Bifurcations and chaotic threshold for a nonlinear system with an irrational restoring force

Nonlinear dynamical systems with an irrational restoring force often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational nonlinearity avoiding the conventional Taylor's expansion to retain the natural characteristics of the system. A series of transformations are proposed to convert the homoclinic orbits of the unperturbed system to the heteroclinic orbits in the new coordinate, which can be transformed back to the analytical expressions of the homoclinic orbits. Melnikov's method is employed to obtain the criteria for chaotic motion, which implies that the existence of homoclinic orbits to chaos arose from the breaking of homoclinic orbits under the perturbation of damping and external forcing. The efficiency of the criteria for chaotic motion obtained in this paper is verified via bifurcation diagrams, Lyapunov exponents, and numerical simulations. It is worthwhile noting that our study is an attempt to make a step toward the solution of the problem proposed by Cao Q J et al. (Cao Q J, Wiercigroch M, Pavlovskaia E E, Thompson J M T and Grebogi C 2008 Phil. Trans. R. Soc. A 366 635).     

气体分子在Co-BN表面吸附的第一性原理研究

采用包含色散力校正的密度泛函理论(DFT-D)方法系统地研究了气体分子(O2, H2, NO, CO, CO2, SO2, H2S, H2O)在Co掺杂单层BN(Co-BN)表面的吸附, 分析了吸附小分子的几何结构, 吸附能, 电荷转移等情况. 结果表明: 1) CO等气体分子主要吸附在Co及其近邻六元环的顶位, 吸附结构的电荷转移表明掺杂原子Co对BN衬底的气敏特性有较好的调制作用; 2) 在Co-BN表面吸附的O2和CO较易被活化, 表明Co-BN可能是一种对CO氧化有较好催化活性的新型催化材料.     

利用白光数字图像频域分析法测量工程高分子材料Ⅲ型裂纹尖端应力强度因子

白光数字图像频域分析法具有测试系统简单,非接触,全场测量等优点,通过频域相关算法分析可以得到三维位移场。推导了用白光数字图像频域分析法的双CCD系统测量三维位移场的公式,并将其应用于Ш型裂纹尖端应力强度因子的测量。     

单分散纳米金尺寸的分步晶种生长控制

以聚乙烯吡咯烷酮(poly(vinylpyrrolidone), PVP)为保护剂, 硼氢化钠为还原剂, 合成了尺寸为(1.9±0.4) nm的单分散金胶体, 再以其作为一级晶种, 并分别用抗坏血酸和PVP为还原剂和保护剂, 通过改变各步晶种尺寸和氯金酸与晶种的摩尔比分步逐级合成了尺寸为3.2、4.7、6.3、8.0、10.3、14.0 nm的系列金纳米颗粒. 以LaMer模型为基础, 对分步晶种生长过程中影响金胶体产物尺寸分布(单分散性)的主要因素进行了讨论. 缓慢加入抗坏血酸并降低氯金酸对晶种的相对量对于单分散金纳米颗粒的控制合成有决定性作用. 快速加入抗坏血酸会因二次成核而导致金颗粒尺寸分布范围变宽.     

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.     

TiC-和TiN-(001)表面吸附性能的密度泛函理论研究

基于密度泛函理论系统研究了碳化钛(TiC)和氮化钛(TiN)非极性(001)表面吸附气体分子和原子的性能。鉴于这些材料拥有不同的电子结构特征,发现受电子的CO分子或未饱和的O和H原子在TiC(001)和TiN(001)表面吸附于不同的活性位点,而供电子的NH3和H2O气体分子或完全饱和的O2和H2分子仅倾向与两个表面的金属原子位点结合。这些吸附特性可能与此类材料表面的电子结构有关。     

第一性原理研究CO在Cu(110)表面的吸附

本文采用基于密度泛函理论的第一性原理方法, 并同时考虑范德华力的作用, 计算并分析了CO在Cu(110)表面的吸附情况. 结果表明: 1) CO在两个表面Cu原子的短桥位位置吸附最强, 吸附能为1.28 eV. 第二稳定吸附位置为表面Cu原子的顶位, 吸附能为1.23 eV. CO在其他两个位置, 表面两个Cu的长桥位和表面四个Cu的中心位的吸附要弱一些, 约为0.86 eV 和 0.83 eV. 2) 在Cu表面吸附的CO的C-O键长有部分拉长, 这与较强的吸附能和电荷转移相应. 3) 电荷分析表明所有吸附的CO整体上从衬底上面获得部分电荷, 约为0.2 个电荷.     

第一性原理研究CO在Cu(110)表面的吸附

本文采用基于密度泛函理论的第一性原理方法,并同时考虑范德华力的作用,计算并分析了CO在Cu(110)表面的吸附情况.结果表明:1)CO在两个表面Cu原子的短桥位位置吸附最强,吸附能为1.28 e V.第二稳定吸附位置为表面Cu原子的顶位,吸附能为1.23 e V.CO在其他两个位置,表面两个Cu的长桥位和表面四个Cu的中心位的吸附要弱一些,约为0.86 e V和0.83 e V.2)在Cu表面吸附的CO的C-O键长有部分拉长,这与较强的吸附能和电荷转移相应.3)电荷分析表明所有吸附的CO整体上从衬底上面获得部分电荷,约为0.2个电荷.