Nonlinear optical properties of C<Subscript>60</Subscript> with explicit time-dependent electron dynamics

An explicit electron dynamics approach has been used to calculate the nonlinear optical properties of C₆₀ and its radical anion. An external perturbation, in the form of an oscillating electric field, induces the time-evolution of the molecular wavefunction. The time-averaged instantaneous dipole moment of the systems gives the molecular response to perturbations of varying field intensities and frequency of oscillation. The polarizabilities and the second-order hyperpolarizabilties have been calculated and are in good qualitative agreement with experimentally available data. In line with previous theoretical and experimental studies, the nonlinear effect is enhanced for the radical species. Contribution to the Fernando Bernardi Memorial Issue.     

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.     

Viewing the noise propagation mechanism in a unidirectional transition cascade from the perspective of stability

Noise and noise propagation are inevitable and play a constructive role in various biological processes. The stability of cell homeostasis is also a critical issue. In the unidirectional transition cascade of colon cells, stem cells (SCs) are the source. They differentiate into transit-amplifying cells (TACs), and TACs differentiate into fully differentiated cells (FDCs). Two differentiation processes are irreversible. The stability factor is introduced so that the noise propagation mechanism from the perspective of stability is studied according to the noise propagation formulas. It is found that the value of the stability factor corresponding to the minimum noise in FDCs may be the best choice to enable colon cells to maintain high stability and low noise of the cascade. Moreover, for the source cell, the total noise only includes intrinsic noise; for the downstream cell with self-proliferation capability, the total noise mainly depends on its intrinsic noise and transmitted noise from upstream cells, and its intrinsic noise is dominant. For the downstream cell without self-proliferation capability, the total noise is mainly determined by transmitted noises from upstream cells, and there is a minimum value. This work provides a new approach for studying the mechanism of noise propagation while considering the stability of cell homeostasis in biological systems.     

复杂网络上的意见动力学对谣言传播的影响

通过在SIR(susceptible-infected-recovered)模型中引入抑制者对谣言的辟谣机制研究了在线社交网络上的意见动力学对谣言传播的影响.在这一模型中,节点可以与自身的邻居组成1个群,传播者可以通过该群传播信息,抑制者也可以在此群中对信息发表意见进行辟谣.辟谣机制在降低未知者对于谣言的接受概率的同时也可以促使传播者向抑制者转变.本文采用ER(Erd?s-Rényi)随机网络、无标度网络以及真实的社交网络研究了抑制者的沉默概率对于谣言传播范围的影响.首先发现,谣言传播的过程以传播者的峰值为界可以分为两个阶段,即谣言自由传播的前期以及抑制者和传播者互相制衡的后期;其次,谣言的传播会随着抑制者的沉默概率的增大而突然暴发.在谣言暴发阈值之下,沉默概率的增大不会导致谣言传播范围显著增大,这是由于未知者在感知到谣言并转变为传播者后又迅速转变为抑制者;而当沉默概率达到谣言暴发阈值时,抑制者将不能控制传播者对谣言的传播从而导致抑制者的降低和谣言的暴发;最后,无标度上的谣言自由传播的前期阶段比随机网络持续的时间更短,从而使无标度上的谣言更难以暴发.本文的模型综合考虑了意见动力学和谣言传播的相互作用,更加真实地模拟了真实世界社交网络中的谣言传播过程.为谣言传播的控制和干预提供了一些有用的思路和见解.     

Dynamic compression-shear response of brittle materials with specimen recovery

A new configuration for compression-shear soft-recovery experiments is presented. This technique is used to investigate various failure mechanisms during dynamic multiaxial loading of an Al₂O₃/SiC nanocomposite and TiB₂. Velocity profiles of the target surface are measured with a variable sensitivity displacement interferometer, yielding normal and transverse velocity-time histories. A dynamic shear stress of approximately 280 MPa is obtained, in the Al₂O₃/SiC nanocomposite, for an imposed axial stress of about 3.45 GPa on a 540 m thick sample. This dynamic shear stress is well below the value predicted by elastic wave propagation theory. This could be the result of stress-induced damage and inelasticity in the bulk of the sample or inelasticity on the sample surface due to frictional sliding. To gain further insight into the possible failure mechanisms, an investigation of compression-shear recovery techniques, with simultaneous trapping of longitudinal and lateral release waves, is conducted.     

幂硬化可压缩材料Ⅰ型动态裂纹尖端奇异场

研究了平面应变条件下幂硬化可压缩材料中定常扩展的Ⅰ型动态裂纹尖端应力应变奇异场．采用Ｊ２流动理论和场量直角坐标分量，得到了应力应变奇异性不同时的裂纹尖端渐近场，其中场量的角变化规律和理想弹塑性材料的完全相同     

龙游牛场古地下洞室群岩柱的长期抗拉强度反演

在龙游县上畈村附近的牛场有一处由2个洞室组成的古地下洞室群。现场调查发现,在其中1号洞的岩柱1上出现了一条竖直的张开裂缝。据分析,这是上覆岩层对该岩柱施加过大荷载的结果,这一发现为本文研究岩体长期抗拉强度提供了条件。作者即以根据牛场古地下洞室群1号洞内岩柱1的拉裂现象为研究对象,根据最大拉应力论来反演岩体的长期抗拉强度。这不仅对长期强度研究具有理论意义,而且在古工程保护方面也具有应用价值。     

阶梯压电层合梁的波动动力学特性

采用行波理论系统地研究了压电阶梯梁的自由振动分析以及强迫响应的分析方法. 基于分布 参数理论研究了压电阶梯梁的波传播特性，忽略柔性梁横向剪切和转动惯量的影响，给出了 梁的轴向和横向的简谐波解. 将压电阶梯梁离散化为单元，考虑压电片的刚度和质量的影响， 建立了节点散射模型. 应用位移连续和力平衡条件，推导了节点的波反射和波传递矩阵，在 此基础上，引入波循环矩阵的概念，给出波循环矩阵、波传递系数矩阵的确定方法. 应用波 循环矩阵可以有效地计算结构的固有频率. 另外，应用波传递系数研究了压电陶瓷作动器位 置对其驱动能力的影响. 得出两个主要结论：1)作动器靠近悬臂梁固定端将有较强的驱动 能力，悬臂梁边界反射行波产生弯曲消失波有利于增大压电波的模态传递系数；2)模态传 递系数与固有频率的灵敏度密切相关，波传递系数越大, 对应该处固有频率变化灵敏度越大. 另外，数值算例表明了行波方法比有限元方法具有更高的计算精度.