Improvement of Bobrovsky–Mayor–Wolf–Zakai Bound

This paper presents a difference-type lower bound for the Bayes risk as a difference-type extension of the Borovkov–Sakhanenko bound. The resulting bound asymptotically improves the Bobrovsky–Mayor–Wolf–Zakai bound which is difference-type extension of the Van Trees bound. Some examples are also given.     

Computable error bounds for approximate periodic solutions of autonomous delay differential equations

In this paper, we prove a result that says: Given an approximate solution and frequency to a periodic solution of an autonomous delay differential equation that satisfies a certain noncriticality condition, there is an exact periodic solution and frequency in a neighborhood of the approximate solution and frequency and, furthermore, numerical estimates of the size of the neighborhood are computed. Methods are outlined for estimating the parameters required to compute the errors. An application to a Van der Pol oscillator with delay in the nonlinear terms is given.     

On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems

The finite element method is applied to the solution of the transient Fokker-Planck equation for several often cited nonlinear stochastic systems accurately giving, for the first time, the joint probability density function of the response for a given initial distribution. The method accommodates nonlinearity in both stiffness and damping as well as both additive and multiplicative excitation, although only the former is considered herein. In contrast to the usual approach of directly solving the backward Kolmogorov equation, when appropriate boundary conditions are prescribed, the probability density function associated with the first passage problem can be directly obtained. Standard numerical methods are employed, and results are shown to be highly accurate. Several systems are examined, including linear, Duffing, and Van der Pol oscillators.     

Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback

We investigate the primary resonance of an externally excited van der Pol oscillator under state feedback control with a time delay. By means of the asymptotic perturbation method, two slow-flow equations on the amplitude and phase of the oscillator are obtained and external excitation-response and frequency-response curves are shown. We discuss how vibration control and high amplitude response suppression can be performed with appropriate time delay and feedback gains. Moreover, energy considerations are used in order to investigate existence and characteristics of limit cycles of the slow-flow equations. A limit cycle corresponds to a two-period modulated motion for the van der Pol oscillator. We demonstrate that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the primary resonance. Analytical results are verified with numerical simulations.     

Nonadiabatic dissociation dynamics of ClHD van der Waals complex initiated by electron detachment of Cl–HD

Nuclear dynamics following the electron detachment of the Cl⁻–HD anion is investigated by a time-dependent wave packet propagation approach. Photodetachment of Cl⁻–HD promotes it to the van der Waals well region of the reactive ClHD potential energy surface. The latter is a manifold of three electronic states coupled by the electronic and (relativistic) spin-orbit coupling. Among the three surfaces, the electronic ground one is of ²Σ_1/2 type and yields products in their electronic ground state. The remaining two, ²Π_3/2 and ²Π_1/2, on the other hand, yield products in their excited electronic states. However, these two can yield products in their electronic ground state via nonadiabatic transitions to the ²Σ_1/2 state. The channel specific, HCl + D or DCl + H or Cl + HD, dissociation probabilities on this latter state are calculated both in the uncoupled and coupled surface situations. Separate initial transitions (via, photodetachment) to the ²Σ_1/2, ²Π_3/2 and ²Π_1/2 adiabatic electronic states of ClHD are considered in order to elucidate the nonadiabatic coupling effects on this important class of chemical reactions initiated by an electron detachment.     

Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes （MWNTs） embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes （DWNTs）. Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invari- able for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.     

一步CVD法制备WS2-MoS2垂直异质结及其表征

本文主要研究了WS₂-MoS₂垂直异质结的制备及其光电性能。以氧化钼(MoO₃)、氧化钨(WO₃)、硫粉(S)作为反应物,采用改良的一步化学气相沉积法(CVD)实现高质量的WS₂-MoS₂垂直异质结的制备。使用拉曼光谱仪(Raman)、光致发光光谱仪(PL)、光学显微镜(OM)、原子力显微镜(AFM)、透射电子显微镜(TEM)、X射线光电子能谱仪(XPS)等设备,对异质结的形貌、元素组成等进行了表征。最后制备了基于WS₂-MoS₂异质结的光电探测器,测量了包括输出特性曲线、转移特性曲线、光电流曲线等光电特性。经测试,WS₂-MoS₂异质结光电探测器在532 nm激光模式下展现了良好的光响应特性,使其能应用于高效率的光电子器件的制备,在微电子学领域具有广阔的应用前景。