Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance: the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O--Br bonds more prone to dissociation.     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.     

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.     

分子高激发振动的经典代数方法研究——以C_2H_2的C-H弯曲振动为例

本文以目前探讨得较多的C2H2的CH弯曲振动为例,说明如何应用代数方法来研究分子的高激发振动。由于分子的高激发振动态具有很强的模间非线性偶合以及能量的传递,传统的动力学方法似乎很难有效地用来研究其性质。问题的核心是高激发振动态由于其量子数很大,因此具有经典(或半经典)的性质。同时模间能量的传递可以用二次量子化算子来表示,而这些算子所具有的代数性质,使得人们可以用几何的概念来描述其性质。因此,整个问题就变为用几何的观点来分析分子的高激发振动态。最后,我们用所得的经典的代数哈密顿量和哈密顿方程对CHtrans弯曲和cis弯曲振动模间能量的传递速度与体系所含能量之高低的关系做了探讨     

Critical conditions for nitrous oxide ignition

The minimum energies of ignition of gaseous nitrous oxide are measured at pressures up to 3 MPa. The minimum pressure at which nitrous oxide burnt out in the reactor completely was 0.5 MPa. It is shown that this pressure depends on the length of the vertically installed cylindrical reactor. At the optimal length, the minimum pressure was as low as 0.3 MPa. The effect of organic lubricants on the ignition energy is discovered. Liquid nitrous oxide failed to be ignited by a flame torch.     

Manifestation of Arnol'd diffusion in quantum systems

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.     

压电式纳米发电机的原理和潜在应用

纤锌矿结构氧化锌纳米线具有半导体性能和压电效应。用导电的原子力显微镜探针针尖去弯曲竖直生长的氧化锌纳米线，在纳米线的内部和外部分别造成压缩和拉伸，这种独特结构导致了弯曲纳米线的内外表面产生反极性的极化电荷，借助半导体性质的氧化锌纳米线和其金属尖部的肖特基势垒将电能暂时储存在氧化锌纳米线内，并可用导电的原子力显微镜探针接通这一电源，向外界输电，从而完美地实现了在纳米尺度上把机械能转化为电能。该纳米发电机的发电效率可以达到17％-30％，此项重要的科学发现将为自发电式纳米器件奠定物理基础。文章介绍了它的工作原理和潜在应用。     

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.     

Continuum spin system as an exactly solvable dynamical system

The continuum limit of a one-dimensional classical spins with nearest neighbour Heisenberg interaction is shown to be an exactly solvable system and that its dynamics describable by the nonlinear Schrödinger equation. N-soliton solutions for the energy density exist.     

Harmonic Inversion of Recurrence Spectra of Nonhydrogen Atom in an Electric Field

An extended harmonic inversion method is analytically continued to approach bifurcation region of the dosed orbits thus to obtain highly resolved spectra of lithium atom in external field. The suitable band-limited signal is generated by a semielassieal uniform approximation. By decimating the selected signal window and solving the algebraic set of nonlinear equations the quantum eigenvalues are properly fitted, which reveal the fine resonance structure hidden in low resolution spectrum. The study is made at the sealed energy ε= -2.7, relevant bifurcation effects and corescattered impacts have to be taken into account. It is demonstrated that the present method is a useful technique for the semiclassieal quantization of system with mixed regular-chaotic classical dynamics.     

中国地区氧化亚氮浓度时空变化特征分析

氧化亚氮是一种重要的温室气体和臭氧损耗物。利用热红外反演大气温湿廓线,由于大气氧化亚氮含量较少且变化幅度不大,一般都当作常量处理。但是在反演氧化亚氮时,由于大气温湿廓线和地表温度等参数相对氧化亚氮变化较大,可能很小的扰动就会覆盖掉氧化亚氮的吸收信号。因此有必要在上千个通道中,选取信噪比最高的通道,反演分析氧化亚氮浓度的时空变化特征,进而掌握我国氧化亚氮浓度的变化规律,为研究我国氧化亚氮排放对气候变化的贡献,制定合理的氧化亚氮减排政策等,提供可靠数据支撑。采取一种优化后的最优敏感廓线通道选取法,利用AIRS数据,基于最优估计法反演氧化亚氮浓度,与TCOON观测网中加拿大站点进行比对,结果显示卫星遥感与地面观测结果一致性较好,相关系数r为0.73,该算法可以推广到IASI和CrIS等热红外高光谱数据,使对氧化亚氮的观测数据增加到20多年,这种长时间序列的产品是对目前地面观测的有效补充。在氧化亚氮反演验证的基础上分析了我国氧化亚氮的年均值变化和月均值变化情况,以及它的空间分布特征。时空变化结果显示,我国氧化亚氮浓度在低纬度地区浓度相对较高,每年在华南地区的夏季达到峰值,月度间变化幅度较大,相比于月度变化,年度之间的变化幅度相对较小。监测结果同时显示,印度、巴基斯坦等国在紧邻我国地区,夏季氧化亚氮浓度较高,因此我国氧化亚氮浓度的时空变化特征除本地排放贡献外,也有一定的外部区域传输影响。     

Dynamics of multicomponent vesicles in a viscous fluid

We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibility of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.     

Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method

Theoretical natural frequencies and modal shapes of the first five modes of vibration are presented for a rotating blade of asymmetric aerofoil cross section, with allowance for shear deflection and rotary inertia. Frequency equations for a rotating blade with asymmetry in one plane are developed by using the Ritz process, in two ways: namely, by proceeding according to the Reissner method and according to the classical potential energy method. In both cases shape functions for the bending moment, shearing force, twisting moment, bending slope, elastic twist and deflection are developed in series form. The results obtained are compared with those existing in the literature; it is found that the Reissner method approach yields more rapid convergence than does the classical potential energy method.     

Ergodic Properties of the Non-Markovian Langevin Equation

We discuss the dissipative dynamics of a classical particle coupled to an infinitely extended heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation is driven by colored noise. Our method works in arbitrary space dimension, and for fully nonlinear systems.     

Scaling properties for a classical particle in a time-dependent potential well

Some scaling properties for a classical particle interacting with a time-dependent square-well potential are studied. The corresponding dynamics is obtained by use of a two-dimensional nonlinear area-preserving map. We describe dynamics within the chaotic sea by use of a scaling function for the variance of the average energy, thereby demonstrating that the critical exponents are connected by an analytic relationship.     

Dissipative quantum chaos: transition from wave packet collapse to explosion

Using the quantum trajectories approach, we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which follows classical chaotic dynamics and whose area is proportional to the Planck constant. At weak dissipation the exponential instability of quantum dynamics on the Ehrenfest time scale dominates and leads to wave packet explosion. The transition from collapse to explosion takes place when the dissipation time scale exceeds the Ehrenfest time. For integrable nonlinear dynamics the explosion practically disappears leaving place to collapse.     

Quantum Phenomena in a Classical Model

This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.     

Unconventional Hamilton-type variational principles for electromagnetic elastodynamics

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.     

Classically induced suppression of energy growth in a chaotic quantum system

Recent experiments with Bose–Einstein condensates (BEC) in traps and speckle potentials have explored the dynamical regime in which the evolving BEC clouds localize due to the influence of classical dynamics. The growth of their mean energy is effectively arrested. This is in contrast with the well-known localization phenomena that originate due to quantum interferences. We show that classically induced localization can also be obtained in a classically chaotic, non-interacting system. In this work, we study the classical and quantum dynamics of non-interacting particles in a double-barrier structure. This is essentially a non-KAM system and, depending on the parameters, can display chaotic dynamics inside the finite well between the barriers. However, for the same set of parameters, it can display nearly regular dynamics above the barriers. We exploit this combination of two qualitatively different classical dynamical features to obtain saturation of energy growth. In the semiclassical regime, this classical mechanism strongly influences the quantum behaviour of the system.