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This make it difficult to know the essence of fluidized beds. In order to viewthe motion behavior of a single particle in a fluidized bed in a reasonable cost, thegas-solid flow in a fluidized bed is modeled by a combined approach of discrete particlemethod and computational fluid dynamics, in which the motion ofindividual Particles is obtained by solving Newton\'s second law of motion and gas flowby the Navier-Stokes equation based on the concept of local average.

为了用数值模拟方法来弥补传统实验方法的不足，达到从单个颗粒的尺度上来研究流化床中颗粒的运动和气体流场的剧烈变化情况的目的，本论文建立了基于用Newton第二定律计算单个颗粒运动轨迹的离散颗粒法和基于区域平均值的计算流体动力学方法的数学模型的建立和求解过程；并依据Newton第三定律建立了DPM模型和CFD模型的耦合模型，编写和调试了DPM和CFD的耦合程序。

It was proved that the root colonization dynamics and density of rhizobium population played an important role in competitive nodulation.

并且发现在此区段的主根瘤发光比例高达90％以上，显著大于此区根段的侧根瘤发光比例，从而说明种子表面的接种根瘤菌主要是沿着主根的伸长而向下扩散定殖。

Neural Network is a non linear dynamics kinetics system, which can do a lot of complex jobs, especially in information science.

神经网络是一个非线性动力学系统，在许多方面都表现出强大的生命力，特别为信息科学界所瞩目。

In this paper, the chaotic characteristic of the Rikitake two-disk dynamo is studied with non linear dynamics theory.

利用非线性动力学理论讨论了Rikitake双盘发电机模型的混沌特性。

Secondly, three kinds of mathematics model of optical vortex beams were introduced here. Then the propagation dynamics of optical vortex beams through the non-axis symmetry system is studied, this chapter includes the introduction of the symmetry vortex beam and the non- symmetry vortex beam, the deduction of the Collins diffract integral formula for the non-axis symmetry system, and the transformation of the vortex beam passing through the non-axis symmetry system has been described by using the numerical simulation. Then the general calculation for the orbit momentum of vortex beams, the matrix form for the orbit momentum of vortex beams, and the photon method to describe the orbit momentum of vortex beams are also introduced here. Finally, the interference about optical vortex beams was studied.

本文对涡旋光束进行了较为全面的介绍和研究，主要内容包括：（1）光学涡旋光束的基本理论，主要是介绍了单个光学涡旋光束在柱坐标中的一些表征，涡旋光束的奇异相位和光学涡旋的相位结构；（2）光学涡旋光束的三种数学模型；（3）光学涡旋光束在非轴对称光学系统中的传播动力学，其中介绍了对称涡旋光束与非对称涡旋光束，推导了非轴对称光学系统的 Collins 衍射积分公式，并利用计算机模拟图描述了对称涡旋光束经过非轴对称光学系统后涡旋形态的改变；（4）涡旋光束轨道角动量的一般计算，涡旋光束轨道角动量的矩阵形式，光子法描述涡旋的轨道角动量；（5）涡旋光束的干涉。

Considering that body forces and surface forces were both non-conservative force, the quasi-Hamilton principle and the quasi-complementary Hamilton principle of non-conservative elasto-dynamics systems were established.

按照广义力和广义位移之间的对应关系，将弹性动力学的基本方程乘上相应的虚量，然后积分，代数相加，并考虑到体积力和面积力均为非保守力，建立了非保守弹性动力学系统的拟Hamilton原理和拟余Hamilton原理。

This model is different from the structural dynamics model in a non-inertial reference frame with large overall motions known.

本文从力学基本原理出发，分析了刚柔耦合零次近似理论失效的原因，深入研究了有大范围运动的柔性体变形场的描述，建立了刚柔耦合一次近似的动力学模型；然后利用上述模型，从非惯性系下的结构动力学问题和大范围运动为自由的刚柔耦合动力学问题这两个层次上进行了刚柔耦合动力学建模理论与性态的研究，采用理论和实验相结合的手段来检验了一次近似刚柔耦合动力学模型的正确性。

In 1987, Kane et al.〓investigated the dynamics of a cantilever beam in a non-inertial reference frame.

建模时如果不考虑这种因素的影响，将会导致错误的结论。1987年，Kane〓对非惯性系下的旋转弹性梁的动力学特性进行研究，指出在转速较大的情况下，按零次近似建模理论进行仿真计算会得到梁的挠度趋于发散失稳这样一个错误的结论。

However, most of these investigations focused on the rotating beams or plates undergoing a prescribed large overall motion, where the effect of large overall motion of the reference frame on elastic deformation was considered but at the same time the beam's elastic deformation couldn't influence the large overall motion of the reference frame because the large overall motion is known a priori. In fact, this kind of problem on the dynamic stiffening is a structural dynamics problem in a non-inertial frame.

值得指出，上述这些研究工作都局限于大范围运动为已知情况下的非惯性系下柔性体的动力学性质，实质上是一个非惯性系下的结构动力学问题，只考虑了大范围运动对变形运动的影响，而没有充分考虑到大范围运动和变形运动之间的相互耦合作用，这种耦合作用是单向的。

In this dissertation,the higher order rigid-flexible coupling dynamic model,which isdifferent from the structural dynamics model in the non-inertial reference frame withlarge overall motions known,which takes the coupling between large overall motionsand deformation motion into account with large overall motions being free,and ofcourse which is more accurate than the zero order model,is established for the first time,based on mechanical principles.

本文从力学基本原理出发，针对大范围运动为自由的刚-柔耦合系统，首次建立了较零次近似更精确的高次耦合动力学模型，与大范围运动为已知的非惯性系下的耦合动力学模型不同，进一步考虑了大范围运动和变形运动的相互耦合作用。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。