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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.

In this thesis, bifurcation phenomena in dynamical systems with cosymmetry and Hamiltonian structure were investigated using numerical methods. Several numerical continuation methods and test functions for detecting bifurcations were presented. The numerical results for various examples are given using a numerical bifurcation analysis toolbox.

"The topology of a network (such as a telecommunications, multiprocessor, or local area network, to name just a few) is usually modelled by a graph in which vertices represent 'nodes' (stations or processors) while undirected or directed edges stand for 'links' or other types of connections, physical or virtual. A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely k-walks and r-trestles." --Abstract. / Doctor of Philosophy

"The topology of a network (such as a telecommunications, multiprocessor, or local area network, to name just a few) is usually modelled by a graph in which vertices represent 'nodes' (stations or processors) while undirected or directed edges stand for 'links' or other types of connections, physical or virtual. A cycle that contains every vertex of a graph is called a hamiltonian cycle and a graph which contains a hamiltonian cycle is called a hamiltonian graph. The problem of the existence of a hamiltonian cycle is closely related to the well known problem of a travelling salesman. These problems are NP-complete and NP-hard, respectively. While some necessary and sufficient conditions are known, to date, no practical characterization of hamiltonian graphs has been found. There are several ways to generalize the notion of a hamiltonian cycle. In this thesis we make original contributions in two of them, namely k-walks and r-trestles." --Abstract. / Doctor of Philosophy

This thesis investigates several different aspects of the physics of few state quantum systems and their use in information processing applications. The main focus is performing high precision computations or experiments using imperfect quantum systems. Specifically looking at methods to calibrate a quantum system once it has been manufactured or performing useful tasks, using a quantum system with only limited spatial or temporal coherence. / A novel method for characterising an unknown two-state Hamiltonian is presented which is based on the measurement of coherent oscillations. The method is subsequently extended to include the effects of decoherence and enable the estimation of uncertainties. Using the uncertainty estimates, the achievable precision for a given number of measurements is computed. This method is tested experimentally using the nitrogen-vacancy defect in diamond as an example of a two-state quantum system of interest for quantum information processing. The method of characterisation is extended to higher dimensional systems and this is illustrated using the Heisenberg interaction between spins as an example. / The use of buried donors in silicon is investigated as an architecture for realising quantum-dot cellular automata as an example of quantum systems used for classical information processing. The interaction strengths and time scales are calculated and both coherent and incoherent evolution are assessed as possible switching mechanisms. The effects of decoherence on the operation of a single cell and the scaling behaviour of a line of cells is investigated. / The use of type-II quantum computers for simulating classical systems is studied as an application of small scale quantum computing. An algorithm is developed for simulating the classical Ising model using Metropolis Monte-Carlo where random number generation is incorporated using quantum superposition. This suggests that several new algorithms could be developed for a type-II quantum computer based on probabilistic cellular automata.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 1854. Adviser: D. A. Goodings.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Carleton University, 2003. / Includes bibliographical references (p. 262-286). Also available in electronic format on the Internet.

Honors Project--Smith College, Northampton, Mass., 2009. / Includes bibliographical references (p. 44).