On vibrational stabilizability of nonlinear systems

Conditions of vibrational stabilizability for trivial solutions of nonlinear systems are derived. Several examples based on the classical equations of the theory of oscillations are given.Dedicated to G. LeitmannThis work was performed under the auspices of the US Department of Energy under Contract No. DE-ACO2-80ER10709.     

Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction

The linear bifurcation theory is used to investigate the stability of soft thin films bonded to curved substrates. It is found that such a film can spontaneously lose its stability due to van der Waals or electrostatic interaction when its thickness reduces to the order of microns or nanometers. We first present the generic method for analyzing the surface stability of a thin film interacting with the substrate and then discuss several important geometric configurations with either a positive or negative mean curvature. The critical conditions for the onset of spontaneous instability in these representative examples are established analytically. Besides the surface energy and Poisson's ratio of the thin film, the curvature of the substrate is demonstrated to have a significant influence on the wrinkling behavior of the film. The results suggest that one may fabricate nanopatterns or enhance the surface stability of soft thin films on curved solid surfaces by modulating the mechanical properties of the films and/or such geometrical properties as film thickness and substrate curvature. This study can also help to understand various phenomena associated with surface instability.     

Unifying some known infinite families of combinatorial 3-designs

In this paper we present a construction of 3-designs by using a 3-design with resolvability. The basic construction generalizes a well-known construction of simple 3-(v,4,3) designs by Jungnickel and Vanstone (1986). We investigate the conditions under which the designs obtained by the basic construction are simple. Many infinite families of simple 3-designs are presented, which are closely related to some known families by Iwasaki and Meixner (1995), Laue (2004) and van Tran (2000, 2001). On the other hand, the designs obtained by the basic construction possess various properties: A theory of constructing simple cyclic 3-(v,4,3) designs by Köhler (1981) can be readily rebuilt from the context of this paper. Moreover many infinite families of simple resolvable 3-designs are presented in comparison with some known families. We also show that for any prime power q and any odd integer n there exists a resolvable 3-(qn+1,q+1,1) design. As far as the authors know, this is the first and the only known infinite family of resolvable t-(v,k,1) designs with t?3 and k?5. Those resolvable designs can again be used to obtain more infinite families of simple 3-designs through the basic construction.     

重力场中的范德瓦耳斯气体

将地球大气近似为重力场中的范德瓦耳斯气体,在绝热过程近似下导出了大气温度、压强随高度的分布,并与理想气体近似结果进行了比较分析.     

范德瓦尔斯气体的卡诺循环效率

以范德瓦尔斯气体为工作物质推导出的卡诺循环效率,只与热源的温度有关,与工作物质是否是理想气体无关.     

基于范阿伦卫星观测的槽区嘶声波冷等离子体色散关系的适用性评估

等离子体层嘶声波对电子的散射损失是地球内外辐射带之间的槽区(1.8≤L≤3)形成的主要机制.冷等离子体色散关系被广泛地运用于量化嘶声波对高能电子的散射效应研究中,而在真实的磁层环境中,热等离子体的存在会修正嘶声波的色散特性.基于范阿伦双星的观测数据,对比了利用磁场观测数据得到的槽区嘶声波观测幅值和反演幅值,并研究了空间位置与地磁活动水平对嘶声波冷等离子体色散关系适用性的影响.结果表明,冷等离子体近似整体上高估了嘶声波的幅值,观测幅值与反演幅值的差异有着很强的日夜不对称性,而没有明显的地磁活动强度依赖性.此外发现,波动磁场的反演强度在低频(高频)处显著低于(高于)观测强度,意味着冷等离子体近似整体上高估(低估)了嘶声波对槽区较低(较高)能量电子的散射强度.研究证明,槽区嘶声波冷等离子体色散关系的适用范围有很强的空间区域与频率局限性,这对深入理解槽区电子的动态演化过程有非常重要的意义.     

On a Theorem of Van de Ven

A result by Van de Ven characterizes linear subspaces as the only closed submanifolds X ? ? ^N for which the normal bundle exact sequence splits. We show that X is linear assuming only the splitting of the same exact sequence when restricted to some curve contained in X .     

The Exit Problem from a Neighborhood of the Global Attractor for Dynamical Systems Perturbed by Heavy-Tailed Lévy Processes

The concept of filtered counting process is used to model several stochastic problems in manufacturing systems. Through a judicious selection of an appropriate response function, several system characteristics are evaluated under distribution-free condition. Applications include a machine shop problem, a machine sequencing problem, a flexible manufacturing problem, a job sequencing problem, a maintenance problem and an inventory problem. The methodology provides a unique, original and simple way to solve a large array of problems     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

Chatter dynamic analysis for Van der Pol Equation with impulsive effect via the theory of flow switchability

In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow’s dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.