According to the model free approach assumption four protein dynamic related parameters, the slow and fast local motion of the NH vector, the generalized order parameter, and the 15N shielding anisotropy can be estimated at each residue by the spectral density functions at the resonant frequencies of N (omega_N) and H (omega_H). In this work, we study the linear and nonlinear estimations of the aforementioned parameters of the two proteins C12A-p8^MTCPI and Pilin from strain K122-4. The principal components of the four parameters of C12A-p8^MTCPI are used to cluster the residues. The results show that the principle components provide useful information about the secondary structure of the protein. Finally, we propose a practical method to examine the model free assumption by characterizing the distribution of the transverse rate R_2 in multifield.

Historically, the analysis of ship motion and loading responses has been performed in the frequency domain with both linear response amplitude operators and wave energy density spectra. This method, therefore, did not account for the nonlinear nature of waves. A more precise method is to obtain the response in the time domain, processing non-linear wave data with a linear response amplitude operator. Since the input is non-linear, even though the system is linear, the output will also be non-linear. This resultant data can then be used to generate a more accurate design of seaworthy vessels. Furthermore the linear frequency domain method does not account for the presence or effects of wave groups. This study shows the improved accuracy in the response obtained by accounting for non-linearities and furthermore indicates that wave groups affect the vertical relative motion of a moored ship (zero-speed).

In this dissertation, we consider modified inexact Newton methods applied to second order nonlinear problems. In the implementation of Newton's method applied to problems with a large number of degrees of freedom, it is often necessary to solve the linear Jacobian system iteratively. Although a general theory for the convergence of modified inexact Newton's methods has been developed, its application to nonlinear problems from nonlinear PDE's is far from complete. The case where the nonlinear operator is a zeroth order perturbation of a fixed linear operator was considered in the paper written by Brown et al.. The goal of this dissertation is to show that one can develop modified inexact Newton's methods which converge at a rate independent of the number of unknowns for problems with higher order nonlinearities. To do this, we are required to first, set up the problem on a scale of Hilbert spaces, and second, to devise a special iterative technique which converges in a higher order Sobolev norm, i.e., H1+alpha(omega) \ H1 0(omega) with 0 < alpha < 1/2. We show that the linear system solved in Newton's method can be replaced with one iterative step provided that the initial iterate is close enough. The closeness criteria can be taken independent of the mesh size. In addition, we have the same convergence rates of the method in the norm of H1 0(omega) using the discrete Sobolev inequalities.

This study focuses on the analysis of measured directional seas using a nonlinear model, named Directional Hybrid Wave Model (DHWM). The model has the capability of decomposing the directional wave field into its free wave components with different frequency, amplitude, direction and initial phase based on three or more time series of measured wave properties. With the information of free waves, the DHWM can predict wave properties accurately up to the second order in wave steepness. In this study, the DHWM is applied to the analyses of the data of Wave Crest Sensor Inter-comparison Study (WACSIS). The consistency between the measurements collected by different sensors in the WACSIS project was examined to ensure the data quality. The wave characteristics at the locations of selected sensors were predicted in time domain and were compared with those recorded at the same location. The degree of agreement between the predictions and the related measurements is an indicator of the consistency among different sensors. To analyze the directional seas in the presence of strong current, the original DHWM was extended to consider the Doppler effects of steady and uniform currents on the directional wave field. The advantage of extended DHWM originates from the use of the intrinsic frequency instead of the apparent frequency to determine the corresponding wavenumber and transfer functions relating wave pressure and velocities to elevation. Furthermore, a new approach is proposed to render the accurate and consistent estimates of the energy spreading parameter and mean wave direction of directional seas based on a cosine-2s model. In this approach, a Maximum Likelihood Method (MLM) is employed. Because it is more tolerant of errors in the estimated cross spectrum than a Directional Fourier Transfer (DFT) used in the conventional approach, the proposed approach is able to estimate the directional spreading parameters more accurately and consistently, which is confirmed by applying the proposed and conventional approach, respectively, to the time series generated by numerical simulation and recorded during the WACSIS project.

The first hyperpolarizability £], which is an important factor in the second-order nonlinear optical effect, of the 5-6-5 heterocyclic rigid-rod chromophores-based derivatives has been systematically investigated in this work, applying the first principle based software CASTEP and the semi-empirical software MOPAC There are four factors chosen for this computational analysis, including the effects of (i) various rigid-rod molecules, (ii) auxiliary ability of various five-member rings, (iii) donor ability, and (iv) conjugation length. Results indicate that the benzobisimidazole (BBI)-based derivatives have larger £] values than those of benzobisthiazole (BBT) and benzobisoxazole (BBO)-based derivatives. The auxiliary donor ability of the pyrrole is larger than that of the thiophene and furan. In general, the £] value of various derivatives studied is parallel to the original donor strength and the trend in the donor is -N(CH3)2 > -NH2 > -OH > -CH3. In addition, the greater the conjugation length in the derivatives is, the higher the £] value. Further, from the analyses on the band-resolved £] values and the orbital density figures, it is found that the major contribution to the enhanced £] comes primarily from an efficient charge transfer from the donor side via the intermediate heterocyclic bridge to the acceptor side. Finally, a comparison between CASTEP and MOPAC reveals that CASTEP is more appropriate and accurate in predicting the optical properties of the heterocyclic-ring-based derivatives.

Abstract Most of literature and studies on prediction of exchange rate focus on main industrial countries with few discussions on the exchange rate of the developing countries. For model residual differences can be found in a linear model, so the linear model will adjust to find equilibrium at a fixed speed. However, it is difficult for the linear model to capture the character of dynamic adjustment behavior if a non-linear adjustment relationship exists (Sarno, 2002). Moreover, in case the trading costs exist in the foreign exchange market or the technical analysis is widely used among traders, then the deviations from equilibrium exchange rate may present a non-linear adjustment trend. In view of this, this study employed the STAR (smooth transition autoregression) model developed by Granger and Terasvirta (1993) to discuss the dynamic adjustment process of the deviations from UIP in the seven countries in Latin America. In most of the experimental studies conducted in the past, it was found difficult to establish the assumptions of uncovered interest parity (UIP). Therefore, this study is aimed to verify the experimental studies on UIP in the Latin America under the non-linear framework by means of non-linear model analysis.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 71-74).

Thesis (Ph. D.)--University of Hong Kong, 1982.

This dissertation presents several solutions on the simulation of weakly nonlinear circuits. The work is motivated by the increasing demand on fast yet accurate simulation methods circuits (IC)s, and the current lack of such methods in the electronic design automation (EDA) / computer-aided design (CAD) community. Three types of frequency domain methods are studied to analyze weakly nonlinear circuits. The first method employs numerical multi-dimensional inverse Laplace transform based on Laguerre function expansion. An adaptive mesh refinement (AMR) technique is developed and its parallel implementation is introduced to speed up the computation. The second method applies a Fourier series based algorithm to invert Laplace transform. The algorithm is straightforward to implement, and gives increasing accuracy with increasing number of frequency sampling points. It employs a fast Fourier transform (FFT)-based method to directly invert the frequency domain solution. Its parallel routine is also studied. The third method is based on Gaver functional. It enjoys a high accuracy independent of the number of sampling points, and for multidimensional simulation, only the diagonal points in the matrix are required to be computer, which can be further speeded up by parallel implementation. Numerical results show that the aforementioned three methods enjoy good accuracy as well as high efficiency. A comparative study is carried out to investigate the strengths and drawbacks of each method. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

Coherent anti-Stokes Raman scattering (CARS) microscopy allows fast, label-free and chemically selective imaging of condensed-phase samples thanks to its high signal sensitivity. It also offers several other advantages such as intrinsic three-dimensional sectioning capability, longer penetration depth and high spatial resolution. In conventional CARS microscopy, two synchronized narrowband laser pulses are typically used to generate signals at a single vibrational resonance, from which vibrational images are constructed. Although this type of CARS methods has been proven to be an excellent visualizing tool for lipid in biological samples, it has two serious problems. First, the ubiquitous nonresonant background smears out vibrational signals, which makes quantitative image analysis very difficult. Second, the chemical information obtained in this method is seriously limited since only a single vibrational resonance is measured, which is far less information than full vibrational spectrum can offer. In the past few years, we have developed several novel CARS imaging techniques that can overcome these issues. All our methods require only a single broadband laser and produce background-free vibrational spectrum by combining the laser pulse shaping and various signal detection schemes. The first one obtains a vibrational spectrum over 800 ~ 1800 cm-1 in a single measurement by simultaneous excitation of multiple vibrational resonances and analysis of spectral interferences between the resonant and nonresonant signals. The second method adopts the spectral focusing mechanism, where stretched broadband pulses are used to excite a single vibrational resonance with great sensitivity. A novel frequency modulation (FM) scheme is invented to eliminate the non-resonant background. Complimentary spectral analysis algorithm is also developed to obtain quantitative CARS signals at the CH stretching region (2800 ~ 3100 cm-1). In this dissertation, the fundamental mechanisms, experimental implementations and various imaging applications of the above CARS methods are described in detail. / text