Many natural systems interact with the interface between air and liquids on a daily basis. Plants like the lotus that have self-cleaning leaf surfaces and animals that intake fluids in a variety of ways are all examples of these systems. Plants and animals exploit interfacial fluid dynamics in a variety of ways to survive in numerous harsh environments. In this thesis, five studies, inspired by natural interactions with interfaces are presented. The first study explores the influence of surface wettability in the dynamics of beams struck by water droplets. This study is inspired by raindrop-leaf interaction in nature. We characterize beam behavior after impact using a simple ODE and also find that a hydrophobic cantilever experiences reduced average torque over time than a cantilever with a hydrophilic surface. In the second study we investigate the fluid dynamics of how dogs lap water with their tongue. Dogs lap because they have incomplete cheeks and cannot suck. When lapping, a dog's tongue pulls a liquid column from the bath, suggesting that the hydrodynamics of column formation are critical to understanding how dogs drink. We measured lapping in nineteen dogs and used the results to generate a physical model of the tongue's interaction with the air-fluid interface. These experiments help to explain how dogs exploit the fluid dynamics of the generated column. The results demonstrate that effects of acceleration govern lapping frequency, which suggests that dogs curl the tongue to create a larger liquid column. Comparing lapping in dogs and cats reveals that, despite similar morphology, these carnivores lap in different physical regimes: a high-acceleration regime for dogs and a low-acceleration regime for cats. In the third study how bats drink on the wing is investigated. Bats are unique in nature in that they are one of the only animals that ingest fluids during non-hovering flight. This behavior has the advantage that bats can drink and maintain flight while hunting for food. We find that bats simply extend the tongue and drag it on the water surface while flying. The bats ingest water that coats the inside of the mouth and tongue after removal from a water bath. Bats also change their wing-beat pattern to avoid hitting the water. We investigate the crown splash instability formed when a rounded rod impacts a fluid bath. The crown splash has been widely studied; however, it has not been seen in the configuration we present. When a rounded rod impacts water, it displaces fluid, and that fluid forms a lamella that climbs up the side of the rod. Depending on the speed of impact, rod size, and other fluid parameters an instability similar to a crown splash forms. In this study, we characterize the growth of the fluid lamella along with the wavelength of the instability. Finally, we investigate the dynamics of squeezed fluids inspired by clapping wet hands. When water splashes, numerous water droplets, rather than fluid threads, are dispersed. This squeezing motion of the hands makes the fluid in between eject and eventually break into drops. In this study, the trajectory of a rim formed by fluid squeezed between two plates is measured and captured by a theoretical model. Additionally, the spacial distribution of the rim perturbation is predicted using Rayleigh-Plateau instability theory. / Ph. D.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

Cross-waves generated by an oscillating wavemaker in a rectangular wave tank are examined when two or more modes are simultaneously unstable. The partial differential equations governing the evolution of the complex amplitude of inviscid cross-waves are shown to be two coupled nonlinear Schrodinger equations with transverse modulations. Energy dissipation in the system is taken into account by the inclusion of a linear viscous damping term into the amplitude equations. A linearized stability analysis is performed on these equations to determine the critical modes, the growth rates and the stability curves. A center manifold analysis is used to reduce the PDE's to a system of ODE's in the neighborhood of a codimension two point where two adjacent spanwise modes are simultaneously nearly marginal. Four possible steady states of the system are found, one of which is a mixed mode state. A Hopf bifurcation from the mixed mode is predicted for a certain region of the parameter plane, suggesting the possibility of energy interchange between the two modes. The stability of the Hopf bifurcation is determined by studying a fifth order problem, where the quintic contributions come from the higher modes as well as the perturbations of damping and detuning.

The methods for analysis of a three degree-of-freedom nonlinear optical support system, subject to periodic and random vibration, are presented. The analysis models were taken from those generated for the dynamic problems related to the NASA Space Infrared Telescope Facility (SIRTF). The models treat the one meter, 116 kilogram (258 pound) primary mirror of the SIRTF as a rigid mass, with elastic elements representing the mirror support structure. Both linear and nonlinear elastic supports are evaluated for the SIRTF. Advanced Continuous Simulation Language (ACSL), a commercially available software package for numerical solution of nonlinear, time-dependent differential equations, was used for all models. The methods presented for handling the nonlinear differential equations can be readily adapted for handling other similar dynamics problems.

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<p> Lanford's theorem is the best known mathematical justification of Boltzmann's equation starting from deterministic classical mechanics. Unfortunately, Lanford's landmark result is only known to hold on a short time interval, whose size is comparable to the mean free time for a particle of gas. This limitation has only been overcome in restrictive perturbative regimes, most notably the case of an extremely rarefied gas of hard spheres in vacuum, which was studied by Illner and Pulvirenti in the 1980s. We give a complete proof of the convergence result due to Illner and Pulvirenti, building on the recent complete proof of Lanford's theorem by Gallagher, Saint-Raymond and Texier. Additionally, we introduce a notion that we call <i>nonuniform chaoticity </i> (classically known as strong one-sided chaos) which is propagated forwards in time under the microscopic dynamics, at least for the full time interval upon which uniform <i>L</i>^&infin; estimates are available for a specific ("tensorized'') solution of the BBGKY hierarchy. </p>

A fluid layer of binary alloy is cooled from above with solidification occurring at the lower boundary. Some latent heat and light material is released at the freezing boundary. We assume, due to a small cooling rate and a large thermal diffusivity, that the net effect of thermal buoyancy is insignificant and convection is mainly driven by compositional buoyancy associated with the release of light material. The freezing interface advances upward at a slow speed as a result of solidified binary alloy. A stability problem is formulated for the eigenvalue R as a function of Q and S, where R is a ratio of the release rate of light material at the lower boundary to that diffused by pressure gradient, Q is associated with light material diffused by pressure gradient and S is a ratio of the specific volume change upon solidification to that due to compositional change. Before the onset of convective instability, material is diffused by the pressure and compositional gradients. Convective instability is possible provided R > 1. For infinite Schmidt number P(,L), instability sets in stationarily at the marginal state and the mode having the smallest minimum eigenvalue becomes dominant. Three different modes of instabilities, depending on Q and S, are shown: cellular convective modes of both long and short wavelength and morphological mode of short wavelength. Morphological instabilities, associated with the unstable growth of the freezing interface, occur when the conducting layer near the freezing interface is constitutionally supercooled. The results indicate that cellular convective modes require R 1 + S. Nonlinear analysis shows that disturbances just past the marginal state behave like (R-R(,c))(' 1/2), where R(,c) is the critical eigenvalue. Subcritical instabilities are possible for cellular convective modes of long wavelength other than rolls. Taking into / account the effect of the curved interface, the surface tension tends to suppress the unstable growth of the freezing interface. For fixed values of Q and S, morphological modes with surface tension have larger minimum eigenvalues than those without surface tension. / Source: Dissertation Abstracts International, Volume: 43-04, Section: B, page: 1170. / Thesis (Ph.D.)--The Florida State University, 1982.

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by Dai Ruoli. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 85-88). / Abstracts in English and Chinese. / ABSTRACT --- p.i / 摘要 --- p.ii / ACKNOWLEDGEMENTS --- p.iii / TABLE OF CONTENTS --- p.iv / LIST OF FIGURES --- p.vi / LIST OF TABLES --- p.ix / Chapter CHAPTER ONE - --- BACKGROUND AND LITERATURE REVIEW --- p.1 / Chapter 1.1 --- Piezoelectric Materials --- p.2 / Chapter 1.2 --- Literature Review on Vibration Control --- p.6 / Chapter 1.2.1 --- Passive control (PCL treatment) --- p.6 / Chapter 1.2.2 --- Active control (PA treatment) --- p.7 / Chapter 1.2.3 --- Active passive hybrid control (ACL and EACL treatment) --- p.8 / Chapter 1.3 --- Finite Element Method --- p.11 / Chapter 1.4 --- Positive Position Feedback Control --- p.12 / Chapter 1.5 --- Damping --- p.13 / Chapter 1.5.1 --- GHM method --- p.13 / Chapter 1.5.2 --- Rayleigh damping --- p.13 / Chapter 1.6 --- Thesis Objectives and Outline --- p.15 / Chapter CHAPTER TWO - --- SYSTEM MODELING --- p.16 / Chapter 2.1 --- Assumptions --- p.17 / Chapter 2.2 --- Elements --- p.18 / Chapter 2.3 --- FEM Matrices --- p.22 / Chapter 2.3.1 --- Element matrices component related to in-plane displacement --- p.22 / Chapter 2.3.2 --- Element matrices component related to bending displacement --- p.30 / Chapter 2.3.3 --- Element matrices component related to shear strain --- p.35 / Chapter 2.3.4 --- Overall element matrices --- p.38 / Chapter 2.3.5 --- Piezoelectric control forces --- p.39 / Chapter 2.4 --- Damping --- p.40 / Chapter 2.4.1 --- Damping due to the viscoelastic materials --- p.40 / Chapter 2.4.2 --- Inherent structural damping --- p.43 / Chapter 2.5 --- Edge Elements --- p.44 / Chapter 2.6 --- Model Reduction --- p.46 / Chapter CHAPTER THREE - M --- ODEL VALIDATION --- p.47 / Chapter 3.1 --- Beam with Passive ACL Damping Treatment --- p.48 / Chapter 3.2 --- Clamped-Clamped Plate with Fully Covered ACL --- p.50 / Chapter 3.3 --- Cantilever Plate with ACL/EACL Patch --- p.52 / Chapter CHAPTER FOUR - --- STUDIES ON EACL PATCH LOCATION --- p.57 / Chapter 4.1 --- Overview of the Numerical Examples --- p.58 / Chapter 4.2 --- Patch Location on Passive Damping Ability --- p.61 / Chapter 4.3 --- Patch Location on Actuating Ability --- p.65 / Chapter 4.4 --- Discussion on Patch Location --- p.69 / Chapter CHAPTER FIVE - --- SYSTEM IMPLEMENTATION --- p.71 / Chapter 5.1 --- Experimental Setup --- p.71 / Chapter 5.1.1 --- Open loop test --- p.72 / Chapter 5.1.2 --- Closed loop test --- p.72 / Chapter 5.2 --- Controller Design --- p.74 / Chapter 5.3 --- Results and Discussion --- p.76 / Chapter CHAPTER SIX - --- CONCLUSION AND FUTURE WORK --- p.81 / Chapter 6.1 --- Summary and Conclusion --- p.81 / Chapter 6.2 --- Recommendations for Future Research --- p.82 / "APPENDIX - PZT data sheet from PIEZO SYSTEMS, INC" --- p.83 / BIBLIOGRAPHY --- p.85

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