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This work describes the use of a broadband spectral source for nonlinear spectroscopy to characterize various materials with potential applications in confocal microscopy, biological sample markers, optical limiting devices and optical switches. The goal is to study the spectrum of nonlinear absorption and the dispersion of nonlinear refraction as well as the dynamics of the nonlinearities by means of femtosecond excite-­probe experiments. The principle is quite simple: if a sample is under the influence of a strong fs excitation pulse and a pro be pulse beam is incident at the same time, or shortly after (within the decay time of the nonlinearity), then the probe pulse will sense the nonlinearity induced by the excitation. If the probe pulse is broadband, a femtosecond white-light continuum (WLC) in our case, we can monitor the nonlinearity induced over the entire continuum spectrum in one laser "shot". The use of femtosecond laser pulses to generate WLC will provide femtosecond time resolution for time-resolved spectroscopy. We built the nonlinear spectrometer and allowed for many degrees of flexibility in terms of choice of wavelengths for pump and probe beams and a dual detection system to cover both visible and infrared spectral ranges. We have the possibility of performing broad band spectral measurements using a spectrometer or selected narrow bandwidth probes incident on Si or Ge photodiodes for improved S/N ratios. The intrinsic properties of the continuum probe demand a careful characterization of its spatial and temporal profile. Know ledge of the dispersion of the index of refraction in various optical elements, including the sample itself, is also required for a correct analysis of the transient absorption raw data, especially for short time-scale dynamics of nonlinear processes. We tested the system using well-characterized semiconductor samples, and the results came out in excellent agreement with those from previous picosecond Z-scan measurements and theoretical modeling. With confidence, we can now measure various organic dyes with enhanced two-photon and excited-state absorption. Our setup is used to conduct a systematic study on similar compounds with modified molecular structures in order to learn about structure-property relations and draw guidelines for future design work.

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An analysis is presented of the linear and geometrically nonlinear static response of "thin" doubly-curved shells of revolution, under internal pressure loading. The analysis is based upon direct numerical integration of the governing differential equations, written in first-order state vector form. It is assumed that the loading and response of the shell are both axially symmetric; the governing equations are thus ordinary differential equations. The geometry of the shell is limited in the analysis by the assumptions of axisymmetry and constant thickness. The shell is allowed to have general composite laminate construction, elastic supports at the edges and internal ring stiffeners. In addition, the analysis allows for the possibility of circumferential line loads at discrete locations along the dome meridian. The problem is a numerically unstable two-point boundary value problem; integrations are performed using the technique of multiple shooting. A development of the multiple shooting technique known as stabilized marching is given. Results achieved by use of the multiple shooting technique are verified by comparison to results of finite element analysis using the finite element analysis codes STAGS and ABAQUS. Parametric studies are performed for ellipsoidal domes constructed of symmetric, 8-ply laminates. The parametric studies examine the effects of dome geometry for a quasi-isotropic laminate first, then examine whether material properties may be adjusted to create a "better" design. Conclusions and recommendations for future work follow. / Ph. D.

A robust technique for performing numerical simulations of nonlinear unsteady aeroelastic behavior is developed. The technique is applied to long-span bridges and the wing of a modern business jet. The heart of the procedure is combining the aerodynamic and structural models. The aerodynamic model is a general unsteady vortex-lattice method. The structural model for the bridges is a rigid roadbed supported by linear and torsional springs. For the aircraft wing, the structural model is a cantilever beam with rigid masses attached at various positions along the span; it was generated with the NASTRAN program. The structure, flowing air, and control devices are considered to be the elements of a single dynamic system. All the governing equations are integrated simultaneously and interactively in the time domain; a predictor-corrector method was adapted to perform this integration. For long-span bridges, the simulation predicts the onset of flutter accurately, and the numerical results strongly suggest that an actively controlled wing attached below the roadbed can easily suppress the wind-excited oscillations. The governing equations for a proposed passive system were developed. The wing structure is modelled with finite elements. The deflections are expressed as an expansion in terms of the free-vibration modes. The time-dependent coefficients are the generalized coordinates of the entire dynamic system. The concept of virtual work was extended to develop a method to transfer the aerodynamic loads to the structural nodes. Depending on the speed of the aircraft, the numerical results show damped responses to initial disturbances (although there are no viscous terms in either the aerodynamic or structural model), merging of modal frequencies, the development of limit-cycle oscillations, and the occurrence of a supercritical Hopf bifurcation leading to motion on a torus. / Ph. D.

Phase noise from radio frequency (RF) oscillators is one of the major limiting factors affecting communication system performance. Phase noise directly effects short-term frequency stability, Bit-Error-Rate (BER), and phase-locked loop adjacent-channel interference. RF oscillator circuits contain at least one active device, usually a transistor. The active device has noise properties which generally dominate the noise characteristic limits of an oscillator. Since all noise sources, except thermal noise, are generally proportional to average current flow through the active device, it is logical that reducing the current flow through the device will lead to lower noise levels. A theory based on the time-varying properties of oscillators proposes that narrowing the current pulse width in the active device will decrease the time that noise is present in the circuit and therefore, decrease phase noise even further. The time-domain waveforms and phase noise of an active-biased 700MHz oscillator are analyzed, showing heavy saturation and high harmonic content. Redesigns of the example oscillator in active-bias and four-resistor-bias configurations show improved phase noise and lower harmonic levels at the output. Five oscillator designs of each bias configuration, each having a different pulse width, are simulated. As predicted by the theory, the narrowest current pulse corresponds to the lowest phase noise of the simulated oscillators. / Master of Science

The threat of capsize in unpredictable seas has been a risk to vessels, sailors, and cargo since the beginning of a seafaring culture. The event is a nonlinear, chaotic phenomenon that is highly sensitive to initial conditions and difficult to repeatedly predict. In extreme sea states most ships depend on an operating envelope, relying on the operator's detailed knowledge of headings and maneuvers to reduce the risk of capsize. While in some cases this mitigates this risk, the nonlinear nature of the event precludes any certainty of dynamic vessel stability. This research presents the use of Lyapunov exponents, a quantity that measures the rate of trajectory separation in phase space, to predict capsize events for both intact and damaged stability cases. The algorithm searches backwards in ship motion time histories to gather neighboring points for each instant in time, and then calculates the exponent to measure the stretching of nearby orbits. By measuring the periods between exponent maxima, the lead-time between period spike and extreme motion event can be calculated. The neighbor-searching algorithm is also used to predict these events, and in many cases proves to be the superior method for prediction. In addition to the ship stability research, the Lyapunov exponents are used in conjunction with bifurcation analysis to determine regions of stable behavior in strange attractors when the system parameters are varied. The boundaries of stability are important for algorithm validation, where these transitions between stable and unstable behavior must be accounted for. / Master of Science

The recent addition of autonomous formation flying spacecraft to the world's satellite fleet provides new motivation to study feedback control techniques. In this thesis, we develop nonlinear orbit control laws for use in spacecraft orbital maneuvers, and spacecraft formation flying. We apply these new control laws to a number of sample maneuvers, including formation stablishment and formation keeping maneuvers for NASA-Goddard's Leonardo-BRDF formation, and coupled orbit, and attitude maneuvers for HokieSat, a spacecraft designed, and built by students at Virginia Tech to fly in the Ionospheric Observation Nanosatellite Formation (ION-F). To provide target orbit states for feedback control, we develop and apply an algorithm to calculate a formation master orbit representing the geometric center of the formation. We also define a new technique for choosing orbital element feedback gains which appropriately scales the gains for orbit maintenance, and provides an excellent starting point for gain optimization. The orbital element feedback control law, augmented by mean motion control, and applied with appropriate gains, forces asymptotic convergence to a spacecraft target orbit, for a large variety of spacecraft maneuvers. / Master of Science

This dissertation deals with some computational and analytic challenges for dynamic process operations using first-principles models. For processes with significant spatial variations, spatially distributed first-principles models can provide accurate physical descriptions, which are crucial for offline dynamic simulation and optimization. However, the large amount of time required to solve these detailed models limits their use for online applications such as nonlinear model predictive control (NMPC). To cope with the computational challenge, we develop computationally efficient and accurate dynamic reduced order models which are tractable for NMPC using temporal and spatial model reduction techniques. Then we introduce an input and state blocking strategy for NMPC to further enhance computational efficiency. To improve the overall economic performance of process systems, one promising solution is to use economic NMPC which directly optimizes the economic performance based on first-principles dynamic models. However, complex process models bring challenges for the analysis and design of stable economic NMPC controllers. To solve this issue, we develop a simple and less conservative regularization strategy with focuses on a reduced set of states to design stable economic NMPC controllers. In this thesis, we study the operation problems of a solid sorbent-based CO2 capture system with bubbling fluidized bed (BFB) reactors as key components, which are described by a large-scale nonlinear system of partial-differential algebraic equations. By integrating dynamic reduced models and blocking strategy, the computational cost of NMPC can be reduced by an order of magnitude, with almost no compromise in control performance. In addition, a sensitivity based fast NMPC algorithm is utilized to enable the online control of the BFB reactor. For economic NMPC study, compared with full space regularization, the reduced regularization strategy is simpler to implement and lead to less conservative regularization weights. We analyze the stability properties of the reduced regularization strategy and demonstrate its performance in the economic NMPC case study for the CO2 capture system.

Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.