PhD Thesis / In this thesis, experiments are described which study the elastocapillary interactions between liquids and taut solid films. The research employs contact angle measurements to elucidate how capillary forces deform compliant solid structures, but also to attain fundamental insight into the energy of interfaces involving amorphous solids. The majority of the work focuses on how capillary deformations of compliant elastic membranes introduce modifications to descriptions of common wetting phenomena. Particular focus is given to studying partial wetting in the presence of compliant membranes in various geometries: droplet on a free-standing membrane, droplet capped by a membrane but sessile on a rigid substrate, and droplet pressed between two free-standing membranes. The mechanical tension in these membranes is found to play an equivalent role as the interfacial tensions. As such, the mechanical tension is incorporated into Young-Dupre's law (capped droplet on a rigid substrate) or Neumann's triangle (droplet on free-standing membrane), leading to departures from the classical wetting descriptions. In addition, one study is conducted investigating how viscous dewetting is affected by the liquid film being capped by an elastic film. The results of this study show that the dewetting rate and rim morphology are dictated by the elastic tension. Another important aspect of the work is demonstrating the utility of anisotropic membrane tension for liquid patterning. A biaxial tension is shown to produce droplets and dewetting holes which are elongated along the high tension direction. The compliant membrane geometry can also be designed to produce droplets and holes with square morphology. In the final project, the surface energy of strained glassy and elastomeric solids is studied. Glassy solids are shown to have strain-dependent surface energies, which implies that surface energy (energy per unit area) and surface stress (force per unit length) are not equivalent for this class of materials by virtue of the Shuttleworth equation. On the other hand, this study provides strong evidence that surface energy and surface stress are equivalent for elastomeric interfaces. / Thesis / Doctor of Philosophy (PhD)

An important phenomenon of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for three systems: the Lorenz-96 model, the Swift-Hohenberg equation, and Rayleigh-Bénard convection. The Lorenz-96 model is a continuous in time and discrete in space phenomenological model that captures important features of atmosphere dynamics. We computed the fractal dimension as a function of system size and external forcing to estimate characteristic length and time scales describing the chaotic dynamics. We found extensive chaos with significant deviations from extensivity for small changes in system size and also the power-law growth of the dimension with increasing forcing. The Swift-Hohenberg equation is a partial differential equation for a scalar field, which has been widely used as a model for the study of pattern formation. We found that the magnitude of the mean flow in this model must be sufficiently large for spiral defect chaos to occur. We also explored the spatiotemporal chaos in experimentally accessible Rayleigh-Bénard convection using large-scale numerical simulations of the Boussinesq equations and the corresponding tangent space equations. We performed a careful study analyzing the impact of variations in the domain size, Rayleigh number, and Prandtl number on the system dynamics and fractal dimension. In addition, we quantified the dynamics of the spectrum of Lyapunov exponents and the leading order Lyapunov vector in an effort to connect directly with the dynamics of the flow field patterns. Further, we numerically studied the synchronization of chaos in convective flows by imposing time-dependent boundary conditions from a principal domain onto an initially quiescent target domain. We identified a synchronization length scale to quantify the size of a chaotic element using only information from the pattern dynamics. We also explored the relationship of this length scale with the pattern wavelength. Finally, we analyzed bioconvection which occurs as the result of the collective behavior of a suspension of swimming microorganisms. We developed a series of simulations to capture the gyrotactic pattern formation of the swimming algae. The results can be compared with the corresponding trend of pattern instabilities observed in the experimental studies. / Ph. D.

We study game theoretic ecological models with cyclic competition in the case where the strategies can be mixed or pure. For both projects, reported in [49] and [50], we employ Monte Carlo simulations to study finite systems. In chapter 3 the results of a previously published paper [49] are presented and expanded upon, where we study the extinction time of four cyclically competing species on different lattice structures using Lotka-Volterra dynamics. We find that the extinction time of a well mixed system goes linearly with respect to the system size and that the probability distribution approximately takes the shape of a shifted exponential. However, this is not true for when spatial structure is added to the model. In that case we find that instead the probability distribution takes on a non-trivial shape with two characteristic slopes and that the mean goes as a power law with an exponent greater than one. This is attributed to neutral species pairs, species who do not interact, forming domains and coarsening. In chapter 4 the results of [50] are reported and expanded, where we allow agents to choose cyclically competing strategies out of a distribution. We first study the case of three strategies and find through both simulation and mean field equations that the probability distributions of the agents synchronize and oscillate with time in the limit where the agents probability distributions can be approximated as continuous. However, when we simulate the system on a one-dimensional lattice and the probability distributions are small and discretized, it is found that there is a drastic transition in stability, where the average extinction time of a strategy goes from being a power law with respect to system size to an exponential. This transition can also be observed in space time images with the emergence of tile patterns. We also look into the case of four cyclically competing strategies and find results similar to that of [49], such as the coarsening of neutral domains. However, the transition from power law to exponential for the average extinction time seen for three strategies is not observed, but we do find a transition from one power law to another with a different slope. This work was supported by the United States National Science Foundation through grants DMR-0904999 and DMR-1205309. / Ph. D.

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

Suspensions of the aerobic bacteria {\it Bacilus subtilis} develop patterns and flows from the interplay of motility, chemotaxis and buoyancy.In sessile drops, such bioconvectively driven flows carry plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom.These dynamics are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics.Concentrated regions in both geometries comprise nearly close-packed populations, forming the collective ``Zooming BioNematic'' (ZBN) phase.This state exhibits large-scale orientational coherence, analogous to the molecular alignment of nematic liquid crystals, coupled with remarkable spatial and temporal correlations of velocity and vorticity, as measured by both novel and standard applications of particle imaging velocimetry.To probe mechanisms leading to this phase, response of individual cells to steric stress was explored, finding that they can reverse swimming direction at spatial constrictions without turning the cell body.The consequences of this propensity to flip the flagella are quantified, showing that "forwards" and "backwards" motion are dynamically and morphologically indistinguishable.Finally, experiments and mathematical modeling show that complex flows driven by previously unknown bipolar flagellar arrangements are induced when {\it B. subtilis} are confined in a thin layer of fluid, between asymmetric boundaries.The resulting driven flow circulates around the cell body ranging over several cell diameters, in contrast to the more localized flows surrounding free swimmers.This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and inter-cellular communication.

In order to successfully incorporate the tremendous possibilities of nanoscale applications into devices and manufacturing, significant studies need to be conducted of the properties and mechanics of materials of this small scale. In this thesis, the effect of repeated scanning of KBr, aluminum, and gold was studied by using a nanoindenter and Atomic Force Microscope (AFM) in varying environments. Additional research was performed to study the environmental effects of gold film scratching using a Taber Shear/Scratch Tester. Scanning of KBr single crystal surface in air with a diamond tip in the Hysitron Triboindenter formed surface ripples 100 nm high, 1 micron apart. It has been observed that the nanoripple's initial height and period increase with the number of repeated scans. The surface ripples form perpendicular to the scanning direction, beginning at the bottom of sloped samples and working their way up the entire scan area. The addition of water to a wear experiment on gold film produced considerably deeper wear areas than its ambient air counterpart in both scanning machines. Scratch testing with a conical diamond tip of 77 µm radius with 125 g normal load also produced deeper wear tracks in water than in ambient air conditions. Several mechanisms may be responsible for the ripples formation, including dislocation dynamics, chatter, piezo hysteresis and others. Most likely there is a combination of effects, with a clear differentiation between nanoripple's origination and propagation. Mechanisms responsible for rippling, including system dynamic response and stick slip behavior are investigated. Topography modification appears to be the main result of ambient wear tests at the nanoscale, whereas much higher wear rate and nanoripples are observed in water. It is possible that this moisture is assisting grain fracture and pull off.

No description available.

Thesis (Ph. D. in Cell and Developmental Biology)--Vanderbilt University, May 2007. / Title from title screen. Includes bibliographical references.

<p>Drylands, comprising arid and semi-arid areas and the dry subtropics, over some 40% of the world's land area and support approximately 2 billion people, including at least 1 billion who depend on dryland agriculture and grazing. 10-20% of drylands are estimated to have already undergone degradation or desertification, and lack of monitoring and assessment remains a key impediment to preventing further desertification. Change in vegetation cover, specifically in the spatial organization of vegetation may occur prior to irreversible land degradation, and can be used to assess desertification risk. Coherent spatial structures arise in the distribution of dryland vegetation where plant growth is localized in regular spatial patterns. Such "patterned vegetation" occurs across a variety of vegetation and soil types, extends over at least 18 million ha, occurs in 5 continents and is economically and environmentally valuable in its own right.</p> <p>Vegetation patterning in drylands arises due to positive feedbacks between hydrological forcing and plant growth so that the patterns change in response to trends in mean annual rainfall. Mathematical models indicate that vegetation patterns collapse to a desertified state after undergoing a characteristic set of transformations so that the condition of a pattern at any point in time can be explicitly linked to ecosystem health. This dissertation focuses on the mathematical description of vegetation patterns with a view to improving such predictions. It evaluates the validity of current mathematical descriptions of patterning for the specific case of small-scale vegetation patterns and proposes alternative hypotheses for their formation. It assesses the significance of seed dispersal in determining pattern form and dynamics for two cases: vegetation growing on flat ground with isotropic patterning, and vegetation growing on slopes and having anisotropic (i.e. directional) patterning. Thirdly, the feedbacks between local biomass density and infiltration capacity, one of the positive feedbacks believed to contribute to patterning, are quantified across a wide range of soil and climatic conditions, and new mathematical descriptions of the biomass-infiltration relationship are proposed. Finally the influence of land surface microtopography on the partitioning of rainfall into infiltration and runoff is assessed.</p> / Dissertation

<p>Negative differential conductivity (NDC) is a nonlinear property of electronic transport for high electric field strength found in materials and devices such as semiconductor superlattices, bulk GaAs and Gunn diodes. In spatially extended systems, NDC can cause rich dynamics such as static and mobile field domains and moving charge fronts. In this thesis, these phenomena are studied theoretically and numerically for semiconductor superlattices. Two classes of models are considered: a discrete model based on sequential resonant tunneling between neighboring quantum wells is used to described charge transport in weakly-coupled superlattices, and a continuum model based on the miniband transport is used to describe charge transport strongly-coupled superlattices.</p> <p>The superlattice is a spatially extended nonlinear system consisting a periodic arrangement of quantum wells (e.g., GaAs) and barriers (e.g., AlAs). Using a discrete model and only considering one spatial dimension, we find that the boundary condition at the injecting contact has a great influence on the dynamical behavior for both fixed voltage and transient response. Static or moving field domains are usually inevitable in this system. In order to suppress field domains, we add a side shunting layer parallel to the growth direction of the superlattice. In this case, the model includes both vertical and lateral spatial degrees of freedom. We first study a shunted weakly-coupled superlattice for a wide range of material parameters. The field domains are found to be suppressed for superlattices with small lateral size and good connection between the shunt and the quantum wells of the superlattice. As the lateral size of the superlattice increases, the uniform field configuration loses its stability to either static or dynamic field domains, regardless of shunt properties. A lower quality shunt generally leads to regular and chaotic current oscillations and complex spatio-temporal dynamics in the field profile. Bifurcations separating static and dynamic behaviors are characterized and found to be dependent on the shunt properties. Then we adopt the model to study the shunted strongly-coupled superlattice with the continuum model. Key structural parameters associated with both the shunt layer and SL are identified for which the shunt layer stabilizes a uniform electric field profile. These results support the possibility to realize a SL-based THz oscillator with a carefully designed structure.</p> <p>Another important behavior of the static field domains in the weakly-coupled superlattice is bistability, i.e., two possible states (i.e., electric field configurations) for a single voltage. Noise can drive the system from one of these states (the metastable state) to the other one (the globally stable state). The process of escape from the metastable state can be viewed as a stochastic first-passage process in a high-dimensional system that possesses complex stability eigenvalues and for which a global potential energy function does not exist. This process is simulated using a stochastic differential equation system which incorporates shot noise. The mean switching time &tau; is fitted to an exponential expression <italic>e</italic><super>(Vth-V)<super>&alpha;</super>/D</super>, where V_th denotes the voltage at the end of the current branch. The exponent &alpha; in the fitting curve deviates from 1.5 which is predicted for a generic one dimensional system. We develop an algorithm to determine an effective locally valid potential. Principal component analysis is applied to find the most probable path for switching from the metastable current state.</p> / Dissertation