To differ from the usually applied Eulerian method for describing the motion of fluid, the governing equations complete in the Lagrangian form for describing three-dimensional progressive and short-crested waves system are derived in this paper. A systematical ordering expansion by an appropriate perturbation approximation is developed, and the exactly satisfactory solutions in a form of functional, up to third-order progressive waves and up to second-order short-crested waves, are obtained. The kinematic properties of the waves, including the surface profile, pressure, the paths of fluid particles, and the mass transport velocity, are then described directly. The obtained solution for the short-crested waves system is successfully verified by reducing to two special cases, one is the two-dimensional simple progressive waves, and the other is the two-dimensional standing waves. Also, the analytical results are compared with experimental data including the surface profiles, the pressures and the paths of fluid particles for validation.

Bacterial communities are fundamental components of many processes occurring in aquatic ecosystems, since through microbial activities substantial amount of matter and energy is transferred from a pool of DOC to higher trophic levels. Previous studies highlighted the beneficial effects of diversity on ecosystem functioning, however studies on the resistance and resilience in microbial communities are scarce. Similarly, studies focusing on factors that might improve resistance or resilience of communities such as the influence of refuges are equally missing, although an understanding of the underlying mechanisms could be very useful in the field of conservation management. In this study, chemostat cultures were used to investigate the influence of a spatial and a temporal refuge on bacterioplankton communities’ resistance and resilience measured in terms of functioning and community composition after applying a salinity pulse disturbance. Respiration rate and substrate utilization were used to estimate bacterial functioning while community composition was determined by using T-RFLP. The perturbation was found to affect bacterial functioning and community composition. Moreover our findings indicate that the resistance and resilience measured in terms of bacterial functioning and community composition were significantly influenced by the provision of refuges.

We studied the effects of varying perturbation magnitude and direction on the postural control process of the central nervous system (CNS) caused by perturbation, before and after sensory loss. The electromyogram (EMG) response to a postural perturbation can be composed by a weighted sum of the center of mass (CoM) kinematics. We extended an existing CoM feedback model which predicted EMG of one muscle for unidirectional perturbations; we used recorded data of bidirectional perturbations, which caused muscle activity in anterior as well as posterior muscles. Modeling the CNS as two delayed feedback controllers, we reconstructed the EMGs of two antagonistic muscles simultaneously that were recorded during postural perturbation experiments on cats. Minimizing the error between predicted and recorded EMG and CoM kinematics, we were able to identify controller gains that would result in the best prediction of the recorded EMGs. We hypothesized that the weights on the CoM kinematics remained constant independent of variations in perturbation magnitude or reversed perturbation direction. We applied our model to data from bidirectional perturbations with varying magnitude, with which the cats were perturbed for a short time in one direction and a longer time in the opposite direction. The gains showed small variation for EMG predictions following long perturbations; however, the prediction of EMG following the initial displacement resulted in large gain variations. We showed that these variations were caused by our optimization methods, which was not able to consistently identify controller gains for short initial movements. Using the weights identified for unidirectional perturbations, we were able to predict muscle activity for both directions with the same gains. This suggests that the weights of the CoM kinematics for each muscle did not change for varying perturbation magnitude. We conclude that varying EMG shapes were induced solely by the variation of the CoM kinematics. We repeated the investigations on data that was recorded from cats suffering from sensory loss and found reduced CoM acceleration feedback.

A methodology of designing a novel sliding surface for a class of large-scale systems with matched and mismatched perturbations is proposed in this thesis. The main idea is that some adaptive mechanisms are embedded both in the sliding surface function and in the controllers, so that not only the mismatched perturbations are suppressed during the sliding mode, but also the information of upper bound of perturbation is not required except the upper bound of perturbation from input channel. The proposed controller of each subsystem contains two parts. The first part is measurable feedback signals, and the second part is an adaptive control mechanism, which is used for overcoming the perturbation of each subsystem as well as interconnections among subsystems. The dynamics of the controlled system can be driven into the sliding surface in a finite time, and the property of asymptotical stability of each subsystem is guaranteed. Two numerical examples are given to demonstrate the feasibility of the proposed methodology.

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the third-order by employing three small perturbation parameters. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is treated separately. All the theoretical results are presented in explicit forms and easy to apply. The bottom effects of different mean water depths and different degrees of undulation, as well as the steepness of incident waves, are clearly described by the theoretical results. In general non-resonant cases, the surface fluctuations deduced from undulated bottom topography decrease as the relative water depth increases and vice versa. The theory can be applied to the cases for wave trains propagating over wavy bottom topography with any arbitrary incident angles which are closer to natural phenomenon in coastal zone. Not only the well-known Bragg resonance but also the higher-order Bragg resonances are included in resonant cases. Unlike previous studies that analyze specific bottom topographies based on prescribed resonant conditions, both Bragg and higher-order Bragg resonances are revealed through the perturbation procedure step by step. For the resonant wave field, the amplification with propagating distance and time is revealed with the aid of the growth of energy flux. This theory is successfully verified by reducing to simpler situations. Also, the analytical results for the special case of two-dimensional wavy bottom are compared with experimental data for validation.

Abstract A simple design methodology of robust adaptive sliding m de utput tracking controllers for a class of MIMO nonlinear mismatched perturbed systems is presented in this thesis.First,the derivatives of tracking error

ABSTRACT Under stationary atmosphere and on uniform depth, this paper treats the standing waves in real fluids formed by two progressive waves possessing same properties but in opposite direction. Being different from the preceding scholars who usually treated the waves in real fluids with boundary layer theory, the author uses complete Navior-Stokes Equ. to analyze the entire flow field. When dealing with the free surface dynamical boundary condition, under the equilibrium of forces, the author takes account of atmosphere pressure, shear stress and surface tension. As for the bottom condition, at first consider the perfect smooth, then no-sliding and sliding condition. After constructing the boundary conditions and the governing equation, perturbation method is used to get those of second order, and the second order solution can be derived. In addition to relative depth , the bottom-adherence affects the bottom boundary effect. No matter in progressive or standing wave fields, we can see the variation of over-shot height, the asymmetric diagrams of fluid particle¡¦s horizontal velocity with phases, the phase difference between the second and first order bottom shear. Besides, in standing wave field, the existence of second-order interaction term not only affects the flow field in the boundary layer but also the field outside it.

Three-dimensional short-crested waves in Lagrangian form was already solved by Wang(2007). By employing the technique of perturbation analysis, the solution for the entire wave filed was obtained and the results are verified to be correct to second-order. The period of the trajectory of fluid particle in short-crested wave field was manifested in Lagrangian form. Consequently, all the characteristics of the flow field can be vividly described including the moving trajectory of fluid particle. To distinguish two different ways that short-crested waves might take place, Wang(2007)¡¦s results were extended to perturbation¡¦s third-order. The mechanism of resonance phenomenon is then clearly explained. In this study, the analytical results for the three-dimensional short-crested wave field correct to third-order were explicitly derived. The fluid particle with different initial positions or different phases has different moving trajectories. Besides, the period of the trajectory of fluid particle varies with different water depths. These are obviously revealed in our perturbation solutions. The three-dimensional short-crested wave system is successfully verified by reducing to two special cases, two-dimensional progressive waves and standing waves. Also, the analytical results were compared with experimental data including the surface profiles, the pressures, and the paths of fluid particles for validation. Furthermore, the mechanism of resonance phenomenon and the property of angular frequency were explained. Thus, the exactness and generality of the results are firm certified.

Abstract¡G This thesis studies the memory effect due to bias perturbation on digital predistortion technique, and employs multi-tone continuous wave signal and digital modulation signals with different bandwidth to discuss the performance of digital predistortion technique. Memory effect makes a great impact on the digital predistortion technique, and bias perturbation is one of the major causes. Lowering the bias perturbation can improve the effectiveness of digital predistortion technique. Another focus of this thesis is to design a Class E power amplifier in 0.18 £gm CMOS process. The power amplifier uses cascode structure to alleviate the breakdown voltage problem and employs power combining technique to achieve impedance transformation on chip for the purpose of increasing the output power and efficiency.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 62-68). Available also in a digital version from Dissertation Abstracts.