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.

Triple-region structure for turbulent-flow in a square duct - a finite-element approach

The Reynolds-averaged Navier-Stokes equations for describing the turbulent flow in a straight square duct are formulated with two different turbulence models. The governing equations are then expanded as a multi-deck structure in a plane perpendicular to the streamwise direction, with each deck characterized by its dominant physical forces as commonly carried out in analytical work using triple-deck expansion. The resulting equations are numerically integrated using higher polynomial (H-P) finite element technique for each cross-sectional plane to be followed by finite difference representation in the streamwise direction until a fully developed state is reached. The computed results using the two different turbulence models show fair agreement with each other, and concur with the vast body of available experimental data. There is also general agreement between our results and the recent numerical works anisotropic k-epsilon turbulence model.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Efficient excitations of radially and azimuthally polarized Nd 3+:YAG ceramic microchip laser by use of subwavelength multilayer concentric gratings composed of Nb2O5/SiO2

Cylindrical vector beams were produced from laser diode end-pumped Nd:YAG ceramic microchip laser by use of two types of subwavelength multilayer gratings as the axisymmetric-polarization output couplers respectively. The grating mirrors are composed of high- and low-refractive-index (Nb2O5/SiO2) layers alternately while each layer is shaped into triangle and concentric corrugations. For radially polarized laser output, the beam power reached 610mW with a polarization extinction ratio ( PER) of 61: 1 and a slope efficiency of 68.2%; for azimuthally polarized laser output, the beam power reached 626mW with a PER of 58: 1 and a slope efficiency of 47.6%. In both cases, the laser beams had near-diffraction limited quality. Small differences of beam power, PER and slope efficiency between radially and azimuthally polarized laser outputs were not critical, and could be minimized by further optimized adjustment to laser cavity and the reflectances of respective grating mirrors. The results manifested, by use of the photonic crystal gratings mirrors and end-pumped microchip laser configuration, CVBs can be generated efficiently with high modal symmetry and polarization purity. (C) 2008 Optical Society of America.

Analysis of the energies of the triple base triplets

Sixty-four sets of three-dimensional models of DNA triplex base triplets (TBT) were built up based on codons by homologous modeling method and their energies were minimized. According to sequence of TBT and orientation of the third ODN strand third, the energies of monomers and water-K+-TBT ternary complexes of TBT were analyzed. The results showed: (i) The energies of the symmetric parallel monomers are generally lower than those of the symmetric anti-parallel monomers of TBT, but the energies of the symmetric parallel ternary complexes are higher than those of the symmetric anti-parallel ternary complexes of TBT. (ii) No matter TBTs are monomers or ternary complexes, the energies of asymmetric parallel TBTs are generally lower than those of the asymmetric anti-parallel ones. (iii) Although the energies of the parallel TBTs are correlated with those of the anti-parallel ones, the energy differences are significant between them. The results here suggest the sequences of TBTs and the orientations of the third ODN strands are two of the key factors that can influence the formation and stability of TBT. (C) 2002 Elsevier Science B.V. All rights reserved.

The comparative analysis of the energies of conjugated triple base triplets and their applications

We built 64 sets of 3D models of DNA triplex base triplets (TBT) and minimized their energies. The TBTs were divided into 32 pairs of conjugated ones on the basis of their sequence characteristic, and the energies of each pair of them were compared and analyzed, the results showed: (i) The duplex DNA of which any strand contains at least a couple of A or T, has a preference for selecting the oligodeoxyribonucleic acid (ODN) strand containing abundant T to form TBT. (ii) The duplex DNA of which any strand contains at least a couple of G or C has a preference for selecting ODN containing abundant G to form symmetric antiparallel TBT, but selecting ODN containing abundant C to form asymmetric parallel TBT. (iii) The duplex DNA of which any strand contains only one of A, T, G or C has a preference for selecting ODN containing abundant pyrimidines (T or C) to form antiparallel TBT. Additionally, two examples of TBTs applications, in designing ODN to form triplex with duplex were presented. The energy calculation result revealed that 15-TCG is the best ligand of the HIV PPT duplex. The comparative analysis of energies of the conjugated TBTs provides directive significance for designing ODN strand that is easy to form triplex in theory. (C) 2002 Elsevier Science B.V. All rights reserved.

1310 nm GaInNAs triple quantum well laser with 13 GHz modulation bandwidth

The emission wavelength of a GaInNAs quantum well (QW) laser was adjusted to 1310 nm, the zero dispersion wavelength of optical fibre, by an appropriate choice of QW composition and thickness and N concentration in the barriers. A triple QW design was employed to enable the use of a short cavity with a small photon lifetime while having sufficient differential gain for a large modulation bandwidth. High speed, ridge waveguide lasers fabricated from high quality material grown by molecular beam epitaxy exhibited a damped modulation response with a bandwidth of 13 GHz.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Mode softening in charge-density excitations of a two-dimensional electron gas driven by Rashba spin-orbit interaction

The electron density response of a uniform two-dimensional (2D) electron gas is investigated in the presence of a perpendicular magnetic field and Rashba spin-orbit interaction (SOI). It is found that, within the Hartree-Fock approximation, a charge density excitation mode below the cyclotron resonance frequency shows a mode softening behavior, when the spin-orbit coupling strength falls into a certain interval. This mode softening indicates that the ground state of an interacting uniform 2D electron gas may be driven by the Rashba SOI to undergo a phase transition to a nonuniform charge density wave state.

Charge-density and spin-density excitations in a two-dimensional electron gas with Rashba spin-orbit coupling

We study theoretically the charge-density and spin-density excitations in a two-dimensional electron gas in the presence of a perpendicular magnetic field and a Rashba type spin-orbit coupling. The dispersion and the corresponding intensity of excitations in the vicinity of cyclotron resonance frequency are calculated within the framework of random phase approximation. The dependence of excitation dispersion on various system parameters, i.e., the Rashba spin-orbit interaction strength, the electron density, the Zeeman spin splitting, and the Coulomb interaction strength is investigated.

Collective and single-particle excitations in coupled quantum wires in magnetic fields

The full spectra of magnetoplasmons and single-particle excitations are obtained of coupled one-dimensional electron gases in parallel semiconductor quantum wires with tunneling. We show the effects of the interwire Coulomb interaction and the tunneling, as well as the magnetic-field-induced localization on the elementary excitations in symmetric and asymmetric coulped quantum wire structures. The interacton and resonance between the plasmon and the intersubband single-particle excitations are found in magnetic fields.

Transmission electron microscopy study of triple-ribbon contrast features in a ZnTe epitaxial layer

A transmission electron microscopy study of triple-ribbon contrast features in a ZnTe layer grown epitaxially on a vicinal GaAs (001) substrate is reported. The ribbons go through the layer as threading dislocations near the [<(11)over bar 2>](111) or [112](<(11)over bar 1>) directions. Each of these (with a 40 nm width) has two narrow parts enclosed by three partial dislocations (with a 20 nm spacing). By contrast analysis and contrast simulation, the ribbons have been shown to be composed of two partially overlapping stacking faults. Their origin is attributed to a forced reaction between two crossing perfect misfit dislocations.

Kondo effect in a triangular triple quantum dots ring with three terminals

For a triangular triple quantum dots (TTQDs) ring with three terminals, when lowering one of the dot-lead coupling to realize the left-right (L-R) reflection symmetry coupling, the internal C-upsilon of the TTQDs is well preserved in the absence of many-body effect for the symmetric distribution of the dot-lead coupling on the molecular orbits. In the presence of Kondo effect, the decrement of one of the dot-lead couplings suppresses the inter-dot hopping. This happens especially for the coupled quantum dot (QD), which decouples with the other two ones gradually to form a localized state near the Fermi level As a result, the internal dynamic symmetry of the TTQDs ring is reduced to L-R reflection symmetry, and simultaneously, the linear conductance is lifted for the new forming molecular orbit near the Fermi level