Control of fluid flows and other systems governed by partial differential-algebraic equations

The motion of fluids, such as air or water, is central to many engineering systems of significant economic and environmental importance. Examples range from air/fuel mixing in combustion engines to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator technologies have raised the intriguing prospect of actively sensing and manipulating the motion of the fluid within these systems, making them ripe for feedback control, provided a suitable control model exists. Unfortunately, the models for many of these systems are described by nonlinear, partial differential-algebraic equations for which few, if any, controller synthesis techniques exist. In stark contrast, the majority of established control theory assumes plant models of finite (and typically small) state dimension, expressed as a linear system of ordinary differential equations. Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory to the class of systems described by partial differential-algebraic equations, that are either linear, or for which a linear approximation is valid. The problems of control system design for infinite-dimensional and algebraically constrained systems are treated separately in this thesis. With respect to the former, a new method is presented that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between low-order models of successively finer spatial resolution. This bound informs the design, on loworder models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual plant. An example is presented on a one-dimensional heat equation. Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic, as well as differential equations. In the case of fluid flows, algebraic constraints typically arise from incompressibility and the application of boundary conditions. A numerical algorithm is presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential and algebraic parts of the system, enabling application of standard control theory without the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the transient growth region of a flat-plate boundary layer, using only wall shear measurements. These separate strands are woven together in the penultimate chapter, where a transient energy controller is designed for a channel-flow system, using wall mounted sensors and actuators

A metropolitan line : Robert LaPalme (1908-1997) : caricature and power in the age of Duplessis (1936-1959)

This dissertation proposes that the caricatures of Robert LaPalme, from his virtuoso celebrity portraits of the 1930s to the graphic political satires that focused on Quebec Premier Maurice Duplessis in the 1950s, provided a body of work that fulfilled the conditions of a "golden age of caricature," as it is characteristically defined in the historiography of caricature studies in European and North American traditions, for the history of visual arts in Quebec. These "national" models are seen as fundamentally metropolitan productions that represent themselves as national in scope by addressing and trading in the identity markings which provide the material for ideological conflicts within national traditions. Robert LaPalme's imagery was developed in concert with a generation of leaders who laid the groundwork for the Quiet Revolution, the secularisation and modernisation of Quebec society, through a dynamic and contesting relationship with the Duplessis administrations of 1936-40 and 1944-59. LaPalme's caricature harnessed urban anxieties and licence, both depending on and mocking them: it represented the breaches between competing images of Quebec that were rehearsed throughout the culture, from the rural/urban ideological split to the swiftly reconfigured ground of sexual behaviour and freedoms. Caricature in LaPalme's hands was the expression of the troubled, corrupt, powerful and exciting city of Montreal as a centre where the future for Quebec was imagined around the wily and traitorous figure of Maurice Duplessis. The thesis examines through a broadly chronological framework LaPalme's treatment of subjects, his visual style, through his approach to the body and space, and his close collaboration with many of the leading artists editors, journalists, publishers and writers of his er

Skeletal muscle differentiation drives a dramatic downregulation of RNA polymerase III activity and differential expression of Polr3g isoforms

Gene regulatory networks underpinning skeletal muscle determination and differentiation have been extensively investigated, providing molecular insights into how cell lineages are established during development. These studies have exclusively focused on the transcriptome downstream of RNA polymerase II (Pol II). RNA polymerase III (Pol III) drives the production of tRNAs and other small RNAs essential for the flow of genetic information from gene to protein and we have found that a specific isoform of a subunit unique to Pol III is expressed early in the myogenic lineage. This points to the possibility that additional regulatory networks exist to control the production of Pol III transcripts during skeletal muscle differentiation. We describe the differential expression of Polr3g and its alternate isoform Polr3gL during embryonic development and using a custom tRNA microarray, we demonstrate their distinct activity on the synthesis of tRNA isoacceptors. We show that Pol III dependent transcripts are dramatically down-regulated during the differentiation of skeletal muscle, as are mRNAs coding for Pol III associated proteins Brf1 and Brf2, while Polr3gL is up-regulated alongside contractile protein genes. Forcing Polr3g expression in this context results in a partial reversal of myogenic differentiatio