磁化史瓦西黑洞的有效势与稳定圆轨道

利用赤道平面上的径向有效势研究带电粒子在有外部磁场的史瓦西黑洞附近的圆轨道运动,发现针对某特定的角动量和较小的外部磁场,稳定圆轨道很难存在;但随着磁感应强度的增大,稳定圆轨道容易形成,并且磁感应强度的增大会导致稳定圆轨道半径逐渐减小.稳定圆轨道半径随着角动量的增大而逐渐增大.角动量和径向距离函数曲线与径向距离和有效势在讨论圆轨道性质上具有同等效果.

贯穿式无心磨削静态成圆稳定性模型与实验验证

为了提升具体加工条件下贯穿式无心磨削试磨中设置参数配置效率,文章建立了反映磨削参数与各阶次谐波误差增长之间定量化关系的静态成圆稳定性模型并对其进行了数值仿真。首先以切入式无心磨削为研究对象,建立了静态成圆稳定性条件。然后以工件与导轮之间的理想线接触为要求,在三维空间内对工件与磨削系统之间几何关系进行分析,并借助齐次坐标变换法将相关参量统一于同一坐标系中进行表征,以此推导出能够求解不同轴向位置处磨削角和工件与导轮接触角的数学表达式,并与切入式无心磨静态成圆稳定性条件相结合,由此建立了贯穿式无心磨削静态成圆稳定性模型。最后对稳定性模型进行了实验验证。实验结果显示,工件各阶次谐波幅值平均下降率与静态成圆稳定性模型计算的各阶次谐波稳定性值呈正相关。表明了模型可以有效预测出实际加工中各阶次谐波幅值的变化情况。

受扰动离散大系统的圆域稳定性

利用复线性变换、加权向量Ｌｙａｐｕｎｏｖ函数和比较原理，得到受扰动离散线性关联大系统圆域稳定性的充分条件。

射频功率放大器设计新方法

常用的射频微波功率放大器CAD设计方法中,保证电路的稳定往往要以损失增益与功率为代价。针对这个缺点,文章以稳定圆为理论基础,提出了一种新的CAD设计方法。这种方法通过设计恰当的偏置电路,然后找出并避开终端阻抗的不稳定区来保证电路稳定,最大限度地提高了增益与输出功率。利用ADS仿真软件对宽禁带SiC器件Cree24060进行了仿真,在2.2GHz处获得100 W的1dB压缩点输出功率与11dB的功率增益,使器件的性能得到充分发挥。

Influences of strain softening and seepage on elastic and plastic solutions of circular openings in nonlinear rock masses

Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.

Stability analysis of ellipse- like suspen-dome structures with low rise-span ratio

To investigate the effects of initial geometric imperfection and material nonlinearity on the stability analysis of the suspen-dome, the steel roof of Jiangsu Culture Sports Center Gymnasium was utilized as a numerical model, and modal analyses were performed. Then, linear buckling analysis,geometric nonlinear stability analysis, geometric nonlinear stability analysis with initial imperfection, and double nonlinear analysis considering material nonlinearity and geometric nonlinearity were discussed in detail to compare the stability performance of the ellipse-like suspen-dome and the single-layer reticulated shell. The results showthat the cable-strut system increases the integrity of the suspen-dome, and moderates the sensibility of the single-layer reticulated shell to initial geometric imperfection. However, it has little influence on integral rigidity, fundamental vibration frequencies, linear ultimate live loads, and geometric nonlinear ultimate live loads without initial imperfection. When considering the material nonlinearity and initial imperfection, a significant reduction occurs in the ultimate stability capacities of these two structures. In this case, the suspen-dome with a lowrise-span ratio is sensitive to the initial imperfection and material nonlinearity. In addition, the distribution pattern of live loads significantly influences the instability modes of the structure, and the uniform live load with full span is not always the most dangerous case.

Tunnel face stability and ground settlement in pressurized shield tunnelling

An analysis of the stability of large-diameter circular tunnels and ground settlement during tunnelling by a pressurized shield was presented. An innovative three-dimensional translational multi-block failure mechanism was proposed to determine the face support pressure of large-shield tunnelling. Compared with the currently available mechanisms, the proposed mechanism has two unique features:(1) the supporting pressure applied to the tunnel face is assumed to have a non-uniform rather than uniform distribution, and(2) the method takes into account the entire circular excavation face instead of merely an inscribed ellipse. Based on the discrete element method, a numerical simulation of the Shanghai Yangtze River Tunnel was carried out using the Particle Flow Code in two dimensions. The immediate ground movement during excavation, as well as the behaviour of the excavation face, the shield movement, and the excavated area, was considered before modelling the excavation process.

Numerical Simulation of Unsteady-State Flowsin Bubble Column Reactors

Unsteady-state operation has been widely applied in chemical engineering, such as optimizing a process, increasing yield and saving energy, etc. But the knowledge of the flow characteristics in bubble column reactors(BCRs) under unsteady state control is far from enough. In order to study the flow structures in this operation, the volume of fluid (VOF) model and the standard k-ε model to simulate the evolution of gas-liquid flow in BCRs under the start-up state are combined. For both the symmetry and asymmetry flow, the layout of the gas-inlets, the gas-in velocity, the liquid viscosity and the aspect ratio of the BCR all have effects on the liquid velocity distribution. The simulation results could provide some information for the design and scale-up of the BCRs.

Distribution of electric field for carbon nanotube assembly: Simulation (I)

The distribution of electric field for the alignment and attachment of carbon nanotubes (CNTs) was simulated. To be attached at the desired place, the aligned and attracted CNTs should be stayed in the desired area called the stable region or the quasi-stable region for an instant where the change of electric field is minimized. Since the conical electrode has the very narrow sized quasi-stable region, few CNTs can be attached. The rectangular electrodes have a wide stable region, so lots of CNTs can be attached. The results indicate that the round electrode which has a proper sized quasi-stable region is more effective for aligning and attaching a single CNT than the conical or rectangular shaped electrodes.

Search for circular and noncircular critical slip surfaces in slope stability analysis by hybrid genetic algorithm

A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and noncircular slip surfaces associated with their minimum safety factors.The slope safety factors of circular and noncircular critical slip surfaces were calculated by the simplified Bishop method and an improved Morgenstern-Price method which can be conveniently programmed,respectively.Comparisons with other methods were made which indicate the high efficiency and accuracy of the HGA approach.The HGA approach was used to calculate one case example and the results demonstrated its applicability to practical engineering.

Stability of perfect and imperfect cylindrical shells under axial compression and torsion

Stability analyses of perfect and imperfect cylindrical shells under axial compression and torsion were presented. Finite element method for the stability analysis of perfect cylindrical shells was put forward through comparing critical loads and the first buckling modes with those obtained through theoretical analysis. Two typical initial defects, non-circularity and uneven thickness distribution, were studied. Critical loads decline with the increase of non-circularity, which exist in imperfect cylindrical shells under both axial compression and torsion. Non-circularity defect has no effect on the first buckling mode when cylindrical shell is under torsion. Unfortunately, it has a completely different buckling mode when cylindrical shell is under axial compression. Critical loads decline with the increase of thickness defect amplitude, which exist in imperfect cylindrical shells under both axial compression and torsion, too. A greater wave number is conducive to the stability of cylindrical shells. The first buckling mode of imperfect cylindrical shells under torsion maintains its original shape, but it changes with wave number when the cylindrical shell is under axial compression.

机械手臂之LQG/LTR最佳控制综合设计

本研究综合计算扭矩法与LQG/LTR对非线性机械手臂系统进行多变量强健控制设计,解决存在于系统内部的不确定性与受到随机干扰情况下的非线性机械手臂系统之控制设计问题,使得非线性机械手臂控制系统具有良好的强健性与满足性能要求。文中首先使用计算扭矩法对非机械手臂系统中各项的估计值进行控制律的设计与回授线性化,并使用变异渐进法对回授系统进行适当的加权扩增;接着使用LQG/LTR设计,使得输出回授控制器(output feedback controller)能够趋近于预先设计的目标回授回路(target feedback loop)。至于非线性机械手臂闭回路系统在形成Lu’re-type问题后,可讨论非线性项之稳定性容许在一定的上界与下界,根据多变量圆稳定准则理论(multivariable circle criterion)探索此控制器之强健性能。文末则以非线性机械手臂系统为范例,进行计算机仿真,验证控制器的有效性与可行性。

Investigation on Multiple Cylindrical Holes Casing Treatment for Transonic Axial Compressor Stability Enhancement

Casing treatment is one possible way of regaining axial compressor operating range. However, most of casing treatments extend the operating range with the cost of efficiency penalty. A new form of multiple cylindrical holes casing treatment(MHCT) with pre-swirl blowing for the NASA Rotor-37 has been designed based on profound understanding of the stall inception. Unsteady numerical simulations have been performed for Rotor-37 with and without MHCT. Parametric studies of the total extraction holes area and their axial locations show that the compressor performance deteriorates as the area ratio increases but the stall margin is extended and there is an optimum extraction holes axial location for stall margin extending. The better configuration of MHCT could extend the stall margin by 6.2% with only 0.23% peak efficiency reduction. Detailed analysis of the physical mechanism behind the stall margin improvement shows that the casing treatment could eliminate the passage blockage by suppressing breakup of tip leakage vortex and decrease the blade load in tip region, which both contribute to improve stall margin of transonic axial compressors.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Rey- nolds number 40〈 Re 〈200 and various rotation rate 8i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method （FVM）. The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re in- creases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θi〈θcrit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Circumferential Propagation of Tip Leakage Flow Unsteadiness for a Low-Speed Axial Compressor

Full-annulus three-dimensional unsteady numerical simulations were conducted for a low-speed isolated axialcompressor rotor, intending to identify the behavior of self-induced unsteady tip leakage flow within multi-bladepassages. There is a critical mass flow rate near stall point, below it, the self-induced unsteadiness of tip leakageflow can propagate circumferentially and thus initiates two circumferential waves. Otherwise, the self-inducedunsteady tip leakage flow oscillates synchronously in each single blade passage. The major findings are: 1) whilethe self-induced unsteadiness of tip leakage flow is a single-passage phenomenon, there exist phase shifts amongblade passages in multi-passage environments then evolving into the first short length wave propagating at abouttwo times of rotor rotation speed after the transient period ends; and 2) the time traces of the pseudo sensors locatedon the rotor blade tips reveal another much longer length-scale wave modulated with the first wave due tophase shift propagating at about half of rotor rotation speed. Features of the short and long length-scale circumferentialwaves are similar to those of rotating instability and modal wave, respectively.

Simulation and Instability Investigation of the Flow around a Cylinder between Two Parallel Walls

The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics(CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method(FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is found that the two eddies attached at the rear of the cylinder have no effect on the flow instability for steady flow, i.e., they don't contribute to the formation of Karman vortex street. The formation of Karman vortex street originates from the combinations of the interaction of two shear layers at two lateral sides of the cylinder and the absolute instability in the cylinder wake. For the flow with Karman vortex street, the initial instability occurs at the region in a vortex downstream of the wake and the center of a vortex firstly loses its stability in a vortex. For pressure driven flow, it is confirmed that the inflection point on the time-averaged velocity profile leads to the instability. It is concluded that the energy gradient theory is potentially applicable to study the flow stability and to reveal the mechanism of turbulent transition.

Molecular dynamics simulation of cylindrical Richtmyer-Meshkov instability

The microscopic-scale Richtmyer-Meshkov(RM) instability of a single-mode Cu-He interface subjected to a cylindrically converging shock is studied through the classical molecular dynamics simulation. An unperturbed interface is first considered to examine the flow features in the convergent geometry, and notable distortions at the circular inhomogeneity are observed due to the atomic fluctuation. Detailed processes of the shock propagation and interface deformation for the single-mode interface impacted by a converging shock are clearly captured. Different from the macroscopic-scale situation, the intense molecular thermal motions in the present microscale flow introduce massive small wavelength perturbations at the single-mode interface, which later significantly impede the formation of the roll-up structure. Influences of the initial conditions including the initial amplitude,wave number and density ratio on the instability growth are carefully analyzed. It is found that the late-stage instability development for interfaces with a large perturbation does not depend on its initial amplitude any more. Surprisingly, as the wave number increases from 8 to 12, the growth rate after the reshock drops gradually. The distinct behaviors induced by the amplitude and wave number increments indicate that the present microscopic RM instability cannot be simply characterized by the amplitude over wavelength ratio(η). The pressure history at the convergence center shows that the first pressure peak caused by the shock focusing is insensitive to η, while the second one depends heavily on it.

Nonexistence of a Globally Stable Supersonic Conic Shock Wave for the Steady Supersonic Isothermal Euler Flow

In this paper, for the full Euler system of the isothermal gas, we show that a globally stable supersonic conic shock wave solution does not exist when a uniform supersonic incoming flow hits an infinitely long and curved sharp conic body.

Numerical Simulation of Unsteady 2-D Compressible Flow Around a Circular Cylinder

A numerical method for solving isentropic compressible now problems is presented. This method uses the vorticity and the density as variables. The crux of the method lies in the numerical simulation of the process of vorticity and density variation. The fundamental equation of a compressible discrete vortex method is derived. Unlike the BiotSavart law in the incompressible fluids, the modified Blot-Savart law in compressible fluid should contain the change of the non-solenoidal. The change of density induces the variation of the fluid velocity. The effects of compressibility on flow past a circular cylinder have been investigated by using the compressible discrete vortex method at a Reynolds number of l.E+6. The Mach number is 0.5. The results show that the form of vortex shedding is different from the incompressible now. The separation positions shift upstream, the wake more wide and the street is not clear like the incompressible.

elliptically birefringent fibers modulation instability ellipticity angle

Previous studies on modulation instabilities（MIs） in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle（0？ ≤θ≤ 90？）. Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric（antisymmetric） CW states, we show that MI gain increases dramatically（reduces first and then enhances greatly） as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ = 45？,reappears across this ellipticity angle, and quickly increases after then.