石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

Measurement of integrated luminosities at BESIII for data samples at center-of-mass energies between 4.0 and 4.6 GeV

The integrated luminosities of data samples collected in the BESIII experiment in 2016–2017 at center-of-mass energies between 4.19 and 4.28 GeV are measured with a precision better than 1% by analyzing large-angle Bhabha scattering events. The integrated luminosities of old datasets collected in 2010–2014 are updated by considering corrections related to detector performance, offsetting the effect of newly discovered readout errors in the electromagnetic calorimeter, which can haphazardly occur.     

Effect of strain on charge density wave order in α-U

The effect of strain on charge density wave (CDW) order in $\alpha$-U is investigated within the framework of relativistic density-functional theory. The energetical stability of $\alpha$-U with CDW distortion is enhanced by the tensile strain along $a$ and $b$ axes, which is similar to the case of negative pressure and normal. However, the tensile strain along $c$ axis suppresses the energetical stability of CDW phase. This abnormal effect could be understood from the emergence of a new one-dimensional atomic chain along $c$ axis in $\alpha$-U. Furthermore, this effect is supported by the calculations of Fermi surface and phonon mode, in which the topological objects and the dynamical instability show opposite behaviors between strains along $a$/$b$ and $c$ axes.     

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

Stabilized Nonconforming Mixed Finite Element Method for Linear Elasticity on Rectangular or Cubic Meshes

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.     

Application of advanced nuclear analytical techniques for the electrocatalyst's characterization: Paving the path for mechanistic investigations

As the application of electrocatalyst continues to expand, envisaging the hidden mechanisms occurring at various length scale affecting the catalytic efficiency became important. To enhance the stability of electrocatalyst and reduce the cost, it is of paramount importance to reveal the active site's dynamics (using in situ techniques for getting the real-time information) which directly affect the reactions such as oxygen evolution reaction, hydrogen evolution reaction, and so on. Since such reactions are crucial for many engineering and scientific applications, in situ characterization techniques are required, which could capture such reactions happening at a different length and time scale. This article analyzes the recent progress made in the field of electrocatalyst's characterization using in situ neutron techniques. The article also paves the future path and has delineated the future challenges involved in multiscale correlative techniques (e.g., neutron techniques in the combination of synchrotron or microscopic techniques) used for getting the multiscale (atomic to micrometer range) mechanistic information about the electrocatalyst's working and degradation.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.