Quantized space-time and its influence on two physical problems

Based on Snyder's idea of quantized space-time, we derive a new generalized uncertainty principle and new modified density of states. Accordingly, we discuss the influence of the modified generalized uncertainty principle on the black hole entropy and the influence of the modified density of states on the Stefan-Boltzman law.     

Structural and electrical studies on Zn2+ doped LiCoPO4

Zinc doped LiCoPO₄ was prepared by two step solid state reaction method. XRD studies ensure the formation of phase pure LiCoPO₄ with olivine phase orthorhombic structure with p_nma phase group. 2θ value of XRD peaks of LiCoPO₄ is found to be shifted upon Zn²⁺ doping. The conductivity of pure LiCoPO₄ is noticed to be increased by one order upon doping of Zn²⁺. The scaling behavior of Z″ indicates that the ion dynamical process are temperature independent for both pure and Zn²⁺ doped LiCoPO₄. The temperature dependence of conductivity for both pure and Zn²⁺ doped sample obeys Arrhenius law of conduction.     

Integrable generalization of the associated Camassa–Holm equation

In this paper, we study an integrable generalization of the associated Camassa–Holm equation. The generalized system is shown to be integrable in the sense of Lax pair and the bilinear Bäcklund transformations are presented through the Bell polynomial technique. Meanwhile, its infinite conservation laws are constructed, and conserved densities and fluxes are given in explicit recursion formulas. Furthermore, a Darboux transformation for the system is derived with the help of the gauge transformation between two Lax pairs. As an application, soliton and periodic wave solutions are given through the Darboux transformation.     

一种外场天线测试转台设计

为了满足天线在野外的测试需要,提出了一种外场天线测试转台的结构设计;该转台采用蜗轮蜗杆传动方式,可实现天线的俯仰和方位运动;文中对转台的组成进行了描述,并针对俯仰部件和方位部件的结构设计分别进行了详细说明,同时分析了转台的受力情况,对驱动力矩和惯量匹配进行了校核计算,从理论上分析了传动精度和测角精度;实际测试表明,该转台结构设计完全达到技术指标要求,能够满足天线外场测试的需要。     

颗粒滚动摩擦系数对堆积特性的影响

为探讨颗粒摩擦系数对堆积特性的影响,利用离散单元法,模拟静摩擦系数固定时,变化滚动摩擦系数对椭球形颗粒堆积角及堆积体的影响.利用自制斜面仪测定了颗粒静摩擦系数,并对滚动摩擦系数与堆积角建立线性方程.结果表明,滚动摩擦系数对颗粒堆积特性有显著影响,颗粒堆积角随滚动摩擦系数增大而增大,边界圆与连续圆间的间隙随滚动摩擦系数增大而减小.依据颗粒堆积过程中旋转动能的变化可以阐述上述结果,建立的滚动摩擦系数与堆积角的线性方程可为具体颗粒物料滚动摩擦系数的获取提供数值测量思路.模拟堆积的过程可为散体物料一些不易测量的参数进行虚拟实验标定.     

Frenkel-Kontorova模型中基底势振动的影响

基于一维Frenkel-Kontorova模型, 研究了振动的基底势对系统纳米摩擦现象的影响. 分别在相邻原子间的距离与周期势场的周期比为不公度(incommensurate)、可公度(commensurate)两种情形下, 探讨了基底势振动的振幅和频率对滞回现象(hysteresis)、最大静摩擦力以及超滑现象的作用机理. 两种情形下, 固定频率, 随着振幅的增大, 滞回区域的面积以及最大静摩擦力都将减小, 对于不同的频率, 减小的趋势不同. 系统甚至产生了超滑现象. 但当频率过大时, 振幅的改变不会影响滞回区域的面积以及最大静摩擦力的大小, 此时与基底不加振动时的情形一致; 当振幅固定, 随着频率的增大, 滞回区域的面积将增大, 对于不同振幅, 增大的趋势不同. 特别地, 对于某些固定的振幅, 最大静摩擦力随着振动频率的增大先逐步减小直至出现超滑现象, 再进一步增大频率, 最大静摩擦力又转而逐步增大. 这一现象类似于共振, 表明存在最佳的振动频率促进系统内所有原子的共同运动, 使得整个系统的最大静摩擦力几乎消失. 另外, 两种情形的区别是, 对于某些固定的频率(如ω= 0.5)和不同的小振幅, 不可公度情形往往具有相同的平均终止速度, 而可公度情形则不同, 表明相同前提下后者具有更复杂的动力学行为. 关键词： Frenkel-Kontorova模型 滞回 最大静摩擦力 超润滑     

缺陷对碳纳米管摩擦与运动行为的影响

本文采用分子动力学方法研究了公度、无公度情况下含空位、Stone-Thrower-Wales(STW)型缺陷的单壁碳纳米管(SWCNT)在石墨基底上的摩擦与运动行为.结果表明,公度时缺陷的存在导致了界面局部无公度,减小了摩擦.随着碳纳米管底部STW缺陷的增多,碳纳米管变形增大,侧向力波动的幅值减小,局部无公度性增强,摩擦减小.含空位缺陷的碳纳米管所受的摩擦力明显大于含STW缺陷的碳纳米管,原因在于含空位缺陷的碳纳米管在运动的后期出现了明显的翻转现象,增大了能量耗散.无公度时,碳纳米管与石墨基底间的摩擦力很小,缺陷对其摩擦力影响不大,原因在于无论是否含有缺陷,碳纳米管与石墨组成的界面的无公度性差别不大.     

高瑞利数下水平自然热对流的幂律关系

采用数值模拟方法，研究了高度和宽度比为1∶10的狭长矩形腔内的水平自然热对流. 根据对瑞利数(Rayleigh数)Ra在10⁴ <Ra<10¹¹内情形的计算结果，将流动分为三个不同的区间：线性区、连续过渡区、1/5次幂律区. 虽然流量和努塞尔数(Nusselt数)Nu随瑞利数的变化都包括了三个参数演化区间，但从一个区间到另外一个参数区间的转变时并不是同步的，其中努塞尔数的转变总是超前流量的转变. 对比前人的研究发现，流量1/3次幂律的结果是由于瑞利数不够高所致. 此外，模拟结果也表明Siggers等的理论分析过高估计了热通量强度，实际的温度边界层内努塞尔数和瑞利数为1/5次幂律关系.     

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

DEPLOYMENT DYNAMICS OF FLEXIBLE SOLAR ARRAYS CONSIDERING FRICTIONAL JOINT

研究了空间漂浮航天器太阳阵展开与锁定过程的刚柔耦合动力学问题. 基于Jourdain 速度变分原理和单项递推组集方法, 建立了太阳阵展开与锁定过程的刚柔耦合多体系统动力学模型,采用虚功率原理推导了铰摩擦对系统动力学方程的贡献. 在以上动力学模型中引入3-D 鬃毛摩擦模型来研究铰链的摩擦特性对太阳阵展开动力学的影响. 所建动力学模型的正确性通过与商业软件ADAMS 和NASTRAN 的联合仿真对比得到了验证,该模型能够有效地预测太阳阵的展开历程以及航天器姿态的动态行为.