Function spaces for liquid crystals

We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters $s$, ${\bf n}$, and ${\bf Q}$, we establish connections between the variational formulations of these theories. We use these results to derive a version of the Oseen-Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director

Analysis of local minima for constrained minimization problems

We consider vectorial problems in the calculus of variations with an additional pointwise constraint. Our admissible mappings ${\bf n}:\mathbb{R}^k\rightarrow \mathbb{R}^d$ satisfy ${\bf n}(x)\in M$, where $M$ is a manifold embedded in Euclidean space. The main results of the paper all formulate necessary or sufficient conditions for a given mapping ${\bf n}$ to be a weak or strong local minimizer. Our methods involve using projection mappings in order to build on existing, unconstrained, local minimizer results. We apply our results to a liquid crystal variational problem to quantify the stability of the unwound cholesteric state under frustrated boundary conditions

A Topological Separation Condition for Fractal Attractors

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We prove that this separation condition is equivalent to the strong Markov property (see definition below). We also show that the set of $N$-tuples of contractive homeomorphisms, which are non-redundant on every level, is a $G_\delta$ set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings be strictly less than one. We give several sufficient conditions for this separation property. For every fixed $N$-tuple of $d\times d$ invertible contraction matrices from a certain class, we obtain density results for $N$-tuples of fixed points which define $N$-tuples of mappings non-redundant on every level.Comment: 19 page

A comparison of data-driven and model-based approaches to quantifying railway risk

This paper presents some of the results of a project sponsored by the UK Railway Safety and Standards Board (RSSB). An earlier statistical evaluation of a previous version of the RSSB Safety Risk Model (SRM), a combined Fault/Event Tree, conducted by Prof Andrew Evans had concluded that the model was unduly pessimistic. We have constructed a hypothesis test based on the relative likelihood techniques using the most recent version of the SRM as the null hypothesis. The results support the SRM being consistent with the historical data. Two significant differences between these two studies are the statistical methods employed to support the analysis and the removal of certain significant conservative assumptions from updating the versions of the SRM. The paper discusses the demands that different model purposes place on these models, and explores the question of whether or not it is meaningful to compare their outputs. The use of expected fatalities as a metric for expressing risk in both models is questioned because of the heavy-tailed form of the distribution for fatality numbers given a fatal accident

Archives, oral traditions and archaeology: Dissonant narratives concerning punitive expeditions on Malakula Island, Vanuatu

ABSTRACT OF THE BOOK: When James Boswell famously lamented the irrationality of war in 1777, he noted the universality of conflict across history and across space – even reaching what he described as the gentle and benign southern ocean nations. This volume discusses archaeological evidence of conflict from those southern oceans, from Palau and Guam, to Australia, Vanuatu and Tonga, the Marquesas, Easter Island and New Zealand. The evidence for conflict and warfare encompasses defensive earthworks on Palau, fortifications on Tonga, and intricate pa sites in New Zealand. It reports evidence of reciprocal sacrifice to appease deities in several island nations, and skirmishes and smaller scale conflicts, including in Easter Island. This volume traces aspects of colonial-era conflict in Australia and frontier battles in Vanuatu, and discusses depictions of World War II materiel in the rock art of Arnhem Land. Among the causes and motives discussed in these papers are pressure on resources, the ebb and flow of significant climate events, and the significant association of conflict with culture contact. The volume, necessarily selective, eclectic and wide-ranging, includes an incisive introduction that situates the evidence persuasively in the broader scholarship addressing the history of human warfare

Re-Visioning the Semantic and Semiotic Registers in the Study of Culture and Religion

The term `God\u27 may be understood as the desire for the complete epistemological condition of thought; language expresses this condition in statements of `meaning.\u27 `Religion\u27 expresses this desire in texts and ritual practice which may be examined by in academic study; however, because the `third term\u27 of religio is understood as the condition of being `bounded to or by,\u27 the study of religion is itself bounded to or by this desire for the completion of thought. This desire cannot be understood as an `alterity\u27 of thought but is rather the internal native or `alter-native\u27 condition of thought itself. Religions are the native residences of this desire, and claim to know the complete condition; however, alter-natively, because thought cannot completely restrict but rather remains itself an expression of the condition, human thought and its culture are open to an unrestricted examination of the expressions of the condition. Each religion expresses itself as a `singularity\u27 of this universal condition of thought; however, because of the native factors in the epistemological condition, specifically, that thought desires but cannot fully express or know the condition, no particular religion can claim hegemony to the expression of the condition: `God\u27 as such is the full expression of thought, yet by the definition of the terms of thought, its expression remains fully its alter-native exception of thought. The thesis first considers the possibility of theory itself through a brief examination of etymological gaps and windows evident in its expression. Next, we examine a possible working theory for the study of religion and the epistemological implications arising from its expression. Thirdly, as a result of these two courses, we examine the semantic and semiotic conditions of what can be `called\u27 `meaning.\u27 The thesis concludes with proposed epistemological strategies for the study of culture and religion, including what are termed the eccentric semantic and semiotic loops, the potentiation of meaning in the instantiation and disinstantiation of language figurations, singularity in meaning expressions, and the unique singularity of religious meaning in what may be termed the exceptional inception of thought

Global minimisers of cholesteric liquid crystal systems

In this paper we examine the modelling and minimisation of cholesteric liquid crystals systems within the Oseen-Frank theory. We focus on a cuboid domain with the frustrated boundary conditions ${\bf n}(0,x,y)=(1,0,0)$ and ${\bf n}(1,x,y)=(0,0,1)$. With general elastic constants, we find the unique global minimisers amongst functions of one variable and prove that these are global minimisers of the entire problem if the cholesteric pitch is sufficiently long. Finally we show that our analysis easily translates over the study the global stability of the constant state ${\bf n}(x,y,z) = (0,0,1)$ with unfrustrated boundary conditions.Comment: Version 2: Acknowledgements added and some small English errors correcte

Use of personal child health records in the UK: findings from the millennium cohort study.

OBJECTIVES: The personal child health record (PCHR) is a record of a child's growth, development, and uptake of preventive health services, designed to enhance communication between parents and health professionals. We examined its use throughout the United Kingdom with respect to recording children's weight and measures of social disadvantage and infant health. DESIGN: Cross sectional survey within a cohort study. SETTING: UK. PARTICIPANTS: Mothers of 18,503 children born between 2000 and 2002, living in the UK at 9 months of age. MAIN OUTCOME MEASURES: Proportion of mothers able to produce their child's PCHR; proportion of PCHRs consulted containing record of child's last weight; effective use of the PCHR (defined as production, consultation, and child's last weight recorded). RESULTS: In all, 16,917 (93%) mothers produced their child's PCHR and 15,138 (85%) mothers showed effective use of their child's PCHR. Last weight was recorded in 97% of PCHRs consulted. Effective use was less in children previously admitted to hospital, and, in association with factors reflecting social disadvantage, including residence in disadvantaged communities, young maternal age, large family size (four or more children; incidence rate ratio 0.87; 95% confidence interval 0.83 to 0.91), and lone parent status (0.88; 0.86 to 0.91). CONCLUSIONS: Use of the PCHR is lower by women living in disadvantaged circumstances, but overall the record is retained and used by a high proportion of all mothers throughout the UK in their child's first year of life. PCHR use is endorsed in the National Service Framework for Children and has potential benefits which extend beyond the direct care of individual children