Peridynamics is an emerging nonlocal continuum theory which allows governing field equations to be applicable at discontinuities. This applicability at discontinuities is achieved by replacing the spatial derivatives, which lose meaning at discontinuities, with integrals that are valid regardless of the existence of a discontinuity. Within the realm of solid mechanics, the peridynamic theory is one of the techniques that has been employed to model material fracture. In this work, the peridynamic theory is used to investigate different fracture problems in order to establish its fidelity for predicting crack growth. Various fracture experiments are modeled and analyzed. The peridynamic predictions are made and compared against experimental findings along with predictions from other commonly used numerical fracture techniques. Additionally, this work applies the peridynamic framework to model heat transfer. Generalized peridynamic heat transfer equation is formulated using the Lagrangian formalism. Peridynamic heat conduction quantites are related to quanties from the classical theory. A numerical procedure based on an explicit time stepping scheme is adopted to solve the peridynamic heat transfer equation and various benchmark problems are considered for verification of the model. This paves the way for the coupling of thermal and structural fields within the framework of peridynamics. The fully coupled peridynamic thermomechanical equations are derived based on thermodynamic considerations, and a nondimensional form of the coupled thermomechanical peridynamic equations is also presented. An explicit staggered algorithm is implemented in order to numerically approximate the solution to these coupled equations. The coupled thermal and structural responses of a thermoelastic semi-infinite bar and a thermoelastic vibrating bar are subsequently investigated.

Geophysical imaging methods significantly enhance our knowledge of subsurface characteristics and their use has become prevalent over a range of subsurface investigations. These methods facilitate the detection and characterization of both metallic and nonmetallic subsurface targets, and can provide spatially extensive information on subsurface structure and characteristics that is often impractical to obtain using standard drilling and sampling procedures alone. Electrical imaging methods such as electrical resistivity tomography (ERT) have proven to be particularly useful in hydrogeologic and geotechnical investigations because of the strong dependence of the electrical properties of soils to water saturation, soil texture, and solute concentration. Given the available geophysical tools as well as their applications, the selection of the appropriate geophysical survey design is an essential part of every subsurface geophysical investigation. Where investigations are located in an area with subsurface information already available, this information may be used as a guide for the design of a geophysical survey. In some instances, no subsurface information is available and a survey must be designed to cover a range of possible circumstances. Yet, in other instances, there may be significant subsurface information available, but because of subsurface complexities, a geophysical survey must still be designed to cover a broad range of possibilities. Demonstrating the application and limitations of ERT in a specific field application, the first investigation presented in this document provides guidance for developing methods to improve the design and implementation of ERT surveys in a complex subsurface environment. The two investigations that follow present the development of a relatively simple optimization approach based on limited forward modeling of the geophysical response for both static and mobile surveys. This process is demonstrated through examples of selecting a limited number of ERT surveys to identify and discriminate subsurface target tunnels (with a simple cylindrical geometry). These examples provide insights into the practical application of the optimization process for improved ERT survey design for subsurface target detection. Because of their relative simplicity, the optimization procedures developed here may be used to rapidly identify optimal array configurations without the need for computationally expensive inversion techniques.

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Electronic Structure Theory has led to a variety of developments and applications. In the Nooijen group the focus is on the development and use of Coupled Cluster based approaches. Coupled Cluster is a very strong and accurate approach to the quantum mechanical problem. The research results presented in the thesis testify to the Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) for being a very accurate and yet computationally inexpensive approach for excited states. This study reveals new features about STEOM and provides promise regarding future improvement in the methodology. STEOM can be used as the first step in the construction of the Vibronic model, which is a strong tool to move to paradigms beyond the Born-Oppenheimer approximation. Spin-Orbit Coupling (SOC) is a very important ingredient required to study relativistic phenomena and its quantum mechanical implementation for many body systems is not straightforward. The most widely used SOC operator in Chemical Physics is the Breit-Pauli operator, which requires employing non-trivial approximations to the Dirac equation to adapt the theory to many body systems. The integration of electronic structure approaches, Vibronic Coupling, and SOC is essential to study the phenomenon of intersystem crossing (transition between spin states) in fine detail. In this thesis a computational benchmark of STEOM is discussed, while the frameworks of Vibronic Coupling and Spin-Orbit Coupling (SOC) are considered on a theoretical level.

G protein-coupled receptors (GPCRs) form a link between the cell and their environment when signaling pathways are activated upon ligand binding. However, the ligands and functions for many GPCRs remain to be determined. G protein-coupled receptor 50 (GPR50) is one such orphan, and its exact role is yet unknown. There is however emerging functional and genetic evidence suggesting a function for GPR50 in psychiatric illness and lipid metabolism. It was hypothesised that investigating GPR50’s protein-protein interactions would lead to a greater understanding of the role of GPR50 in normal brain functioning and in mental illness. Putative protein interactors were initially isolated by a yeast two-hybid study and were further tested here. To address GPR50’s links to mental illness, the GPR50∆502-505 deletion variant associated with mood disorders was also investigated. To test this hypothesis I sought to confirm some of the key yeast two-hybrid interactions. Using co-immunoprecipitation and immunocytochemistry the interaction of GPR50 with reticulon family members Nogo-A, Nogo-C and RTN3, and with cell-cell adhesion molecule CDH8 and lipid-associated protein ABCA2 were validated. In order to identify the location of interactions, subcellular fractionation of mouse brain and rt-PCR and immunohistochemistry in developing and adult mouse brain were performed. GPR50 and several interactors were found to be enriched at the synapse by subcellular fractionation of whole adult brain, and at embryonic day 18 (E18) and 5 weeks by rt-PCR. Colocalisation of GPR50 and interactors was found in the amygdala, hypothalamus, cortex and specific brain stem nuclei by immunohistochemistry. The discovery of GPR50 expression in noradrenergic, serotonergic and dopaminergic nuclei in the adult brain stem suggests a further role for GPR50 in neurotransmitter signaling and stress. To investigate the function of GPR50 two assays were performed that measure processes which are known to be affected by Nogo and RTN3: The first assay was a neurite outgrowth assay in Neuroscreen-1 cells, a PC12 cell clone. A significant increase in neurite length was detected after transient overexpression of GPR50 and this effect was increased in the GPR50∆502-505/T532A variant. Additionally GPR50-overexpression resulted in an increase in filopodia formation suggesting a role in actin dynamics. As a second functional assay in vitro BACE1 activity assays were performed in HEK293 cells. GPR50 but not GPR50∆502-505/T532A overexpression resulted in a significant increase in BACE1 activity. Lastly a final series of pilot experiments were performed to gain insight into the secondary structure of the C-terminal domain and the effects of the polymorphisms on structure. The 35kDa GPR50 C-terminal domain was purified and Circular Dichroism studies indicated a predominantly unstructured protein with increased a- helical content in the GPR50∆502-505 variant. The results in this thesis indicate a role for GPR50 in neuronal development and synaptic functioning. The results also strengthen an association with major mental illness, with links to several disease mechanisms.

Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. Such a heteroclinic network is generated, where the phases cluster into three groups, within a specific regime of parameters when the phase oscillators are globally coupled using the function $g(\varphi) = -\sin(\varphi + \alpha) + r \sin(2\varphi + \beta)$. The resulting network switches between 30 partially synchronised states for a system of $N=5$ oscillators. Considering the states that are visited and the time spent at those states a spatio-temporal code can be generated for a given navigation around the network. We explore this phenomenon further by investigating the effect that noise has on the system, how this system can be used to generate a spatio-temporal code derived from specific inputs and how observation of a spatio-temporal code can be used to determine the inputs that were presented to the system to generate a given coding. We show that it is possible to find chaotic attractors for certain parameters and that it is possible to detail a genetic algorithm that can find the parameters required to generate a specific spatio-temporal code, even in the presence of noise. In closing we briefly explore the dynamics where $N>5$ and discuss this work in relation to winnerless competition.

Photosystem II is a unique enzyme which catalyzes light induced water oxidation. This process is driven by highly oxidizing ensemble of four Chl molecules, PD1, PD2, ChlD1 and ChlD2 called, P680. Excitation of one of the Chls in P680 leads to the primary charge separation, P680+Pheo-. Pheo- transfers electrons sequentially to the primary quinone acceptor QA and the secondary quinone acceptor QB. P680+ in turn extracts electrons from Mn4CaO5 cluster, a site for the water oxidation. There are two redox active tyrosines, TyrZ and TyrD, found in PSII. They are symmetrically located on the D1 and D2 central proteins. Only TyrZ acts as intermediate electron carrier between P680 and Mn4CaO5 cluster, while TyrD does not participate in the linear electron flow and stays oxidized under light conditions. Both tyrosines are involved in PCET. The reduced TyrD undergoes biphasic oxidation with the fast (msec-sec time range) and the slow (tens of seconds time range) kinetic phases. We assign these phases to two populations of PSII centers with proximal or distal water positions. We also suggest that the TyrD oxidation and stability is regulated by the new small lumenal protein subunit, PsbTn. The possible involvement of PsbTn protein in the proton translocation mechanism from TyrD is suggested. To assess the possible localization of primary cation in P680 the formation of the triplet state of P680 and the oxidation of TyrZ and TyrD were followed under visible and far-red light. We proposed that far-red light induces the cation formation on ChlD1. Transmembrane interaction between QB and TyrZ has been studied. The different oxidation yield of TyrZ, measured as a S1 split EPR signal was correlated to the conformational change of protein induced by the QB presence at the QB-site. The change is transferred via H-bonds to the corresponding His-residues via helix D of the D1 protein.

Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.

A pair of nonidentical two-level atoms, separated by a fixed distance R, interact through photon exchange. The system is described by a state vector which is assumed to be a superposition of four "essential states": (1) the first atom is excited, the second one is in the ground state, and no photon is present, (2) the first atom is in its ground state, the second one is excited, and no photon is present, (3) both atoms are in their ground states and a photon is present, and (4) both atoms are excited and a photon is also present. The system is initially in state (1). The probabilities of each atom being excited are calculated for both the minimally-coupled interaction and the multipolar interaction in the electric dipole approximation. For the minimally-coupled interaction Hamiltonian, the second atom has a probability of being instantaneously excited, so the interaction is not retarded. For the multipolar interaction Hamiltonian, the second atom is not excited before the retardation time, which agrees with special relativity. For the minimally-coupled interaction the nonphysical result occurs because the unperturbed Hamiltonian is not the energy operator in the Coulomb gauge. For the multipolar Hamiltonian in the electric dipole approximation the unperturbed Hamiltonian is the energy operator. An active view of unitary transformations in nonrelativistic quantum electrodynamics is used to derive transformation laws for the potentials of the electromagnetic field and the static Coulomb potential. For a specific choice of unitary transformation the transformation laws for the potentials are used in the minimally-coupled second-quantized Hamiltonian to obtain the multipolar Hamiltonian, which is expressed in terms of the quantized electric and magnetic fields.

Multi band technology helps in getting multiple operating frequencies using a single microwave device. This thesis presents the design of dual and tri band microwave devices using coupled transmission line structures. Chapter 2 presents the design of a novel dual band transmission line structure using coupled lines. In chapter 3, Design of a dual band branch line coupler and a dual band Wilkinson power divider are proposed using the novel dual band transmission line structure presented in the previous chapter. In chapter 4, Design of a tri band transmission line structure by extending the dual band structure is presented. The Conclusion and future work are presented in chapter 5.