-layer mode （mode T） both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Gortler number while the mode W dominates at larger G/Srtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Gortler number is in the high value range in which the crossover of these two modes takes place. Such high Gortler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Gortler modes. The effects of the Mach number on the multiple Gortler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma ≥4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions （Region T, T-W, W-T and W） around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.

Transition prediction of the supersonic boundary layer on a cone under the consideration of receptivity to slow acoustic waves

Transition prediction of the supersonic boundary layer on a cone with small angle of attack and Mach number 3.5 is investi-gated under the consideration of receptivity to slow acoustic waves, as the acoustic waves are the main environmental distur-bances in a conventional, i.e. non-quiet, wind tunnel. It is shown that the e-N method can still yield fairly satisfactory results incomparison with those obtained in wind tunnel experiments, provided that the boundary layer receptivity to slow acousticwaves is properly taken into account, including the dependence of the amplitude of disturbances on the frequency andstream-wise location. Neither the conventional e-N method nor the improved e-N method can yield correct result of transitionprediction, because the receptivity mechanisms considered there are not in accord with the real situation in the wind tunnel.

Conductance Spectra in Graphene-Superconductor Junctions

The conductance spectra of a graphene ribbon and graphene-superconductor （G-S） junctions are investi- gated, using the tight-binding model and non-equilibrium Green＇s function formalism. It is found that the quantized conductance related to graphene＇s edge-states is robust against perturbations in the model parameters for a graphene monolayer ribbon with the zigzag boundary. With appropriate a new bound state with odd-frequency symmetry is found in conductance amplitude is followed model parameter of the spin-orbit interaction strength, the G-S junction. An enhancement in the zero-energy

Characteristics of nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation （DNS）. It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance （wavepacket） in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting （T-S） waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.

The reliability of the improved e^N method for the transition prediction of boundary layers on a flat plate

The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.

Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows,nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient.In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers,the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5,6 and 8 are analyzed by numerical simulations.It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level.The most rapidly amplified 3-D disturbances are Klebanoff type(K-type)disturbances which have the same frequency as the 2-D disturbance.Among these K-type 3-D disturbances,the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher.Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages,the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.