First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. 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 the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

关于湍流中术语Coherent Structure的中文译法

<正> 中文术语“拟序结构”来源于湍流研究中的英文术语“coherent structure”。 70年代初,对剪切层和自由射流的实验观察发现,这些湍流流动中存在着大尺度的涡旋结构。当初他们称之为大尺度“序的(ordered)”或“有组织的(organized)”结构,它对剪切流如混合层,边界层、射流和尾流的早期发展起着决定性的作用。1974年3月26—29日在英国Southampton召开的专题讨论会上,不少学者称之为“coherent

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

Numerical simulation of coherent structure in two-dimensional compressible mixing layers

The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

A delay model for noise-induced bi-directional switching

Many biological systems can switch between two distinct states. Once switched, the system remains stable for a period of time and may switch back to its original state. A gene network with bistability is usually required for the switching and stochastic effect in the gene expression may induce such switching. A typical bistable system allows one-directional switching, in which the switch from the low state to the high state or from the high state to the low state occurs under different conditions. It is usually difficult to enable bi-directional switching such that the two switches can occur under the same condition. Here, we present a model consisting of standard positive feedback loops and an extra negative feedback loop with a time delay to study its capability to produce bi-directional switching induced by noise. We find that the time delay in the negative feedback is critical for robust bi-directional switching and the length of delay affects its switching frequency.

Two mechanisms for population inversion via two-colour coherent excitation in three-level systems

We analyse the physical origin of population inversion via continuous wave two-colour coherent excitation in three-level systems by dressing the inverted transition. Two different mechanisms are identified as being responsible for the population inversion. For V-configured systems and cascade (E) configured systems with inversion on the lower transition, the responsible mechanism is the selective trapping of dressed states, and the population inversion approaches the ideal value of 1. For Lambda-configured systems and Xi-configured systems with inversion on the upper transition, population inversion is based on the selective excitation of dressed states, with the population inversion tending towards 0.5. As the essential difference between these two mechanisms, the selective trapping of dressed states occurs in systems with strong decay into dressed states while the selective excitation appears in systems with strong decay out of dressed states.

Coherent quantum control of atomic and molecular processes by using the technique of laser pulses

Several schemes for coherent quantum control of atomic and molecular processes have been proposed and investigated by using the techniques of adiabatic passage and ultrashort pulses, respectively. Some interesting results have been found.

Coherent population transfer with chirped few-cycle laser pulses in an excited-doublet four-level system

The behavior of population transfer in an excited-doublet four-level system driven by linear polarized few-cycle ultrashort laser pulses is investigated numerically. It is shown that almost complete population transfer can be achieved even when the adiabatic criterion is not fulfilled. Moreover, the robustness of this scheme in terms of the Rabi frequencies and chirp rates of the pulses is explored.

Imaging properties of coherent anti-Stokes Raman scattering microscope

The coherent anti-Stokes Raman scattering (CARS) microscope with the combination of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labelling. CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscope. In this paper, the intensity distribution and the polarization property of the optical field near the focus was calculated. By using the Green function, the precise analytic solution to the wave equation of a Hertzian dipole source was obtained. We found that the intensity distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscope (e.g. the point spread function) will fail to describe the imaging properties of the CARS microscope.

The intensity distributions of collected signals in coherent anti-Stokes Raman scattering microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy with the combining of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labeling. The CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscopy. In this paper, we calculated the propagation of CARS signals by using the wave equation in medium and the slowly varying envelope approximation (SVEA), and find that the intensity angular distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscopy (e.g.. the point spread function) will fail to descript the imaging properties of CARS microscopy. (c) 2004 Elsevier B.V. All rights reserved.

Creation of arbitrary coherent superposition states in four-level systems

Using the technique of stimulated Raman adiabatic passage, we propose schemes for creating arbi- trary coherent superposition states of atoms in four-level systems: a A-type system with twofold final states and a four-level ladder system. With the use of a control field, arbitrary coherent superposition states are created without the condition of multiphoton resonance. Suitable manipulation of detunings and the control field can create either a single state or any superposition states desired. (c) 2005 Pleiades Publishing, Inc.

Laser-driven coherent betatron oscillation in a laser-wakefield cavity

The origin of beam disparity in emittance and betatron oscillation orbits, in and out of the polarization plane of the drive laser of laser-plasma accelerators, is explained in terms of betatron oscillations driven by the laser field. As trapped electrons accelerate, they move forward and interact with the laser pulse. For the bubble regime, a simple model is presented to describe this interaction in terms of a harmonic oscillator with a driving force from the laser and a restoring force from the plasma wake field. The resulting beam oscillations in the polarization plane, with period approximately the wavelength of the driving laser, increase emittance in that plane and cause microbunching of the beam. These effects are observed directly in 3D particle-in-cell simulations.

Coherent linking of periodic nano-ripples on a ZnO crystal surface induced by femtosecond laser pulses

We demonstrate the coherent linking of periodic nano-ripples formed on the surface of ZnO crystals induced by femtosecond laser pulses. By adjusting the distance between two laser scanning zones, the periodic nano-ripples induced by two separated laser writing processes can be coherently linked and the ZnO nanograting with much longer grooves is therefore produced. The length limitation of this kind of nanograting previously set by the laser focus size is thus overcome. The micro-Raman mapping technique is used to evaluate the quality of coherent linking, and the underlying physics is discussed. The demonstrated scheme is promising for producing large-size self-organized nanogratings induced by femtosecond laser pulses.