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.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

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.

Numerical Solution for Polymer Transient Flows in a Circle Bounded Composite Formation

A new numerical model for transient flows of polymer solution in a circular bounded composite formation is presented in this paper. Typical curves of the wellbore transient pressure are yielded by FEM. The effects of non-Newtonian power-law index, mobility and boundary distance have been considered. It is found that for the mobility ratio larger than 1, which is favorable for the polymer flooding, the pressure derivative curve in log-log form rises up without any hollow. On the other hand, if the pressure derivative curve has a hollow and then is raised up, we say that the polymer flooding fails. Finally, the new model has been extended to more complicated boundary case.

Measurement of thermal rise-time of a laser diode based on spectrally resolved waveforms

Thermal resistance and thermal rise-time are two basic parameters that affect most of the performances of a laser diode greatly. By measuring waveforms received after a spectroscope at wavelengths varied step-by-step, the spectrally resolved waveforms can be converted to calculate the thermal rise-time. Basic formulas for the spectrum variation of a laser diode and the measurement set-up by using a Boxcar are described in the paper. As an example, the thermal rise-time of a p-side up packaged short-pulse laser diode was measured by the method to be 390 mu s. The method will be useful in characterizing diode lasers and LID modules in high-power applications. (c) 2005 Elsevier B.V. All rights reserved.

Stabilization of Uncertain Nonholonomic Dynamic Systems with Bounded Inputs

The sliding mode approach and the multi-step control strategy are exploited to propose a stabilizing controller for uncertain nonholonomic dynamic systems with bounded inputs. This controller can stabilize the system to an arbitrarily small neighborhood about its equilibrium in a finite time .Its application to a nonholonomic wheeled mobile robot is described. Simulation result shows that the proposed controller is effective

Influence Of Free Surface Curvature Of A Liquid Layer On The Critical Marangoni Convection

The Pearson instability was suggested to discuss the onset of Marangoni convection in a liquid layer of large Prandtl number under an applied temperature difference perpendicular to the free surface in the microgravity environment. In this case, the temperature distribution on the curved free surface is nonuniform, and the thermocapillary convection is induced and coupled with the Marangoni convection. In the present paper the effect of volume ratio of the liquid layer on the critical Marangoni convection and the corresponding spatial variation of the convection structure in zero-gravity condition were numerically investigated by two-dimensional model. (C) 2008 Elsevier Ltd. All rights reserved.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.

Quantum path control in few-optical-cycle regime

We theoretically show that selection of a single quantum path in high-order harmonics generation can be realized in a few-optical-cycle regime with two-color schemes. We also demonstrate, in theory as well, the generation of spectrally smooth and ultrabroad extreme ultraviolet supercontinuum in argon gas which can produce single similar to 79 as pulses with currently available ultrafast laser sources. Our finding can be beneficial for generating isolated sub-100 as extreme ultraviolet pulses.

Spectral narrowing of negatively chirped femtosecond pulse by cross-phase modulation in a single-mode optical fiber

We demonstrate theoretically that the negatively chirped femtosecond laser pulse can be spectrally narrowed by cross-phase modulation. The new view is well Supported by numerical simulation. The negative chirp method in fibers might be useful in all optical wavelength switching applications. (c) 2005 Elsevier B.V. All rights reserved.

光谱色散后的相位调制光束衍射特性研究

用数值方法研究了激光驱动器系统中使用光谱色散平滑单元后光束的衍射特性、模拟结果表明，光谱色散会使光束衍射光斑变大，近场空间强度均匀性改善，而远场光斑内部存在光强接近于均匀分布的区域．进一步分析了光谱色散平滑单元中相位调制器的调制深度、调制频率及光栅色散系数等主要元件参数对光束传输特性的影响，发现在一定情况下光斑内部会出现较强的强度调制。

Synthesis of Zidovudine Derivatives with Anti-HIV-1 and Antibacterial Activities

Twelve novel zidovudine derivatives were prepared by modifying 5 '-hydroxyl group of sugar moiety (1-8) and 5-methyl group of thymidine nucleus (9-12) and characterized spectrally. The compounds were evaluated for anti-HIV-1, antitubercular and antibacter

Structural and optical properties of InAs/In0.52Al0.48As self-assembled quantum wires on InP(001)

Six-stacked InAs/In0.52Al0.48As self-assembled quantum wires (QWRs) on InP(001) by molecular-beam epitaxy (MBE) have been studied by high-resolution transmission electron microscopy (HRTEM) and polarized PL measurements. We obtained the chemical lattice fringe (CLF) image of InAs self-assembled QWRs embedded in the In0.52Al0.48As matrix by the interference between the (002)-diffracted beam and the transmitted beam in the image plane of the objective lens. The results show that the InAs QWRs were bounded by (113), (001) and (114) facets. Both the size and strain distribution in QWRs were determined. It was found that with the growth of successive periods, the height and height fluctuation of InAs QWRs decreased from the bottom period to the upper one. Some suggestions are put forward for further improving the uniformity of the stacked InAs QWRs. (c) 2005 Elsevier B.V. All rights reserved.

Self-limiting MBE growth and characterization of three-dimensionally confined nanostructures on patterned GaAs(311)A substrates

The formation of triangular-shaped dot-like (TD) structures grown by molecular beam epitaxy on GaAs (311)A substrates patterned with square- and triangular-shaped holes is compared. On substrates patterned with square-shaped holes, TD structures are formed via the pinch-off of two symmetrically arranged {111} planes which develop freely in the regions between the holes on the original substrate surface, while the (111)A sidewalls of the as-etched holes develop a rough morphology during growth. The evolution of the rough ( 1 1 1)A sidewalls is eliminated on substrates patterned with triangular shaped holes resulting in similar TD structures with highly improved uniformity over the entire pattern. Spectrally and spatially resolved cathodoluminescence spectroscopy reveals the lateral variation of the quantum-well confinement energy in the TD structures generating distinct lateral energy barriers between the top portion and the nearby smooth regions with efficient radiative recombination. Formation of TD structures provides a new approach Do fabricate three-dimensionally confined nanostructures in a controlled manner.