Perturbation to Mei Symmetry and Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates

Based on the concept of adiabatic invariant, the perturbation to Meisymmetry and adiabatic invariants for nonholonomic mechanical systems interms of quasi-coordinates are studied. The definition of the perturbationto Mei symmetry for the system is presented, and the criterion of theperturbation to Mei symmetry is given. Meanwhile, the Mei adiabaticinvariants for the perturbed system are obtained.     

水基流延成型和热压烧结制备碳化硼陶瓷及性能研究

以工业碳化硼粉末为原料、采用Si3N4磨球磨损法引入Si3N4烧结助剂,采用水基流延成型和热压烧结方法制备了碳化硼陶瓷.研究了氧含量、分散剂、pH值等因素对B4C陶瓷浆料分散性能的影响,采用XRD、SEM等对碳化硼陶瓷的物相、显微结构和第二相分布进行了表征,并测试了样品的维氏硬度、断裂韧性、抗弯强度和弹性模量.结果表明:经醇洗后的碳化硼粉末中氧化硼含量降低,有利于B4C陶瓷浆料的分散稳定.采用球磨磨损引入了Si3N4粉,在B4C基体中通过原位反应形成第二相SiC和BN,SiC和BN第二相颗粒在B4C基体中弥散分布均匀.在2100 ℃热压烧结样品的维氏硬度、抗弯强度、断裂韧性和弹性模量分别达到30.2 GPa、596.5 MPa、3.36 MPa·m1/2和362.3 GPa.     

New Conserved Quantities of Noether--Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.     

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible.     

单壁碳纳米管中稳态机械波的激发条件研究

通过分子动力学模拟,对单壁碳纳米管中稳态机械波的激发条件进行了详细的研究.利用所施加的周期性机械外力,使单壁碳纳米管产生局部径向形变,该形变将以单壁碳纳米管的管壁为弹性媒质传播开去,从而在单壁碳纳米管中形成机械波;机械波产生的条件依赖于单壁碳纳米管波动系统能量的维持和受迫振动区域形变方向的控制;稳定机械波形成的最佳条件是碳纳米管的形变度和受迫振动频率之间的最优匹配,以及由此形成的单壁碳纳米管在周期性外力作用下产生的共振.     

围压状态下的混凝土本构模型

利用已有不同围压下的混凝土三向压缩试验, 分析研究不同围压条件对混凝土强度和应力-应变关系的影响。试验表明, 把混凝土简单视为脆性材料的观点并不符合实际情况, 塑性特征也是混凝土材料主要力学特征。由热力学定律出发, 本文提出了多次方形式的屈服函数和与围压状态相关联的损伤标准化函数, 提出了考虑围压状态的混凝土本构模型。试验结果与数值计算比较表明, 该本构关系可以很好地描述混凝土在不同围压状态下的力学损伤发展和脆-塑性转换力学特征, 也可以描述拉伸作用下的应力-应变关系, 具有一定的普遍意义。     

New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

By virtue of the completeness of Wigner operator and Weyl correspondence we construct a general equation for deriving pure state density operators. Several important examples are considered as the applications of this equation, which shows that our approach is effective and convenient for deducing these entangled state representations.     

Mechanical Properties of Ni-Coated Single Graphene Sheet and Their Embedded Aluminum Matrix Composites

The effects of Ni coating on the mechanical behaviors of single graphene sheet and their embedded Al matrix composites under axial tensionare investigated using molecular dynamics (MD) simulation method. Theresults show that the Young's moduli and tensile strength of grapheneobviously decrease after Ni coating. The results also show that the mechanical properties of Al matrix can be obviously increased by embedding asingle graphene sheet. From the simulation, we also find that the Young'smodulus and tensile strength of the Ni-coated graphene/Al composite isobviously larger than those of the uncoated graphene/Al composite. Theincreased magnitude of the Young's modulus and tensile strength ofgraphene/Al composite are 52.27 and 32.32 at 0.01 K, respectively,due to Ni coating. By exploring the effects of temperature on the mechanicalproperties of single graphene sheet and their embedded Al matrix composites, it is found that the higher temperature leads to the lower critical strain and tensile strength.     

Weak Noether symmetry for a nonholonomic controllable mechanical system

This paper discusses the weak Noether symmetry for a nonholonomic controllable mechanical system of Chetaev type, and presents expressions of three kinds of conserved quantities obtained by using weak Noether symmetry. Finally, the application of these new results is illustrated by an example.     

基于箭形累积损伤的裂纹尖端力学:奇异性分级和多尺度分段

在适度的空间和时间尺度组合下,裂纹既可在几个月中蠕变几个纳米,也能在几秒钟内扩展10km.虽然裂纹的尖端没有实际的质量,但是它能通过激活周围的物质而处于高能量状态.依赖于材料的损伤方向,激活质量的减少和增加可发生在尺度转变之前或之后.每个尺度区的分段阈值被假定为与裂纹尖端速度的平方a~2和激活质量密度M的乘积有关:W=M_(↓↑)a_(↑↓)~2和D=M~(↓↑)a_(↑↓)~2.W和D分别被称为直接吸收和自耗散能量密度.正如下标/上标符号所示,激活的质量密度M_(↓↑)和M~(↓↑)与裂纹尖端速度a变化趋势相反,既可增加也可减少.a~2和M的互补效应隐含着常用于宇宙物理学建模的膨胀和/或收缩的物理过程.在用于尺度敏感的裂纹尖端的行为时,激活的质量密度有相同的解释.分段时的多尺度可以由…皮观、纳观、微观和宏观…组成.因此,形象地说,材料损伤过程可以通过裂纹扩展过程中非均匀的总体和局部能量的传递来模拟.疲劳裂纹扩展引起的材料损伤被用来阐释由大到小和由慢到快的尺度/时间序,热力学中的冷→热和有序→无序转换.这一过程正巧与宇宙演化的箭形方向相反,宇宙演化遵循小→大和快→慢,而热力学相反,遵循热→冷和无序→有序.为了表示由损伤萌生所造成的类裂缝型缺陷的不均匀性,提出了一个被称为裂纹尖端力学(crack tip mechanics,CTM)的新模式.涉及的范围是模拟原子列之间的界面裂纹或连续体中分叉的切口.假如需要的话,尺寸和时间的范围可以复盖从皮观到宏观甚至更大.虽然采用疲劳裂纹来说明CTM的基本原理,在宇宙物理学背景中与直接吸收和自耗散相关的膨胀和收缩的情况可以描述裂纹周围激活质量的行为,它们可看为能量的汇或源.奇异性被用来捕获能量的源或汇的特性,物理上,两者作为界面的一部分,从数学上看则是不连续的线的一部分.能量从一种形式变为另一种形式取决于能量吸收或耗散的箭形损伤时间,这之中牵涉到尺度分段和奇异性强度的联合应用.材料组分随时间的劣化是根据指定的设计寿命导出的,从而使材料的响应与加载率的时间历史匹配.2024-T3铝板的皮观/纳观/微观/宏观开裂模型用来说明什么地方可以增加结构的寿命部分.皮观/纳观/微观/宏观/结构系统的性能随时间劣化可以用9个尺度转变物理参数来描述:纳观/微观区有3个(μ_(na/mi)~*,σ_(na/mi)~*,d_(na/mi)~*),微观/宏观区有3个(μ_(mi/ma)~*,σ_(mi/ma)~*,d_(mi/ma)~*),皮观/纳观区有3个(μ_(pi/na)~*,σ_(pi/na)~*,d_(pi/na)~*).下标pi,na,mi,ma和struc分别表示皮观、纳观、微观、宏观和结构.只要知道两个相连的尺度敏感参数,在较低尺度的时间相关的局部物理参数就完成了分析连续体的形式论,虽然它们并不需要用实验来知道.更具体地说,根据皮观→纳观→微观→宏观分别有1.25/1.00/0.75/0.50的λ奇异性强度,皮观裂纹、纳观裂纹、微观裂纹和宏观裂纹的转变特征是从时间箭形的指定的寿命预期来确定的.附加的0.25强度的奇异性可用于结构元件.回想起来,λ=0.5相应于断裂力学中的应力分量与r~(0.5)成反比,r是与宏观裂纹尖端的距离.微观裂纹、纳观裂纹和皮观裂纹分别赋予r~(-0.75),r~(-1.0),r~(-1.25)的奇异性.箭形时间(以年为单位)取决于问题的定义.设备的关键部件可用1.5~±/2.5~±/3.5~±/5.5~±寿命分布和总寿命为13~±年(a)的皮观/纳观/微观/宏观尺度来设计运行.上标±表示多于或少于实际运行的时间.累进损伤被假定为发生在皮观→纳观→微观→宏观方向.同样的方案用于20年总寿命的2024-T3铝板的疲劳损伤,按照1.5~±/2.5~±/3.5~±/5.5~±/7.0~±的方式将它的寿命分布在皮观、纳观、微观、宏观和结构的尺度上,这样的指定只是满足在每个尺度范围内损伤内部材料结构所用的能量匹配,因此可以强制执行在总寿命的跨度内精确的时间相关的材料性能劣化过程.