Comparison of non-linear optical susceptibilities of KNbO3 and LiNbO3

From the chemical bond viewpoint, second-order non-linear optical (NLO) tenser coefficients of KNbO3 and LiNbO3 crystals have been calculated. By using the bond-valence theory of complex crystals and the modified bond-charge model, we were able to determine contributions of each type of constituent chemical bond to the total second-order NLO susceptibility. The tenser values thus calculated are in good agreement with experimental data. From the comparison of NLO tenser coefficients of these two crystals, we found that the major NLO contributors are KO12 groups and LiO6 octahedra not the distorted NbO6 octahedra. The difference between their NLO properties arises from their different structural characters, and the high coordination number of constituent elements in KNbO3 makes its valence electrons become more delocalised compared with those of LiNbO3. (C) 1997 Elsevier Science Ltd. All rights reserved.

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.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

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.

Non-Linear Wave-Induced Transient Response of Soil Around a Trenched Pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot’s poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Linear chirp control of infrared signal in a biased semiconductor thin film

Ultrashort light-matter interactions between a linear chirped pulse and a biased semiconductor thin film GaAs are investigated. Using different chirped pulses, the dependence of infrared spectra on chirp rate is demonstrated for a 5 fs pulse. It is found that the infrared spectra can be controlled by the linear chirp of the pulse. Furthermore, the infrared spectral intensity could be enhanced by two orders of magnitude via appropriately choosing values of the linear chirp rates. Our results suggest a possible scheme to control the infrared signal.

Control of polarization signal distortion by frequency domain phase conjugation in optical fiber systems

Optical frequency domain phase conjugation (FDPC) is based on phase conjugation of spectrum of an input signal. It is equivalent to the phase conjugation and the time reversal of the temporal envelope of an input signal. The use of FDPC to control polarization signal distortion in birefringent optical fiber systems is proposed. Evolution of polarization signals in the system using midway FDPC is analyzed theoretically and simulated numerically. It is shown that the distortion of polarization signals can be controlled effectively by FDPC. The impairments due to dispersion and nonlinear effects can be suppressed simultaneously.

Effects of atmosphere visibility on performances of non-line-of-sight ultraviolet communication systems

Dependence of performances of non-line-of-sight (NLOS) solar-blind ultraviolet (UV) communication systems on atmosphere visibility is investigated numerically by correlating the propagation of UV radiation with the visibility. A simplified solar-blind UV atmospheric propagation model is introduced, and the NLOS UV communication system model is constituted based on the single scattering assumption. Using the model, numerical simulation is conducted for two typical geometry configurations and different modulation formats. The results indicate that the performance of the NLOS UV communication system is insensitive to variation of visibility in quite a large range, and deteriorates significantly only in very low-visibility weather, and is also dependent on the geometry configuration of the system. The results also show that the pulse position modulation (PPM) is preferable due to its high-power efficiency to improve the system performance. (c) 2007 Elsevier GmbH. All rights reserved.

Ultrafast non-linear optical properties of Ge20As25Se55 chalcogenide films

The non-resonant third-order non-linear optical properties of amorphous Ge20As25Se55 films were studied experimentally by the method of the femtosecond optical heterodyne detection of optical Kerr effect. The real and imaginary parts of complex third-order optical non-linearity could be effectively separated and their values and signs could be also determined, which were 6.6 x 10(-12) and -2.4 x 10(-12) esu, respectively. Amorphous Ge20As25Se55 films showed a very fast response in the range of 200 fs under ultrafast excitation. The ultrafast response and large third-order non-linearity are attributed to the ultrafast distortion of the electron orbitals surrounding the average positions of the nucleus of Ge, As and Se atoms. The high third-order susceptibility and a fast response time of amorphous Ge20As25Se55 films makes it a promising material for application in advanced techniques especially in optical switching. (c) 2005 Elsevier B.V. All rights reserved.

Non-resonant third-order non-linear optical properties of amorphous GeSe2 film

The real and imaginary parts of third-order susceptibility of amorphous GeSe2 film were measured by the method of the femtosecond optical heterodyne detection of optical Kerr effect at 805 nm with the 80 fs ultra fast pulses. The results indicated that the values of real and imaginary parts were 8.8 x 10(-12) esu and -3.0 x 10(-12) esu, respectively. An amorphous GeSe2 film also showed a very fast response within 200 fs. The ultra fast response and large third-order non-linearity are attributed to the ultra fast distortion of the electron orbits surrounding the average positions of the nucleus of Ge and Se atoms. (c) 2005 Elsevier B.V. All rights reserved.

Continuous weak measurement and feedback control of a solid-state charge qubit: A physical unravelling of non-Lindblad master equation

Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.

Processing network models of energy/environment systems

Processing networks are a variant of the standard linear programming network model which are especially useful for optimizing industrial energy/environment systems. Modelling advantages include an intuitive diagrammatic representation and the ability to incorporate all forms of energy and pollutants in a single integrated linear network model. Added advantages include increased speed of solution and algorithms supporting formulation. The paper explores their use in modelling the energy and pollution control systems in large industrial plants. The pollution control options in an ethylene production plant are analyzed as an example. PROFLOW, a computer tool for the formulation, analysis, and solution of processing network models, is introduced.

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.