Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses

We present an efficient method to generate a ultrashort attosecond (as) pulse when a model He+ ion is exposed to the combination of an intense few-cycle chirped laser pulse and its 27th harmonics. By solving the time-dependent Schroumldinger equation, we found that high-order harmonic generation (HHG) from He+ ion is enhanced by seven orders of magnitude due to the presence of the harmonic pulse. After optimizing the chirp of the fundamental pulse, we show that the cut-off energy of the generated harmonics is extended effectively to I-p+25.5U(p). As a result, an isolated 26-as pulse with a bandwidth of 170.5 eV can be obtained directly from the supercontinuum around the cut-off of HHG. To better understand the physical origin of HHG enhancement and attosecond pulse emission, we perform semiclassical simulations and analyze the time-frequency characteristics of attosecond pulse.

High-order harmonic generation and multi-photon ionization of Na-2 in laser fields

In this paper high-order harmonic generation (HHG) spectra and the ionization probabilities of various charge states of small cluster Na-2 in the multiphoton regimes are calculated by using time-dependent local density approximation (TDLDA) for one-colour (1064 nm) and two-colour (1064 nm and 532 nm) ultrashort (25 fs) laser pulses. HHG spectra of Na2 have not the large extent of plateaus due to pronounced collective effects of electron dynamics. In addition, the two-colour laser field can result in the breaking of the symmetry and generation of the even order harmonic such as the second order harmonic. The results of ionization probabilities show that a two-colour laser field can increase the ionization probability of higher charge state.

Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

On the design of the piecewise linear vibration absorber

This paper explores the potential of the piecewise linear vibration absorber in a system subject to narrow band harmonic loading. Such a spring is chosen because the design of linear springs is common knowledge among engineers. The two-degrees-of-freedom system is solved by using the Incremental Harmonic Balance method, and response aspects such as stiffness crossing frequency and jump behaviour are discussed. The effects of mass, stiffness, natural frequency ratios, and stiffness crossing positions on the suppression zone are probed. It is shown that a hardening absorber can deliver a wider bandwidth than a linear one over a range of frequencies. The absorber parameters needed to produce good designs have been determined and the quality of the realized suppression zone is discussed. Design guidelines are formulated to aid the parameter selection process.

Molecular/Cluster Statistical Thermodynamics Methods To Simulate Quasi-Static Deformations At Finite Temperature

The rapid evolution of nanotechnology appeals for the understanding of global response of nanoscale systems based on atomic interactions, hence necessitates novel, sophisticated, and physically based approaches to bridge the gaps between various length and time scales. In this paper, we propose a group of statistical thermodynamics methods for the simulations of nanoscale systems under quasi-static loading at finite temperature, that is, molecular statistical thermodynamics (MST) method, cluster statistical thermodynamics (CST) method, and the hybrid molecular/cluster statistical thermodynamics (HMCST) method. These methods, by treating atoms as oscillators and particles simultaneously, as well as clusters, comprise different spatial and temporal scales in a unified framework. One appealing feature of these methods is their "seamlessness" or consistency in the same underlying atomistic model in all regions consisting of atoms and clusters, and hence can avoid the ghost force in the simulation. On the other hand, compared with conventional MD simulations, their high computational efficiency appears very attractive, as manifested by the simulations of uniaxial compression and nanoindenation. (C) 2008 Elsevier Ltd. All rights reserved.

Concentrated-Mass Cantilever Enhances Multiple Harmonics In Tapping-Mode Atomic Force Microscopy

The natural frequencies of a cantilever probe can be tuned with an attached concentrated mass to coincide with the higher harmonics generated in a tapping-mode atomic force microscopy by the nonlinear tip-sample interaction force. We provide a comprehensive map to guide the choice of the mass and the position of the attached particle in order to significantly enhance the higher harmonic signals containing information on the material properties. The first three eigenmodes can be simultaneously excited with only one carefully positioned particle of specific mass to enhance multiple harmonics. Accessing the interaction force qualitatively based on the high-sensitive harmonic signals combines the real-time material characterization with the imaging capability. (C) 2008 American Institute of Physics.

Convergence of attractors

The system of coupled oscillators and its time-discretization (with constant stepsize h) are considered in this paper. Under some conditions, it is showed that the discrete systems have one-dimensional global attractors l(h) converging to l which is the global attractor of continuous system.

Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

具有摩擦阻尼结点之结构动力分析

本文将增量谐波平衡法(Incremental Harmonic Balance Method, I. H. B Method)结合组抗方法用于分析具有摩擦结点之结构稳态动力响应。这方法之主要优点是能将线性结构与摩擦结点分开来考虑。当摩擦结点之自由度远小于线性结构之自由度时,计算是很经济的。发展了一个分析这种系统之计算程序可与一般有限元结构分析程序如SAPV或ADINA相连,作为后处理程序。

具有局部非线性元件的结构动力分析

谐波增量平衡法在描述非线性力时计及多谐分量,是处理强非线性的一个有效方法.在本文中,此法被推广于分析局部非线性结构的稳态响应.被分析的结构分解为若干子结构,所有非线性元件均位于子结构的分界面上.系统的响应用谐波增量平衡法(Incremental Harmonic Balance Method,简称I.H.B法)结合F.F.T.(快速福里哀变换)技术与状态空间的模态综合法分析之.