受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

基于耦合Ginzburg-Landau方程的石墨烯锁模光纤激光器的暗暗孤子解及其稳定性

以耦合Ginzburg-Landau方程为模型,对石墨烯锁模光纤激光器中脉冲的动力学行为进行了详细地研究.首先,采用拟解法推导了该方程组的啁啾类暗暗孤子对解;其次,对啁啾类暗暗孤子对的传输特性及稳定性进行了数值研究.结果表明:合理选择系统参数,不仅可以得到啁啾类暗暗孤子对的精确解,而且该精确解还可以在一定的扰动下稳定传输.相关结果将为设计和改善石墨烯锁模光纤激光器的性能提供一定的理论依据.     

Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by H¨older norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in H¨older normThe obtained results,generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.     

Amorphous Aggregation of Amyloid Beta 1‐40 Peptide in Confined Space

The amorphous aggregation of Aβ1‐40 peptide is addressed by using micromolding in capillaries. Both the morphology and the size of the aggregates are modulated by changing the contact angle of the sub‐micrometric channel walls. Upon decreasing the hydrophilicity of the channels, the aggregates change their morphology from small aligned drops to discontinuous lines, thereby keeping their amorphous structure. Aβ1‐40 fibrils are observed at high contact angles.     

Quantum theory as a description of robust experiments: Derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.     

On the uniqueness of semi-wavefronts for non-local delayed reaction–diffusion equations

We establish the uniqueness of semi-wavefront solution for a non-local delayed reaction–diffusion equation. This result is obtained by using a generalization of the Diekmann–Kaper theory for a nonlinear convolution equation. Several applications to the systems of non-local reaction–diffusion equations with distributed time delay are also considered.     

An iterative starting method to control parasitism for the Leapfrog method

The Leapfrog method is a time-symmetric multistep method, widely used to solve the Euler equations and other Hamiltonian systems, due to its low cost and geometric properties. A drawback with Leapfrog is that it suffers from parasitism. This paper describes an iterative starting method, which may be used to reduce to machine precision the size of the parasitic components in the numerical solution at the start of the computation. The severity of parasitic growth is also a function of the differential equation, the main method and the time-step. When the tendency to parasitic growth is relatively mild, computational results indicate that using this iterative starting method may significantly increase the time-scale over which parasitic effects remain acceptably small. Using an iterative starting method, Leapfrog is applied to the cubic Schrödinger equation. The computational results show that the Hamiltonian and soliton behaviour are well-preserved over long time-scales.