Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

DYNAMICS OF THE SHORT TERM AND LONG TERM AVIAN DISTRIBUTIONS IN NORTH AMERICA - THE ROLES OF VEGETATION HEIGHT HETEROGENEITY AND CLIMATIC FACTORS

Understanding how biodiversity spatially distribute over both the short term and long term, and what factors are affecting the distribution, are critical for modeling the spatial pattern of biodiversity as well as for promoting effective conservation planning and practices. This dissertation aims to examine factors that influence short-term and long-term avian distribution from the geographical sciences perspective. The research develops landscape level habitat metrics to characterize forest height heterogeneity and examines their efficacies in modelling avian richness at the continental scale. Two types of novel vegetation-height-structured habitat metrics are created based on second order texture algorithms and the concepts of patch-based habitat metrics. I correlate the height-structured metrics with the richness of different forest guilds, and also examine their efficacies in multivariate richness models. The results suggest that height heterogeneity, beyond canopy height alone, supplements habitat characterization and richness models of two forest bird guilds. The metrics and models derived in this study demonstrate practical examples of utilizing three-dimensional vegetation data for improved characterization of spatial patterns in species richness. The second and the third projects focus on analyzing centroids of avian distributions, and testing hypotheses regarding the direction and speed of these shifts. I first showcase the usefulness of centroids analysis for characterizing the distribution changes of a few case study species. Applying the centroid method on 57 permanent resident bird species, I show that multi-directional distribution shifts occurred in large number of studied species. I also demonstrate, plain birds are not shifting their distribution faster than mountain birds, contrary to the prediction based on climate change velocity hypothesis. By modelling the abundance change rate at regional level, I show that extreme climate events and precipitation measures associate closely with some of the long-term distribution shifts. This dissertation improves our understanding on bird habitat characterization for species richness modelling, and expands our knowledge on how avian populations shifted their ranges in North America responding to changing environments in the past four decades. The results provide an important scientific foundation for more accurate predictive species distribution modeling in future.

Integration of virus-like particle macromolecular bioreceptors in electrochemical biosensors

Rapid, sensitive and selective detection of chemical hazards and biological pathogens has shown growing importance in the fields of homeland security, public safety and personal health. In the past two decades, efforts have been focusing on performing point-of-care chemical and biological detections using miniaturized biosensors. These sensors convert target molecule binding events into measurable electrical signals for quantifying target molecule concentration. However, the low receptor density and the use of complex surface chemistry in receptors immobilization on transducers are common bottlenecks in the current biosensor development, adding to the cost, complexity and time. This dissertation presents the development of selective macromolecular Tobacco mosaic virus-like particle (TMV VLP) biosensing receptor, and the microsystem integration of VLPs in microfabricated electrochemical biosensors for rapid and performance-enhanced chemical and biological sensing. Two constructs of VLPs carrying different receptor peptides targeting at 2,4,6-trinitrotoluene (TNT) explosive or anti-FLAG antibody are successfully bioengineered. The VLP-based TNT electrochemical sensor utilizes unique diffusion modulation method enabled by biological binding between target TNT and receptor VLP. The method avoids the influence from any interfering species and environmental background signals, making it extremely suitable for directly quantifying the TNT level in a sample. It is also a rapid method that does not need any sensor surface functionalization process. For antibody sensing, the VLPs carrying both antibody binding peptides and cysteine residues are assembled onto the gold electrodes of an impedance microsensor. With two-phase immunoassays, the VLP-based impedance sensor is able to quantify antibody concentrations down to 9.1 ng/mL. A capillary microfluidics and impedance sensor integrated microsystem is developed to further accelerate the process of VLP assembly on sensors and improve the sensitivity. Open channel capillary micropumps and stop-valves facilitate localized and evaporation-assisted VLP assembly on sensor electrodes within 6 minutes. The VLP-functionalized impedance sensor is capable of label-free sensing of antibodies with the detection limit of 8.8 ng/mL within 5 minutes after sensor functionalization, demonstrating great potential of VLP-based sensors for rapid and on-demand chemical and biological sensing.