Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r) = r^s, $2<s <\infty$. Writing the coupling constant as $1/\epsilon^2$ we study the limit $\epsilon \to 0$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity \Omega tends to infinity as a power of $1/\epsilon$. The case of asymptotically homogeneous potentials is also discussed.Comment: LaTex2e, 16 page

Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps

We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as $1/\epsilon^2$ and we are interested in the limit $\epsilon\to 0$ (TF limit) with the angular velocity $\Omega$ depending on $\epsilon$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when $\Omega$ tends to infinity as a power of $1/\epsilon$. If $\Omega(\epsilon)=\Omega_0/\epsilon$ a ``hole'' (i.e., a region where the density becomes exponentially small as $1/\epsilon\to\infty$) develops for $\Omega_0$ above a certain critical value. If $\Omega(\epsilon)\gg 1/\epsilon$ the hole essentially exhausts the container and a ``giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyse the detailed vortex structure we prove that rotational symmetry is broken in the ground state for ${\rm const.}|\log\epsilon|<\Omega(\epsilon)\lesssim \mathrm{const.}/\epsilon$.Comment: LaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physic

Explaining Individual Differences in Executive Functions Performance in Multilinguals: The Impact of Code-Switching and Alternating Between Multicultural Identity Styles

This study sheds new light on the relative impact of switching between languages and switching between cultures on Executive Functions (EFs) in bilinguals. Several studies have suggested that bilingualism has a measurable impact on executive functioning, presumably due to bilinguals’ constant practice in dealing with two languages, or two cultures. Yet, the evidence on the relative contribution of culture and bilingualism to EFs is not well understood, because disentangling language, culture and immigration status is very difficult. The novelty of our approach was to keep the language pair and immigration status constant, whilst the cultural identity of participants was systematically varied, and measured at the individual level (not just at group level). Two groups of Turkish–English bilinguals, all adult immigrants to the United Kingdom, took part in the study, but one group (n = 29) originated from mainland Turkey and the other (n = 28) from Cyprus. We found that the bilinguals experienced smaller Conflict Effects on a Flanker task measuring inhibition, by comparison with monolingual British participants (n = 30). The key variable explaining EF performance variance at the individual level turned out to be bilinguals’ Multicultural Identity Style. In particular those who indicated that they attempted to alternate between different British and Turkish (Cypriot) identity styles were found to have shorter RTs on incongruent trials of the Flanker task. The two multicultural identity variables, Alternating and Hybrid Identity Styles, together explained 32% in RTs over and above Education, Working Memory and Nonverbal reasoning (overall explained variance 49%). Thus, the data provide strong evidence for the impact of culture on EFs. We suggest that, as a result of their daily practice in recognizing cultural cues which highlight the need to switch to a different cultural frame, multicultural bilinguals develop a heightened context-sensitivity, and this gives them an advantage over monolinguals in a Flankers task. Our approach, which draws on models from cross-cultural psychology, bilingualism and executive functioning, illustrates the importance of theory building in which sociolinguistic and cultural variables are integrated into models of EFs

L1 transfer in the acquisition of manner and path in Spanish by native speakers of English

In this article the authors argue that L1 transfer from English is not only important in the early stages of L2 acquisition of Spanish, but remains influential in later stages if there is not enough positive evidence for the learners to progress in their development (Lefebvre, White, & Jourdan, 2006). The findings are based on analyses of path and manner of movement in stories told by British students of Spanish (N = 68) of three different proficiency levels. Verbs that conflate motion and path, on the one hand, are mastered early, possibly because the existence of Latinate path verbs, such as enter and ascend in English, facilitate their early acquisition by British learners of Spanish. Contrary to the findings of Cadierno (2004) and Cadierno and Ruiz (2006), the encoding of manner, in particular in boundary crossing contexts, seems to pose enormous difficulties, even among students who had been abroad on a placement in a Spanish-speaking country prior to the data collection. An analysis of the frequency of manner verbs in Spanish corpora shows that one of the key reasons why students struggle with manner is that manner verbs are so infrequent in Spanish. The authors claim that scarce positive evidence in the language exposed to and little or no negative evidence are responsible for the long-lasting effect of transfer on the expression of manner

(In)Complete acquisition of Turkish among Turkish German bilinguals in Germany and Turkey: an analysis of complex embeddings in narratives

Although most researchers recognise that the language repertoire of bilinguals can mvary, few studies have tried to address variation in bilingual competence in any detail. This study aims to take a first step towards further understanding the way in which bilingual competencies can vary at the level of syntax by comparing the use of syntactic embeddings among three different groups of Turkish/German bilinguals. The approach of the present paper is new in that different groups of bilinguals are compared with each other, and not only with monolingual speakers, as is common in most studies in the field. The analysis focuses on differences in the use of embeddings in Turkish, which are generally considered to be one of the more complex aspects of Turkish grammar. The study shows that young Turkish/German bilingual adults who were born and raised in Germany use fewer, and less complex embeddings than Turkish/German bilingual returnees who had lived in Turkey for eight years at the time of recording. The present study provides new insights in the nature of bilingual competence, as well as a new perspective on syntactic change in immigrant Turkish as spoken in Europe

Assumptions behind grammatical approaches to code-switching: when the blueprint is a red herring

Many of the so-called ‘grammars’ of code-switching are based on various underlying assumptions, e.g. that informal speech can be adequately or appropriately described in terms of ‘‘grammar’’; that deep, rather than surface, structures are involved in code-switching; that one ‘language’ is the ‘base’ or ‘matrix’; and that constraints derived from existing data are universal and predictive. We question these assumptions on several grounds. First, ‘grammar’ is arguably distinct from the processes driving speech production. Second, the role of grammar is mediated by the variable, poly-idiolectal repertoires of bilingual speakers. Third, in many instances of CS the notion of a ‘base’ system is either irrelevant, or fails to explain the facts. Fourth, sociolinguistic factors frequently override ‘grammatical’ factors, as evidence from the same language pairs in different settings has shown. No principles proposed to date account for all the facts, and it seems unlikely that ‘grammar’, as conventionally conceived, can provide definitive answers. We conclude that rather than seeking universal, predictive grammatical rules, research on CS should focus on the variability of bilingual grammars