Calculations of nonlinear optical responses of isomorphous crystals NaClO3 And NaBrO3 with natural optical activity

This work considers the isomorphous optically active crystals NaClO3 and NaBrO3. The connection between their second-order nonlinear optical (NLO) responses and chemical bond structures is established, starting from the experimental optical activities. The calculation reproduces the well-known experimental fact that crystals of NaClO3 and NaBrO3 with similar structures have different signs of optical rotation and of second harmonic generation (SHG). Unlike previous bond charge models, the method may include more than one type of bond in the calculation, and therefore may be used to study the optical activity and nonlinear optical properties of more general crystals. (C) 1998 Elsevier Science B.V. All rights reserved.

Bond-charge calculation of nonlinear optical susceptibilities of LiXO3 type complex crystals

Second order nonlinear optical (NLO) tensor coefficients of LiXO3 (X = I, Nb, Ta) type crystals have been evaluated on the basis of the dielectric theory of complex crystals and the modified bond charge model. The current method is capable of calculating single bond contributions to the total second order NLO susceptibility. The tenser values thus calculated agree well with experimental data. By introducing the subformula equation and the concept of the effective charge of one valence electron, we are able to successfully treat such complex crystals as LiXO3 type compounds. In addition, the bond charge expression is modified to a more reasonable form for complex crystals. (C) 1998 Elsevier Science B.V.

Nonlinear optical properties of (B3O7)(5-) and (B3O6)(3-) groups

From the chemical bond viewpoint, LiB3O5 (LBO) crystal has been studied by using the bond valence theory of complex crystals. Chemical bond parameters and linear and nonlinear optical (NLO) properties of each type of constituent chemical bonds are quantitatively determined. Because of the different crystal structure characteristics of LBO from those of beta-BaB2O4 (BBO), the two anionic groups, (B3O7)(5-) in LBO and (B3O6)(3-) in BBO, play different roles in contributions to their own total NLO tensor coefficients of LBO and BBO, respectively. By comparison, we find that planar (B3O6)(3-) groups are the ideal structure model, leading to little cancellation of contributions of each kind of bond in these groups, and this gives us a useful guide to design new NLO materials in the future.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

NONLINEAR GRAVITY-WAVES IN DEEP-WATER

In consideration of the problem on the boundary condition of nonlinear free water wave, coordinate transform is used to handle the free boundary. Supposing the solution form be the traveling wave, the ordinary differential equations of the one-order autonomous system with two variables are caused, then expanding the nonlinear terms at the equilibrium point with the Taylor expansion, we obtained the solution to traveling wave. The linear approximate equation near the equilibrium point is the small amplitude wave. A new nonlinear periodic traveling wave and nonlinear dispersion relation are shown when expanding to the second-order terms. A conclusion that the expansion of dispersion relation does not contain any odd-power terms of wave steepness and because of the nonlinear effort an oscillate structure is produced in the vertical direction is drawn.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Recovery of linear and nonlinear heart rate dynamics after coronary artery bypass grafting surgery

Background: Conventional coronary artery bypass grafting (C-CABG) and off-pump CABG (OPCAB) surgery may produce different patients' outcomes, including the extent of cardiac autonomic (CA) imbalance. the beneficial effects of an exercise-based inpatient programme on heart rate variability (HRV) for C-CABG patients have already been demonstrated by our group. However, there are no studies about the impact of a cardiac rehabilitation (CR) on HRV behaviour after OPCAB. the aim of this study is to compare the influence of both operative techniques on HRV pattern following CR in the postoperative (PO) period.Methods: Cardiac autonomic function was evaluated by HRV indices pre- and post-CR in patients undergoing C-CABG (n = 15) and OPCAB (n = 13). All patients participated in a short-term(approximately 5 days) supervised CR programme of early mobilization, consisting of progressive exercises, from active-assistive movements at PO day 1 to climbing flights of stairs at PO day 5.Results: Both groups demonstrated a reduction in HRV following surgery. the CR programme promoted improvements in HRV indices at discharge for both groups. the OPCAB group presented with higher HRV values at discharge, compared to the C-CABG group, indicating a better recovery of CA function.Conclusion: Our data suggest that patients submitted to OPCAB and an inpatient CR programme present with greater improvement in CA function compared to C-CABG.

Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

High speed nonlinear optical components for next-generation optical communications

Electronic signal processing systems currently employed at core internet routers require huge amounts of power to operate and they may be unable to continue to satisfy consumer demand for more bandwidth without an inordinate increase in cost, size and/or energy consumption. Optical signal processing techniques may be deployed in next-generation optical networks for simple tasks such as wavelength conversion, demultiplexing and format conversion at high speed (≥100Gb.s-1) to alleviate the pressure on existing core router infrastructure. To implement optical signal processing functionalities, it is necessary to exploit the nonlinear optical properties of suitable materials such as III-V semiconductor compounds, silicon, periodically-poled lithium niobate (PPLN), highly nonlinear fibre (HNLF) or chalcogenide glasses. However, nonlinear optical (NLO) components such as semiconductor optical amplifiers (SOAs), electroabsorption modulators (EAMs) and silicon nanowires are the most promising candidates as all-optical switching elements vis-à-vis ease of integration, device footprint and energy consumption. This PhD thesis presents the amplitude and phase dynamics in a range of device configurations containing SOAs, EAMs and/or silicon nanowires to support the design of all optical switching elements for deployment in next-generation optical networks. Time-resolved pump-probe spectroscopy using pulses with a pulse width of 3ps from mode-locked laser sources was utilized to accurately measure the carrier dynamics in the device(s) under test. The research work into four main topics: (a) a long SOA, (b) the concatenated SOA-EAMSOA (CSES) configuration, (c) silicon nanowires embedded in SU8 polymer and (d) a custom epitaxy design EAM with fast carrier sweepout dynamics. The principal aim was to identify the optimum operation conditions for each of these NLO device configurations to enhance their switching capability and to assess their potential for various optical signal processing functionalities. All of the NLO device configurations investigated in this thesis are compact and suitable for monolithic and/or hybrid integration.

On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.