This thesis considers a novel problem of obtaining global channel state information (CSI) at every node in an ad-hoc wireless network. A class of protocols for dissemination and estimation are developed which attempt to minimize the staleness of the estimates throughout the network. This thesis also provides an optimal protocol for CSI dissemination in networks with complete graph topology and a near optimal protocol in networks having incomplete graph topology. In networks with complete graph topology, the protocol for CSI dissemination is shown to have a resemblance to finding Eulerian tours in complete graphs. For networks having incomplete graph topology, a lower bound on maximum staleness is given and a near optimal algorithm based on finding minimum connected dominating sets and proper scheduling is described in this thesis.

The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the equation; these parameters represent the “strength” of the driving and damping terms. Moreover, numerical continuation allows us to show, for fixed parameters, the ground and some of the excited state solutions of this equation. Finally, for the values of the parameters that do not produce a stable radially symmetric solution, our dynamical computations show the emergence of rotating vortex lattices.

The Wiggins-Holmes extension of the generalized Melnikov method (GMM) is applied to weakly damped parametrically excited cross waves with surface tension in a long rectangular wave channel in order to determine if these cross waves are chaotic. The Lagrangian density function for surface waves with surface tension is simplified by transforming the volume integrals to surface integrals and by subtracting the zero variation integrals. The Lagrangian is written in terms of the three generalized coordinates (or, equivalently the three degrees of freedom) that are the time-dependent components of the velocity potential. A generalized dissipation function is assumed to be proportional to the Stokes material derivative of the free surface. The generalized momenta are calculated from the Lagrangian and the Hamiltonian is determined from a Legendre transformation of the Lagrangian. The first order ordinary differential equations derived from the Hamiltonian are usually suitable for the application of the GMM. However, the cross wave equations of motion must be transformed in order to obtain a suspended system for the application of the GMM. Only three canonical transformations that preserve the dynamics of the cross wave equations of motion are made because of an extension of the Herglotz algorithm to nonautonomous systems. This extension includes two distinct types of the generalized Herglotz algorithm (GHA). The system of nonlinear nonautonomous evolution equations determined from Hamilton's equations of motion of the second kind are averaged in order to obtain an autonomous system. The unperturbed system is analyzed to determine hyperbolic saddle points that are connected by heteroclinic orbits The perturbed Hamiltonian system that includes surface tension satisfies the KAM nondegeneracy requirements; and the Melnikov integral is calculated to demonstrate that the motion is chaotic. For the perturbed dissipative system with surface tension, the Melnikov integral is identically zero implying that a higher dimensional GMM is necessary in order to demonstrate by the GMM that the motion is chaotic. However, numerical calculations of the largest Liapunov characteristic exponent demonstrate that the perturbed dissipative system with surface tension is also chaotic. A chaos diagram is computed in order to search for possible regions of the damping parameter and the Floquet parametric forcing parameter where chaotic motions may exist. / Graduation date: 1999

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

This thesis encloses quantum chemical calculations performed in the framework of density functional response theory for evaluating electron paramagnetic resonance (EPR) spin Hamiltonian parameters of various spin-labels in different environments. These parameters are the well known electronic g-tensor and the nitrogen hyperfine coupling constants, which are extensively explored in this work for various systems. A special attention was devoted to the relationships that form between the structural and spectroscopic properties that can be accounted for as an environmental inuence. Such environmental effects were addressed either within a fully quantum mechanical formalism, involving simplified model structures that still capture the physical properties of the extended system, or by employing a quantum mechanics/molecular mechanics (QM/MM) approach. The latter implies that the nitroxide spin label is treated quantum mechanically, while the environment is treated in a classical discrete manner, with appropriate force fields employed for its description. The state-of- the art techniques employed in this work allow for an optimum accounting of the environmental effects that play an important role for the behaviour of EPR properties of nitroxides spin labels. One achievement presented in this thesis includes the first theoretical con_rmation of an empirical assumption that is usually made for inter-molecular distance measurement experiments in deoxyribonucleic acid (DNA), involving pulsed electron-electron double resonance (PELDOR) and site-directed spin labeling (SDSL) techniques. This refers to the fact that the EPR parameters of the spin-labels are not affected by their interaction with the nucleobases from which DNA is constituted. Another important result presented deals with the inuence of a supramolecular complex on the EPR properties of an encapsulated nitroxide spin-label. The enclusion complex affects the hydrogen bonding topology that forms around the R2NO moiety of the nitroxide. This, on the other hand has a major impact on its structure which further on governs the magnitude of the spectroscopic properties. The projects and results presented in this thesis offer an example of successful usage of modern quantum chemistry techniques for the investigation of EPR parameters of spin-labels in complex systems. / <p>QC 20130318</p>

The interaction of nanoparticles with biological systems, especially interactions with cell membranes, has been a subject of active research due to its numerous applications in many areas of soft-matter and biological systems. Within only a few relevant physical parameters profound structural properties have been discovered in the context of simple coarse-grained theoretical models. In this Thesis we study the structure of a tubular membrane adhering to two rigid cylindrical particles on a basis of a free-energy model that uses Helfrich energy for the description of the membrane. A numerical procedure is developed to solve the shape equations that determine the state of lowest energy. Several phase transitions exist in the system, arising from the competition between the bending energy of the membrane and the adhesion energy between the membrane and the particles. A continuous adhesion transition between the free and bound states, as well as several discontinuous shape transitions are identified, depending on the physical parameters of the system. The results are then generalized into a single phase diagram separating free, symmetric- and asymmetric-wrapping states in the phase space of the size of the particles and the adhesion energy. We show that for a relatively small size of the membrane tube the interaction between the cylinders becomes attractive in the strong curvature regime, leading to aggregation of the particles in the highly curved area of the tube that is characteristically different from the aggregation in a related three-dimensional system. For a relatively large membrane tube size the cylinders prefer to have a non-zero separation, even in the completely engulfed state. This indicates that, i) the spontaneous curvature of the membrane may play a role in the sign of the interaction of two colloidal particles adhered to a membrane and ii) cylindrical particles can aggregate on membrane tubes and vesicles if the curvature of the membrane around the aggregation region is sufficiently large.

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

Various civil and military applications of UAVs, or ground robots, require a set of vehicles to monitor a group of targets. Routing problems naturally arise in this setting where the operators of the vehicles have to plan the paths suitably in order to optimize the use of resources available such as sensors, fuel etc. These vehicles may differ either in their structural (design and dynamics) or functional (sensing) capabilities. This thesis addresses an important routing problem involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves dividing the routing problem into two sub-problems: Partitioning and Sequencing. Partitioning the targets involves finding two distinct sets of targets, each corresponding to one of the vehicles. We then find a sequence in which these targets need to be visited in order to optimize the use of resources to the maximum possible extent. The sequencing problem can be solved either by Christofides algorithm or the Lin-Kernighan Heuristic (LKH). The problem of partitioning is tackled by solving a Linear Program (LP) obtained by relaxing some of the constraints of an Integer Programming (IP) model for the problem. We observe the performance of two LP models for the partitioning. The first LP model is obtained by relaxing only the integrality constraints whereas in the second model relaxes both integrality and degree constraints. The algorithms were implemented in a C++ environment with the help of Concert Technology for CPLEX, and Boost Graph Libraries. The performance of these algorithms was studied for 50 random instances of varying problem sizes. It was found that on an average, the algorithms based on the first LP model provided better (closer to the optimum) solutions as compared to those based on the second LP model. We also observed that for both the LP models, the average quality of solutions given by the heuristics were found to be better ( within 5% of the optimum) than the average quality of solutions obtained from the approximation algorithm (between 30 - 60% of the optimum depending on the problem size).

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 71-78). Also available on the Internet.