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.

The operation of multiquantum-well barriers

The multiquantum barrier (MQB), proposed by Iga et al in 1986, has been shown by several researchers to be an effective structure for improving the operating characteristics of laser diodes. These improvements include a reduction in the laser threshold current and increased characteristic temperatures. The operation of the MQB has been described as providing an increased barrier to electron overflow by reflecting high energy electrons trying to escape from the active region of the laser.This is achieved in a manner analogous to a Bragg reflector in optics. This thesis presents an investigation of the effectiveness of the MQB as an electron reflector. Numerical models have been developed for calculating the electron reflection due to MQB. Novel optical and electrical characterisation techniques have been used to try to measure an increase in barrier height due to the MQB in AlGaInP.It has been shown that the inclusion of MQB structures in bulk double heterostructure visible laser diodes can halve the threshold current above room temperature and the characteristic temperature of these lasers can be increased by up to 20K.These improvements are shown to occur in visible laser diodes even with the inclusion of theoretically ineffective MQB structures, hence the observed improvement in the characteristics of the laser diodes described above cannot be uniquely attributed to an increased barrier height due to enhance electron reflection. It is proposed here that the MQB improves the performance of laser diodes by proventing the diffusion of zinc into the active region of the laser. It is also proposed that the trapped zinc in the MQB region of the laser diode locally increases the p-type doping bringing the quasi-Fermi level for holes closer to the valence band edge thus increasing the barrier to electron overflow in the conduction band.

High speed optical communication systems: From modulation formats to radically new fibres

High volumes of data traffic along with bandwidth hungry applications, such as cloud computing and video on demand, is driving the core optical communication links closer and closer to their maximum capacity. The research community has clearly identifying the coming approach of the nonlinear Shannon limit for standard single mode fibre [1,2]. It is in this context that the work on modulation formats, contained in Chapter 3 of this thesis, was undertaken. The work investigates the proposed energy-efficient four-dimensional modulation formats. The work begins by studying a new visualisation technique for four dimensional modulation formats, akin to constellation diagrams. The work then carries out one of the first implementations of one such modulation format, polarisation-switched quadrature phase-shift keying (PS-QPSK). This thesis also studies two potential next-generation fibres, few-mode and hollow-core photonic band-gap fibre. Chapter 4 studies ways to experimentally quantify the nonlinearities in few-mode fibre and assess the potential benefits and limitations of such fibres. It carries out detailed experiments to measure the effects of stimulated Brillouin scattering, self-phase modulation and four-wave mixing and compares the results to numerical models, along with capacity limit calculations. Chapter 5 investigates hollow-core photonic band-gap fibre, where such fibres are predicted to have a low-loss minima at a wavelength of 2μm. To benefit from this potential low loss window requires the development of telecoms grade subsystems and components. The chapter will outline some of the development and characterisation of these components. The world's first wavelength division multiplexed (WDM) subsystem directly implemented at 2μm is presented along with WDM transmission over hollow-core photonic band-gap fibre at 2μm. References: [1]P. P. Mitra, J. B. Stark, Nature, 411, 1027-1030, 2001 [2] A. D. Ellis et al., JLT, 28, 423-433, 2010.

Nanoporous InP: anodic formation and growth mechanism in aqueous electrolytes

Porous layers can be formed electrochemically on (100) oriented n-InP substrates in aqueous KOH. A nanoporous layer is obtained underneath a dense near-surface layer and the pores appear to propagate from holes through the near-surface layer. In the early stages of the anodization transmission electron microscopy (TEM) clearly shows individual porous domains that appear to have a square-based pyramidal shape. Each domain appears to develop from an individual surface pit which forms a channel through this near-surface layer. We suggest that the pyramidal structure arises as a result of preferential pore propagation along the <100> directions. AFM measurements show that the density of surface pits increases with time. Each of these pits acts as a source for a pyramidal porous domain. When the domains grow, the current density increases correspondingly. Eventually the domains meet, forming a continuous porous layer, the interface between the porous and bulk InP becomes relatively flat and its total effective surface area decreases resulting in a decrease in the current density. Current-time curves at constant potential exhibit a peak and porous layers are observed to form beneath the electrode surface. The density of pits formed on the surface increases with time and approaches a plateau value. Porous layers are also observed in highly doped InP but are not observed in wafers with doping densities below ~5 × 1017 cm-3. Numerical models of this process have been developed invoking a mechanism of directional selectivity of pore growth preferentially along the <100> lattice directions. Manipulation of the parameters controlling these curves shows that the fall-off in current is controlled by the rate of diffusion of electrolyte through the pore structure with the final decline in current being caused by the termination of growth at the pore tips through the formation of passivating films or some other irreversible modification of the pore tips.

Modelling and control of a floating oscillating water column

A novel numerical model of a Bent Backwards Duct Buoy (BBDB) Oscillating Water Column (OWC) Wave Energy Converter was created based on existing isolated numerical models of the different energy conversion systems utilised by an OWC. The novel aspect of this numerical model is that it incorporates the interdependencies of the different power conversion systems rather than modelling each system individually. This was achieved by accounting for the dynamic aerodynamic damping caused by the changing turbine rotational velocity by recalculating the turbine damping for each simulation sample and applying it via a feedback loop. The accuracy of the model was validated using experimental data collected during the Components for Ocean Renewable Energy Systems (CORES) EU FP-7 project that was tested in Galway Bay, Ireland. During the verification process, it was discovered that the model could also be applied as a valuable tool when troubleshooting device performance. A new turbine was developed and added to a full scale model after being investigated using Computational Fluid Dynamics. The energy storage capacity of the impulse turbine was investigated by modelling the turbine with both high and low inertia and applying three turbine control theories to the turbine using the full scale model. A single Maximum Power Point Tracking algorithm was applied to the low-inertia turbine, while both a fixed and dynamic control algorithm was applied to the high-inertia turbine. These results suggest that the highinertia turbine could be used as a flywheel energy storage device that could help minimize output power variation despite the low operating speed of the impulse turbine. This research identified the importance of applying dynamic turbine damping to a BBDB OWC numerical model, revealed additional value of the model as a device troubleshooting tool, and found that an impulse turbine could be applied as an energy storage system.

Energy conversion: a comparison of fix- and self-referenced wave energy converters

The paper presents an investigation of fix-referenced and self-referenced wave energy converters and a comparison of their corresponding wave energy conversion capacities from real seas. For conducting the comparisons, two popular wave energy converters, point absorber and oscillating water column, and their power conversion capacities in the fixed-referenced and self-referenced forms have been numerically studied and compared. In the numerical models, the deviceâ s power extractions from seas are maximized using the correspondingly optimized power take-offs in different sea states, thus their power conversion capacities can be calculated and compared. From the comparisons and analyses, it is shown that the energy conversion capacities of the self-referenced devices can be significantly increased if the motions of the device itself can be utilized for wave energy conversion; and the self-referenced devices can be possibly designed to be compliant in long waves, which could be a very beneficial factor for device survivability in the extreme wave conditions (normally long waves). In this regards, the self-referenced WECs (wave energy converters) may be better options in terms of wave energy conversion from the targeted waves in seas (frequently the most occurred), and in terms of the device survivability, especially in the extreme waves when compared to the fix-referenced counterparts.