Artificial opal photonic crystals and inverse opal structures - fundamentals and applications from optics to energy storage

Photonic crystals (PhCs) influence the propagation of light by their periodic variation in dielectric contrast or refractive index. This review outlines the attractive optical qualities inherent to most PhCs namely the presence of full or partial photonic band gaps and the possibilities they present towards the inhibition of spontaneous emission and the localization of light. Colloidal self-assembly of polymer or silica spheres is one of the most favoured and low cost methods for the formation of PhCs as artificial opals. The state of the art in growth methods currently used for colloidal self-assembly are discussed and the use of these structures for the formation of inverse opal architectures is then presented. Inverse opal structures with their porous and interconnected architecture span several technological arenas - optics and optoelectronics, energy storage, communications, sensor and biological applications. This review presents several of these applications and an accessible overview of the physics of photonic crystal optics that may be useful for opal and inverse opal researchers in general, with a particular emphasis on the recent use of these three-dimensional porous structures in electrochemical energy storage technology. Progress towards all-optical integrated circuits may lie with the concepts of the photonic crystal, but the unique optical and structural properties of these materials and the convergence of PhC and energy storage disciplines may facilitate further developments and non-destructive optical analysis capabilities for (electro)chemical processes that occur within a wide variety of materials in energy storage research.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Police accountability in Ireland: an analysis of the problems posed by the legal, constitutional and political dimensions and how they might be addressed

The concept of police accountability is not susceptible to a universal or concise definition. In the context of this thesis it is treated as embracing two fundamental components. First, it entails an arrangement whereby an individual, a minority and the whole community have the opportunity to participate meaningfully in the formulation of the principles and policies governing police operations. Second, it presupposes that those who have suffered as victims of unacceptable police behaviour should have an effective remedy. These ingredients, however, cannot operate in a vacuum. They must find an accommodation with the equally vital requirement that the burden of accountability should not be so demanding that the delivery of an effective police service is fatally impaired. While much of the current debate on police accountability in Britain and the USA revolves around the issue of where the balance should be struck in this accommodation, Ireland lacks the very foundation for such a debate as it suffers from a serious deficit in research and writing on police generally. This thesis aims to fill that gap by laying the foundations for an informed debate on police accountability and related aspects of police in Ireland. Broadly speaking the thesis contains three major interrelated components. The first is concerned with the concept of police in Ireland and the legal, constitutional and political context in which it operates. This reveals that although the Garda Siochana is established as a national force the legal prescriptions concerning its role and governance are very vague. Although a similar legislative format in Britain, and elsewhere, have been interpreted as conferring operational autonomy on the police it has not stopped successive Irish governments from exercising close control over the police. The second component analyses the structure and operation of the traditional police accountability mechanisms in Ireland; namely the law and the democratic process. It concludes that some basic aspects of the peculiar legal, constitutional and political structures of policing seriously undermine their capacity to deliver effective police accountability. In the case of the law, for example, the status of, and the broad discretion vested in, each individual member of the force ensure that the traditional legal actions cannot always provide redress where individuals or collective groups feel victimised. In the case of the democratic process the integration of the police into the excessively centralised system of executive government, coupled with the refusal of the Minister for Justice to accept responsibility for operational matters, project a barrier between the police and their accountability to the public. The third component details proposals on how the current structures of police accountability in Ireland can be strengthened without interfering with the fundamentals of the law, the democratic process or the legal and constitutional status of the police. The key elements in these proposals are the establishment of an independent administrative procedure for handling citizen complaints against the police and the establishment of a network of local police-community liaison councils throughout the country coupled with a centralised parliamentary committee on the police. While these proposals are analysed from the perspective of maximising the degree of police accountability to the public they also take into account the need to ensure that the police capacity to deliver an effective police service is not unduly impaired as a result.

Formation and characterisation of ordered porous vanadium oxide inverse opal materials for Li-ion batteries

This thesis presents several routes towards achieving artificial opal templates by colloidal self-assembly of polystyrene (PS) or poly(methyl methacrylate) (PMMA) spheres and the use of these template for the fabrication of V2O5 inverse opals as cathode materials for lithium ion battery applications. First, through the manipulation of different experimental factors, several methods of affecting or directing opal growth towards realizing different structures, improving order and/or achieving faster formation on a variety of substrates are presented. The addition of the surfactant sodium dodecyl sulphate (SDS) at a concentration above the critical micelle concentration for SDS to a 5 wt% solution of PMMA spheres before dip-coating is presented as a method of achieving ordered 2D PhC monolayers on hydrophobic Au-coated silicon substrates at fast and slow rates of withdrawal. The effect that the degree of hydrophilicity of glass substrates has on the ordering of PMMA spheres is next investigated for a slow rate of withdrawal under noise agitation. Heating of the colloidal solution is also presented as a means of affecting order and thickness of opal deposits formed using fast rate dip coating. E-beam patterned substrates are shown as a means of altering the thermodynamically favoured FCC ordering of polystyrene spheres (PS) when dip coated at slow rate. Facile routes toward the synthesis of ordered V2O5 inverse opals are presented with direct infiltration of polymer sphere templates using liquid precursor. The use of different opal templates, both 2D and 3D partially ordered templates, is compared and the composition and arrangement of the subsequent IO structures post infiltration and calcination for various procedures is characterised. V2O5 IOs are also synthesised by electrodeposition from an aqueous VOSO4 solution at constant voltage. Electrochemical characterisation of these structures as cathode material for Li-ion batteries is assessed in a half cell arrangement for samples deposited on stainless steel foil substrates. Improved rate capabilities are demonstrated for these materials over bulk V2O5, with the improvement attributed to the shorter Li ion diffusion distances and increased electrolyte infiltration provided by the IO structure.

Problems with drawing lines: Theo-geographies of the Catholic parish in Ireland

While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.

The inverse limit of GIT quotients of Grassmannians by the maximal torus

There are finitely many GIT quotients of

3D vanadium oxide inverse opal growth by electrodeposition

Three-dimensional vanadium pentoxide (V2O5) material architectures in the form of inverse opals (IOs) were fabricated using a simple electrodeposition process into artificial opal templates on stainless steel foil using an aqueous solution of VOSO4.χH2O with added ethanol. The direct deposition of V2O5 IOs was compared with V2O5 planar electrodeposition and confirms a similar progressive nucleation and growth mechanism. An in-depth examination of the chemical and morphological nature of the IO material was performed using X-ray crystallography, X-ray photoelectron spectroscopy, Raman scattering and scanning/transmission electron microscopy. Electrodeposition is demonstrated to be a function of the interstitial void fraction of the artificial opal and ionic diffusivity that leads to high quality, phase pure V2O5 inverse opals is not adversely affected by diffusion pathway tortuosity. Methods to alleviate electrodeposited overlayer formation on the artificial opal templates for the fabrication of the porous 3D structures are also demonstrated. Such a 3D material is ideally suited as a cathode for lithium ion batteries, electrochromic devices, sensors and for applications requiring high surface area electrochemically active metal oxides.