Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Computational modeling of defects in nanoscale device materials

This PhD thesis concerns the computational modeling of the electronic and atomic structure of point defects in technologically relevant materials. Identifying the atomistic origin of defects observed in the electrical characteristics of electronic devices has been a long-term goal of first-principles methods. First principles simulations are performed in this thesis, consisting of density functional theory (DFT) supplemented with many body perturbation theory (MBPT) methods, of native defects in bulk and slab models of In0.53Ga0.47As. The latter consist of (100) - oriented surfaces passivated with A12O3. Our results indicate that the experimentally extracted midgap interface state density (Dit) peaks are not the result of defects directly at the semiconductor/oxide interface, but originate from defects in a more bulk-like chemical environment. This conclusion is reached by considering the energy of charge transition levels for defects at the interface as a function of distance from the oxide. Our work provides insight into the types of defects responsible for the observed departure from ideal electrical behaviour in III-V metal-oxidesemiconductor (MOS) capacitors. In addition, the formation energetics and electron scattering properties of point defects in carbon nanotubes (CNTs) are studied using DFT in conjunction with Green’s function based techniques. The latter are applied to evaluate the low-temperature, low-bias Landauer conductance spectrum from which mesoscopic transport properties such as the elastic mean free path and localization length of technologically relevant CNT sizes can be estimated from computationally tractable CNT models. Our calculations show that at CNT diameters pertinent to interconnect applications, the 555777 divacancy defect results in increased scattering and hence higher electrical resistance for electron transport near the Fermi level.

Properties of molecules in tunnel junctions

Molecular tunnel junctions involve studying the behaviour of a single molecule sandwiched between metal leads. When a molecule makes contact with electrodes, it becomes open to the environment which can heavily influence its properties, such as electronegativity and electron transport. While the most common computational approaches remain to be single particle approximations, in this thesis it is shown that a more explicit treatment of electron interactions can be required. By studying an open atomic chain junction, it is found that including electron correlations corrects the strong lead-molecule interaction seen by the ΔSCF approximation, and has an impact on junction I − V properties. The need for an accurate description of electronegativity is highlighted by studying a correlated model of hexatriene-di-thiol with a systematically varied correlation parameter and comparing the results to various electronic structure treatments. The results indicating an overestimation of the band gap and underestimation of charge transfer in the Hartree-Fock regime is equivalent to not treating electron-electron correlations. While in the opposite limit, over-compensating for electron-electron interaction leads to underestimated band gap and too high an electron current as seen in DFT/LDA treatment. It is emphasised in this thesis that correcting electronegativity is equivalent to maximising the overlap of the approximate density matrix to the exact reduced density matrix found at the exact many-body solution. In this work, the complex absorbing potential (CAP) formalism which allows for the inclusion metal electrodes into explicit wavefunction many-body formalisms is further developed. The CAP methodology is applied to study the electron state lifetimes and shifts as the junction is made open.

Simplified PRBMs of spatial compliant multi-beam modules for planar motion

PRBMs (pseudo-rigid-body models) have been becoming important engineering technologies/methods in the field of compliant mechanisms to simplify the design and analysis through the use of the knowledge body of rigid-body mechanisms coupling with springs. This article addresses the PRBMs of spatial multi-beam modules for planar motion, which are composed of three or more symmetrical wire/slender beams parallel to each other where the planar twisting DOF (degree of freedom) is assumed to be very small for specific applications/loading conditions. Simplified PRBMs are firstly proposed through replacing each beam in spatial multi-beam module with a rigid-body link plus two identical spherical joints at its two ends. The characteristics factor, bending stiffness and twisting stiffness for the spherical joint are determined. Load-displacement equations are then derived for a class of spatial multi-beam modules and general spatial multi-beam modules using the virtual work principle and kinematic relationships. Finally, nonlinear FEA (finite element analysis) is employed with comparisons with the PRBMs. The present PRBMs have shown the ability to predict the primary nonlinear constraint characteristics such as load-stiffening effect, cross-axis coupling in the two primary translational directions and buckling load.

Interaction strengths and net effects in food web models

Understanding how dynamic ecological communities respond to anthropogenic drivers of change such as habitat loss and fragmentation, climate change and the introduction of alien species requires that there is a theoretical framework able to predict community dynamics. At present there is a lack of empirical data that can be used to inform and test predictive models, which means that much of our knowledge regarding the response of ecological communities to perturbations is obtained from theoretical analyses and simulations. This thesis is composed of two strands of research: an empirical experiment conducted to inform the scaling of intraspecific and interspecific interaction strengths in a three species food chain and a series of theoretical analyses on the changes to equilibrium biomass abundances following press perturbations. The empirical experiment is a consequence of the difficulties faced when parameterising the intraspecific interaction strengths in a Lotka-Volterra model. A modification of the dynamic index is used alongside the original dynamic index to estimate intraspecific interactions and interspecific interaction strengths in a three species food. The theoretical analyses focused on the effect of press perturbations to focal species on the equilibrium biomass densities of all species in the community; these perturbations allow for the quantification of a species total net effect. It was found that there is a strong and consistent positive relationship between a species body size and its total net effect for a set of 97 synthetic food webs and also for the Ythan Estuary and Tuesday Lake food webs (empirically described food webs). It is shown that ecological constraints (due to allometric scaling) on the magnitude of entries in the community matrix cause the patterns observed in the inverse community matrix and thus explain the relationship between a species body mass and its total net effect in a community.

Investigations into the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy and maternal immune activation

The amygdala is a limbic structure that is involved in many of our emotions and processing of these emotions such as fear, anger and pleasure. Conditions such as anxiety, autism, and also epilepsy, have been linked to abnormal functioning of the amygdala, owing to improper neurodevelopment or damage. This thesis investigated the cellular and molecular changes in the amygdala in models of temporal lobe epilepsy (TLE) and maternal immune activation (MIA). The kainic acid (KA) model of temporal lobe epilepsy (TLE) was used to induce Ammon’s-horn sclerosis (AHS) and to investigate behavioural and cytoarchitectural changes that occur in the amygdala related to Neuropeptide Y1 receptor expression. Results showed that KA-injected animals showed increased anxiety-like behaviours and displayed histopathological hallmarks of AHS including CA1 ablation, granule cell dispersion, volume reduction and astrogliosis. Amygdalar volume and neuronal loss was observed in the ipsilateral nuclei which was accompanied by astrogliosis. In addition, a decrease in Y1 receptor expressing cells in the ipsilateral CA1 and CA3 sectors of the hippocampus, ipsi- and contralateral granule cell layer of the dentate gyrus and ipsilateral central nucleus of the amygdala was found, consistent with a reduction in Y1 receptor protein levels. The results suggest that plastic changes in hippocampal and/or amygdalar Y1 receptor expression may negatively impact anxiety levels. Gamma-aminobutyric acid (GABA) is the main inhibitory neurotransmitter in the brain and tight regulation and appropriate control of GABA is vital for neurochemical homeostasis. GABA transporter-1 (GAT-1) is abundantly expressed by neurones and astrocytes and plays a key role in GABA reuptake and regulation. Imbalance in GABA homeostasis has been implicated in epilepsy with GAT-1 being an attractive pharmacological target. Electron microscopy was used to examine the distribution, expression and morphology of GAT-1 expressing structures in the amygdala of the TLE model. Results suggest that GAT-1 was preferentially expressed on putative axon terminals over astrocytic processes in this TLE model. Myelin integrity was examined and results suggested that in the TLE model myelinated fibres were damaged in comparison to controls. Synaptic morphology was studied and results suggested that asymmetric (excitatory) synapses occurred more frequently than symmetric (inhibitory) synapses in the TLE model in comparison to controls. This study illustrated that the amygdala undergoes ultrastructural alterations in this TLE model. Maternal immune activation (MIA) is a risk factor for neurodevelopmental disorders such as autism, schizophrenia and also epilepsy. MIA was induced at a critical window of amygdalar development at E12 using bacterial mimetic lipopolysaccharide (LPS). Results showed that MIA activates cytokine, toll-like receptor and chemokine expression in the fetal brain that is prolonged in the postnatal amygdala. Inflammation elicited by MIA may prime the fetal brain for alterations seen in the glial environment and this in turn have deleterious effects on neuronal populations as seen in the amygdala at P14. These findings may suggest that MIA induced during amygdalar development may predispose offspring to amygdalar related disorders such as heightened anxiety, fear impairment and also neurodevelopmental disorders.