Complex nonlinear and chaotic responses have been recently observed in various compliant ocean systems. These systems are characterized by a nonlinear mooring restoring force and a coupled fluid-structure interaction exciting force. A general class of ocean mooring system models is formulated by incorporating a variable mooring configuration and the exact form of the hydrodynamic excitation. The multi-degree of freedom system, subjected to combined parametric and external excitation, is shown to be complex, coupled and strongly nonlinear. Stability analysis by a Liapunov function approach reveals global system attraction which ensures that solutions remain bounded for small excitation. Construction of the system's Poincare map and stability analysis of the map's fixed points correspond to system stability of near resonance periodic orbits. Investigation of nonresonant solutions is done by a local variational approach. Tangent and period doubling bifurcations are identified by both local stability analysis techniques and are further investigated to reveal global bifurcations. Application of Melnikov's method to the perturbed averaged system provides an approximate criterion for the existence of transverse homoclinic orbits resulting in chaotic system dynamics. Further stability analysis of the subharmonic and ultraharmonic solutions reveals a cascade of period doubling which is shown to evolve to a strange attractor. Investigation of the bifurcation criteria obtained reveals a steady state superstructure in the bifurcation set. This superstructure identifies a similar bifurcation pattern of coexisting solutions in the sub, ultra and ultrasubharmonic domains. Within this structure strange attractors appear when a period doubling sequence is infinite and when abrupt changes in the size of an attractor occur near tangent bifurcations. Parametric analysis of system instabilities reveals the influence of the convective inertial force which can not be neglected for large response and the bias induced by the quadratic viscous drag is found to be a controlling mechanism even for moderate sea states. Thus, stability analyses of a nonlinear ocean mooring system by semi-analytical methods reveal the existence of bifurcations identifying complex periodic and aperiodic nonlinear phenomena. The results obtained apply to a variety of nonlinear ocean mooring and towing system configurations. Extensions and applications of this research are discussed. / Graduation date: 1992

We study the chaotic phase synchronization (CPS) between the external periodically driving signals and the nonlinear dynamic systems. The periodical signal was applied to drive the Chua circuit system with two-scroll attractor and the four-scroll attractor circuit system. The phase synchronization between the outputs of these two circuit systems and the driving signals were investigated. Besides, the chaotic phase synchronization of the periodically pump-modulated microchip Nd:YVO4 laser and the microchip Nd:YVO4 laser with optical feedback were also examined in this study. Phase synchronization (PS) transition of these periodically driven nonlinear dynamic systems exhibited via the stroboscopic technique and recurrence probability. The recurrence probability and correlation probability of recurrence were utilized to estimate the degree of PS. In this thesis, the degree of PS was studied by taking into account the amplitude and frequency of the external driving signal. The experimental compatible numerical simulations also reflected the fact that the Arnold tongues are experimentally and numerically exhibited in the periodically driven nonlinear dynamic systems.

Chaotically modulated signals are used in various engineering areas such as communication systems, signal processing applications, automatic control systems. Because chaotically modulated signal sequences are broadband and noise-like signals, they are used to carry binary signals especially in secure communication systems. In this thesis, a target tracking problem under interference at chaotic communication systems is investigated. Simulating the chaotic communication system, noise-like signal sequences are generated to carry binary signals. These signal sequences are affected by Gaussian channel noise and interference while passing through the communication channel. At the receiver side, target tracking is performed using Optimum Decoding Based Smoothing Algorithm. The estimation performances of optimum decoding based smoothing algorithm at one dimensional chaotic systems and nonlinear chaotic algorithm map are presented and compared with the performance of the Extended Kalman Filter application.

In many systems, instabilities can lead to time-dependent behavior, and instabilities can act as mechanisms for sustained chaos; an understanding of the dynamical modes governing instability is thus essential for prediction and/or control in such systems. In this thesis work, we have developed an approach toward characterizing instabilities quantitatively, from experiments on the prototypical Rayleigh-Bénard convection system. We developed an experimental technique for preparing a given convection pattern using rapid optical actuation of pressurized SF6, a greenhouse gas. Real-time analysis of convection patterns was developed as part of the implementation of closed-loop control of straight roll patterns. Feedback control of the patterns via actuation was used to guide patterns to various system instabilities. Controlled, spatially localized perturbations were applied to the prepared states, which were observed to excite the dominant system modes. We extracted the spatial structure and growth rates of these modes from analysis of the pattern evolutions. The lifetimes of excitations were also measured, near a particular instability; a critical wavenumber was found from the observed dynamical slowing near the bifurcation. We will also describe preliminary results of using a state estimation algorithm (LETKF) on experimentally prepared non-periodic patterns in a cylindrical convection cell.

Baigiamajame magistro darbe nagrinėjama darnios nekilnojamojo turto plėtros problemos ir tendencijos, pateikiamos pasaulinės urbanizacijos keliamos grėsmės ir chaotiškos plėtros problematika, aprašomos Lietuvos gyvenamųjų pastatų plėtros perspektyvos ir atliekama pasirinktų Lietuvoje vykdomų nekilnojamojo turto plėtros projektų analizė. / The tends and problems of sustainable real estate development are analysed, the global threat posed by urbanization and chaotic development issues are given, Lithuanian residential development perspectives are described and analyzed in the final master's work.

This thesis considers a communication system with chaotic modulation. Noise-like signals are generated by chaotic systems with different parameters to modulate binary digital signals. Demodulation is performed by both the Extended Kalman Filter (EKF) and Optimum Decoding Based Smoothing Algorithm (ODSA). Simulations are performed using both of these algorithms for different parameters affecting the performance of the communication system. Simulation results of these algorithms are compared.

The research presented in this thesis was motivated by the desire to understand the flow field within a new digital microfluidic device currently under development. This required an investigation of the dynamics of a droplet migrating along the surface of another fluid due to interfacial surface tension gradients. The quantitative analysis of the flow field presented in this thesis provides the first known solution for the velocity field in a migrating droplet confined to an interface. The first step towards gaining insight into the flow field was accomplished by using the method of reflections to obtain an analytical model for a submerged droplet migrating near a free surface. The submerged droplet model enabled the analysis of the velocity field and droplet migration speed and their dependence on the fluid properties. In general, the migration velocity of a submerged droplet was found to differ dramatically from the classic problem of thermocapillary migration in an unbounded substrate. A boundary-collocation scheme was developed to determine the flow field and migration velocity of a droplet floating trapped at the air-substrate interface. The numerical method was found to produce accurate solutions for the velocity and temperature fields for nearly all parameters. This numerical scheme was used to judge the accuracy of the flow field obtained by the submerged droplet model. In particular, the model was tested using parameter values taken from a digital microfluidic device. It was determined that the submerged droplet model captured most of the flow structure within the microfluidic droplet. However, for a slightly different choice of parameters, agreement between the two methods was lost. In this case, the numerical scheme was used to uncover novel flow structures.

Thesis (doctoral)--Rijksuniversiteit te Utrecht, 1983. / "Stellingen": [6] p. inserted. Includes bibliographical references (p. 253-257) and index.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 204-214).

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