Bifurcation analysis in a frustrated nematic cell

Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the cell width grow, we study the behaviour of this unique solution. Restricting ourselves to a certain interval of temperature, we prove that this solution becomes unstable at a critical value of the cell width. Moreover, we show that this loss of stability comes with the appearance of two new solutions: there is a symmetric pitchfork bifurcation. This picture agrees with numerical simulations performed by P. Palffy-Muhorray, E.C. Gartland and J.R. Kelly. Some of the methods that we use in the present paper apply to other situations, and we present the proofs in a general setting. More precisely, the paper contains the proof of a general uniqueness result for a class of perturbed quasilinear elliptic systems, and general considerations about symmetric solutions and their stability, in the spirit of Palais' Principle of Symmetric Criticality

The Saturnian Kilometric Radiation before the Cassini Grand Finale

The Saturnian Kilometric Radiation (SKR) is radiated from the auroral regions surrounding the kronian magnetic poles, above the ionosphere up to a few planetary radii. It directly compares to the auroral radio emissions emanating from other planetary magnetospheres such as the Earth and the giant planets. Our knowledge on SKR relied on remote observations of Voyager (flybys in 1980 and 1981) and Ulysses (distant observations in the 1990s) until Cassini started to orbit Saturn in 2004. Since then, it has been routinely observed from a large set of remote locations, but also in situ for the first time at a planet other than Earth. This article reviews the state of the art of SKR average remote properties, the first insights brought by in situ passes within its source region, together with some remaining questions before the Cassini Grand Finale and its close-in polar orbits.Comment: Refereed article; Proceedings of the 8th International Workshop on Planetary, Solar and Heliospheric Radio Emissions (PRE VIII), Seggauberg, Austria, Oct. 25-27, 201

Uniaxial symmetry in nematic liquid crystals

Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied, except in very symmetric situations. For one- and two-dimensional configurations, we characterize completely the uniaxial equilibria: they must have constant director. In the three dimensional case we focus on the model problem of a spherical droplet with radial anchoring, and show that any uniaxial equilibrium must be spherically symmetric. It was known before that uniaxiality can sometimes be broken by energy minimizers. Our results shed a new light on this phenomenon: we prove here that in one or two dimensions uniaxial symmetry is always broken, unless the director is constant. Moreover, our results concern all equilibrium configurations, and not merely energy minimizers.Comment: contains a new presentation of results in arXiv:1307.0295, and new result

Is there language teaching after global English?

This study documents a case of language education decline, and the role that distance-teaching expertise, allied with Information and Communication Technology (ICT) experience, can play in alleviating the problem. In the United Kingdom a number of factors have led to a crisis in the teaching and learning of European Languages Other Than English (ELOTE). One of the main determiners is the dominance of English as a lingua franca for Continental Western European countries, and another the political reluctance of the part of British governments to engage fully with the European Union. In the country where English is the mother tongue, the position of ELOTE is particularly critical. After quantifying the decline in demand for these languages, I will look at different ways in which language-teaching professionals have attempted to fight back, and I will focus on the benefits that may be derived from a strategy that combines ICT capacity with distance-learning methodologies, using the UK Open University (UKOU) as an example. The lessons drawn by that institution in different discipline areas over two decades will be applied to languages

Interactive task design: Metachat and the whole learner

In this chapter the focus is on conversations about language between adult learners online, in synchronous and asynchronous postings. Socio-affective and social-semiotic perspectives are used, thus distancing the work somewhat from cognitive ways of looking at tasks. Because adults come to the task with diverse knowledge of both L2 and L1, the expectation is that metalinguistic interaction will enable them to swap expert and novice roles with each other within the constantly changing dynamics of the classroom. This if shown to be the case would advance an educational agenda favouring learner-directedness. Secondly, as metalinguistic conversations develop in directions that the learners feel like following, a greater degree of contingency can arise. This is considered in this paper as motivational for adults, and also as progressive, following van Lier (1996: 180) for whom in a contingent conversation "the agenda is shared by all participants and educational reality may be transformed". However, in seeking to satisfy his condition of contingency, the problem of designing tasks for greater spontaneity proves difficult. Therefore this study provide an ethnographic account of metalinguistic conversations by learners engaged in an online task, Simuligne, designed to address this difficulty. After studying data from the project forums, chat rooms and emails, we introduce a new perspective on the function of these conversations, which holds pointers for task design

Usages, contre-usages: nouvelles cultures des formations virtuelles

Based on a study of virtual language learning via real-time multimodal platforms, this article has a focus on usage in teleconferencing. In particular, the relationship between the structure of a particular platform (Lyceum) and the usage that is developed within it is examined. To do so, the author introduces the notion of affordance. Using four analytical dimensions derived from social semiotics, discourse, design, production and distribution of the artefact used for teleconferencing, the author presents examples of appropriation, some in line with the aims of the platform designers, others created by the users to counter what appear to be communicative failings of the platform