The Global Dynamics of Discrete Semilinear Parabolic Equations

A class of scalar semilinear parabolic equations possessing absorbing sets, a Lyapunov functional, and a global attractor are considered. The gradient structure of the problem implies that, provided all steady states are isolated, solutions approach a steady state as $t \to \infty$. The dynamical properties of various finite difference and finite element schemes for the equations are analysed. The existence of absorbing sets, bounded independently of the mesh size, is proved for the numerical methods. Discrete Lyapunov functions are constructed to show that, under appropriate conditions on the mesh parameters, numerical orbits approach steady state solutions as discrete time increases. However, it is shown that insufficient spatial resolution can introduce deceptively smooth spurious steady solutions and cause the stability properties of the true steady solutions to be incorrectly represented. Furthermore, it is also shown that the explicit Euler scheme introduces spurious solutions with period 2 in the timestep. As a result, the absorbing set is destroyed and there is initial data leading to blow up of the scheme, however small the mesh parameters are taken. To obtain stabilization to a steady state for this scheme, it is necessary to restrict the timestep in terms of the initial data and the space step. Implicit schemes are constructed for which absorbing sets and Lyapunov functions exist under restrictions on the timestep that are independent of initial data and of the space step; both one-step and multistep (BDF) methods are studied

Preliminary and Working Pile Load Tests in Simsima Limestone

A load testing program was undertaken to determine the working capacity of drilled shafts in Simsima Limestone, the predominant founding stratum in Doha, Qatar. The drilled shafts ranged from 500 mm to 1,500 mm in diameter and gained capacity from both side and base resistance within the Simsima Limestone. The weathering profile of the Simsima Limestone is complex with the degree of weathering likely to increase or decrease with depth. For the purposes of design, the limestone was characterized into three grades of weathering (A, B, and C) and the pile load testing program focused on testing each of these zones. The load testing program consisted of a series of instrumented Osterberg-cell tests, conventional jack and reaction-frame tests, highstrain dynamic tests, and tension tests to determine the pile-rock interactions within the various zones of Simsima Limestone. The load test results are presented and the findings summarized. Construction of the working piles raised concerns about the effect of softening with time for the exposed limestone during drilling. Extrapolation of the results of the load testing program and additional high-strain dynamic testing were used to address these issues. The results of the tests are presented and compared to the design assumptions with suggestions made to optimize future designs

Decentralized Model Predictive Control of a Multiple Evaporator HVAC System

Vapor compression cooling systems are the primary method used for refrigeration and air conditioning, and as such are a major component of household and commercial building energy consumption. Application of advanced control techniques to these systems is still a relatively unexplored area, and has the potential to significantly improve the energy efficiency of these systems, thereby decreasing their operating costs. This thesis explores a new method of decentralizing the capacity control of a multiple evaporator system in order to meet the separate temperature requirements of two cooling zones. The experimental system used for controller evaluation is a custom built small-scale water chiller with two evaporators; each evaporator services a separate body of water, referred to as a cooling zone. The two evaporators are connected to a single condenser and variable speed compressor, and feature variable water flow and electronic expansion valves. The control problem lies in development of a control architecture that will chill the water in the two tanks (referred to as cooling zones) to a desired temperature setpoint while minimizing the energy consumption of the system. A novel control architecture is developed that relies upon time scale separation of the various dynamics of the system; each evaporator is controlled independently with a model predictive control (MPC) based controller package, while the compressor reacts to system conditions to supply the total cooling required by the system as a whole. MPC’s inherent constraint-handling capability allows the local controllers to directly track an evaporator cooling setpoint while keeping superheat within a tight band, rather than the industrially standard approach of regulating superheat directly. The compressor responds to system conditions to track a pressure setpoint; in this configuration, pressure serves as the signal that informs the compressor of cooling demand changes. Finally, a global controller is developed that has knowledge of the energy consumption characteristics of the system. This global controller calculates the setpoints for the local controllers in pursuit of a global objective; namely, regulating the temperature of a cooling zone to a desired setpoint while minimizing energy usage

Distributed Control of HVAC&R Networks

Heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems are a major component of worldwide energy consumption, and frequently consist of complex networks of interconnected components. The ubiquitous nature of these systems suggests that improvements in their energy efficiency characteristics can have significant impact on global energy consumption. The complexity of the systems, however, means that decentralized control schemes will not always suffice to balance competing goals of energy efficiency and occupant comfort and safety. This dissertation proposes control solutions for three facets of this problem. The first is a cascaded control architecture for actuators, such as electronic expansion valves, that provides excellent disturbance rejection and setpoint tracking characteristics, as well as partial nonlinearity compensation without a compensation model. The second solution is a hierarchical control architecture for multiple-evaporator vapor compression systems that uses model predictive control (MPC) at both the supervisory and component levels. The controllers leverage the characteristics of MPC to balance energy efficiency with occupant comfort. Since the local controllers are decentralized, the architecture retains a degree of modularity—changing one component does not require changing all controllers. The final contribution is a new distributed optimization algorithm that is rooted in distributed MPC and is especially motivated by HVAC&R systems. This algorithm allows local level optimizers to iterate to a centralized solution. The optimizers have no knowledge of any plant other than the plant they are associated with, and only need to communicate with their immediate neighbors. The efficacy of the algorithm is displayed with two sets of examples. One example is simulation based, wherein a building is modeled in the EnergyPlus software suite. The other is an experimental example. In this example, the algorithm is applied to a multiple evaporator vapor compression system. In both cases the design method is discussed, and the ability of the algorithm to reduce energy consumption when properly applied is demonstrated

Hornblendite delineates zones of mass transfer through the lower crust

Geochemical signatures throughout the layered Earth require significant mass transfer through the lower crust, yet geological pathways are under-recognized. Elongate bodies of basic to ultrabasic rocks are ubiquitous in exposures of the lower crust. Ultrabasic hornblendite bodies hosted within granulite facies gabbroic gneiss of the Pembroke Valley, Fiordland, New Zealand, are typical occurrences usually reported as igneous cumulate hornblendite. Their igneous features contrast with the metamorphic character of their host gabbroic gneiss. Both rock types have a common parent; field relationships are consistent with modification of host gabbroic gneiss into hornblendite. This precludes any interpretation involving cumulate processes in forming the hornblendite; these bodies are imposter cumulates. Instead, replacement of the host gabbroic gneiss formed hornblendite as a result of channeled high melt flux through the lower crust. High melt/rock ratios and disequilibrium between the migrating magma (granodiorite) and its host gabbroic gneiss induced dissolution (grain-scale magmatic assimilation) of gneiss and crystallization of mainly hornblende from the migrating magma. The extent of this reaction-replacement mechanism indicates that such hornblendite bodies delineate significant melt conduits. Accordingly, many of the ubiquitous basic to ultrabasic elongate bodies of the lower crust likely map the ‘missing’ mass transfer zones

Colour alignment for relative colour constancy via non-standard references

Relative colour constancy is an essential requirement for many scientific imaging applications. However, most digital cameras differ in their image formations and native sensor output is usually inaccessible, e.g., in smartphone camera applications. This makes it hard to achieve consistent colour assessment across a range of devices, and that undermines the performance of computer vision algorithms. To resolve this issue, we propose a colour alignment model that considers the camera image formation as a black-box and formulates colour alignment as a three-step process: camera response calibration, response linearisation, and colour matching. The proposed model works with non-standard colour references, i.e., colour patches without knowing the true colour values, by utilising a novel balance-of-linear-distances feature. It is equivalent to determining the camera parameters through an unsupervised process. It also works with a minimum number of corresponding colour patches across the images to be colour aligned to deliver the applicable processing. Two challenging image datasets collected by multiple cameras under various illumination and exposure conditions were used to evaluate the model. Performance benchmarks demonstrated that our model achieved superior performance compared to other popular and state-of-the-art methods.Comment: 14 pages, 8 figures, 2 tables, accepted by IEEE Transactions on Image Processin