失重条件下对称充液陀螺的不稳定行为研究

对于质心固定的，充满粘性均匀液体的旋转对称陀螺在失重条件下绕对称长轴旋转态的小扰动不稳定及其极限行为进行了研究，所给出的定理3比以往的不稳定定理[4]为强，且反映的信息量多很多。关于初始大扰动后的渐近行为，对文[8]已给出但未严格证明的两条定理给出了严格证明，它由定理1和定理2所描述。

An experimental study of the influence of weak convection on perikinetic coagulation

A remarkably increased coagulation rate for 2-mu m PS spheres was previously reported for a perikinetic coagulation experiment performed under microgravity conditions (1998, R. Folkersma, A. J. G. van Diemen, and H. N. Stein, J. Colloid Interface Sci. 206, 482); from this experiment, it was assumed that the leading factor slowing the coagulation process under normal gravitation was free convection due to gravity (1998, R. Folkersma, and H. N. Stein, J. Colloid Interface Sci. 206, 494). To test the influence of free convection as a single-effect factor on the coagulation process, a ground-based experiment was constructed. The coagulation rate of 2-mu m PS spheres dispersed in water was determined by measuring the turbidity of the dispersion solution while convection-driven flows in the solution were checked with a visual magnification system. We found that it was possible to cease free convection-driven particle flows on the ground, as long as the experiments were carefully operated. The strength of convection was controlled by changing the temperature gradient applied to the sample cell. By monitoring both the coagulation rate and convection-driven flows simultaneously, our experiments showed that weak free convection (maximum speed <150 mu m/s) actually has negligible effects on the coagulation rate.

Viscosity-induced mode splitting and potential energy criterion for mode stability

This paper points out that viscosity can induce mode splitting in a uniform infinite cylinder of an incompressible fluid with self-gravitation, and that the potential energy criterion cannot be appropriate to all normal modes obtained, i.e., there will be stable modes with negative potential energy (<0). Therefore the condition >0 is not necessary, although sufficient, for the stability of a mode in an incompressible static fluid or magnetohydrodynamics (MHD) system, which is a correction of both Hare's [Philos. Mag. 8, 1305 (1959)] and Chandrasekhar's [Hydrodynamic and Hydromagnetic Stability (Oxford U.P., Oxford, 1961), p. 604] stability criterion for a mode. These results can also be extended to compressible systems with a polytropic exponent.

Instabilities of a liquid film flowing down an inclined porous plane

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alpha(BJ) on the instability of the system.

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the "visible" brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

输电线巡检机器人行走动力特性与位姿分析

根据跨越超高压输电线路障碍物的类型,提出一种新的双臂自主越障巡检机器人机构。该机器人采用复合轮爪机构在架空地线上连续行走并跨越障碍。由于架空地线呈悬链线状,机器人在连续行走过程中会出现上坡和下坡,对行走动力特性的影响非常明显。在上坡时行走电动机提供驱动力矩,在下坡时行走电动机提供制动力矩,以保持匀速巡线。详细分析了机器人在架空地线上行走时所处的加速、匀速、减速和停止的各个状态,驱动机器人所需的驱动力矩以及它们与机构参数之间的关系,并应用优化方法给出各个状态电动机驱动力矩最小时,机器人机构参数对应的最优解,为巡检机器人的设计和控制系统方案的确定提供了理论依据。

层状反倾向结构岩质边坡变形机理及稳定性研究

Toppling is a major failure model in anti-dip layered rock slopes. Because of the limited by testing means and experimental apparatus, present research on the deformation mechanism and stability analysis are mainly focus on the 2-Dimensional deformation, and the research really based on 3-Dimension is still limited. Therefore, based on the present research station, the article rely on the important hydroelectric project of typical anti-dip layered rock slopes -- The left bank slope of Long-tan hydropower-station in Guang Xi, China, and focused on the influencing factors, deformation mechanism and stability analysis of anti-dip layered rock slopes, three problems as follows are researched in this paper. (1) Deformation influencing factor analysis on ant-dip layered rock slopes Three influencing factors are included: geological factor, engineering factor and environmental factor. It is concluded that the toppling deformation of anti-dip layered rock slopes are more sensitive to geological and engineering factors, but less sensitive to environmental factor. In addition, the sensitivity of various factors to the rock toppling deformation is also arranged sequentially as follows: construction, gravitation, rainfall (underground water) and rock structure intensity, etc. (2) 3D deformation study on the anti-dip layered toppling rock slopes Used 3D Distinct Element Method (3DEC) analyzed the 3D deformation characteristic of anti-dip layered rock slops. It can be seen that the toppling characteristics are obvious when the inter-angle between slope direction and layer striking direction is under 20o, when the inter-angle is over 20o and equal or less than 40o，the toppling deformation characteristics decrease sharply with increase of inter-angle, when the inter-angle is over 40o , the slope deformation is not controlled by joints but influenced by other failure mode. Therefore, in order to quantify the toppling characteristics, a differential value of displacement vector angle between layered rock slope and block rock slope is proposed as a key index to distinguish failure model for anti-dip layered rock slopes, and it was applied to study the toppling of the rock slopes at Guangxi Long-tan hydropower station, China. The results indicated that the index was effective and instructive for analyzing the anti-dip layered rock slopes. (3) Stability analysis methods Because of the imperfection of some present slope analysis methods, based on slope failure mode and those three influencing factors, “slope stability entropy” method is defined in this paper, which makes good use of the sensitivity of relational matrix to influencing factors on slope stability and the qualification characteristics for information entropy to the irregularity of slope deformation. By this method, not only the randomness of geologic body on the base of dynamic analysis of slope failure mode is fully concerned, but also it makes the analysis time-saving and simple. Finally, the research findings were used to the engineering example successfully, and rational conclusion has been obtained.

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.