Solitons in one-dimensional interacting Bose-Einstein system

A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.Comment: Latex, 14 pages, No figur

The economic and innovation contribution of universities: a regional perspective

Universities and other higher education institutions (HEIs) have come to be regarded as key sources of knowledge utilisable in the pursuit of economic growth. Although there have been numerous studies assessing the economic and innovation impact of HEIs, there has been little systematic analysis of differences in the relative contribution of HEIs across regions. This paper provides an exploration of some of these differences in the context of the UK’s regions. Significant differences are found in the wealth generated by universities according to regional location and type of institution. Universities in more competitive regions are generally more productive than those located in less competitive regions. Also, traditional universities are generally more productive than their newer counterparts, with university productivity positively related to knowledge commercialisation capabilities. Weaker regions tend to be more dependent on their universities for income and innovation, but often these universities under-perform in comparison to counterpart institutions in more competitive regions. It is argued that uncompetitive regions lack the additional knowledge infrastructure, besides universities, that are more commonly a feature of more competitive regions

How Chaotic is the Stadium Billiard? A Semiclassical Analysis

The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the marginally stable family of bouncing ball orbits. I show that this belief is erroneous. The Gutzwiller trace formula is not applicable for the phase space dynamics near the bouncing ball orbits. Unstable periodic orbits close to the marginally stable family in phase space cannot be treated as isolated stationary phase points when approximating the trace of the Green function. Semiclassical contributions to the trace show an $\hbar$ - dependent transition from hard chaos to integrable behavior for trajectories approaching the bouncing ball orbits. A whole region in phase space surrounding the marginal stable family acts, semiclassically, like a stable island with boundaries being explicitly $\hbar$-dependent. The localized bouncing ball states found in the billiard derive from this semiclassically stable island. The bouncing ball orbits themselves, however, do not contribute to individual eigenvalues in the spectrum. An EBK-like quantization of the regular bouncing ball eigenstates in the stadium can be derived. The stadium billiard is thus an ideal model for studying the influence of almost regular dynamics near marginally stable boundaries on quantum mechanics.Comment: 27 pages, 6 figures, submitted to J. Phys.

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Beyond compliance: teacher education practice in a performative framework

publication-status: Publishe

The ambivalent shadow of the pre-Wilsonian rise of international law

The generation of American international lawyers who founded the American Society of International Law in 1906 and nurtured the soil for what has been retrospectively called a “moralistic legalistic approach to international relations” remains little studied. A survey of the rise of international legal literature in the U.S. from the mid-19th century to the eve of the Great War serves as a backdrop to the examination of the boosting effect on international law of the Spanish American War in 1898. An examination of the Insular Cases before the US Supreme Court is then accompanied by the analysis of a number of influential factors behind the pre-war rise of international law in the U.S. The work concludes with an examination of the rise of natural law doctrines in international law during the interwar period and the critiques addressed.by the realist founders of the field of “international relations” to the “moralistic legalistic approach to international relation

To what extent does a regional dialect and accent impact on the development of reading and writing skills?

The issue of whether a regional accent and/or dialect impact(s) on the development of literacy skills remains current in the UK. For decades the issue has dogged debate about education outcomes, portable skills and employability. The article summarizes research on the topic using systematic review methodology. A scoping review was undertaken with the research question ‘To what extent does a regional dialect and accent impact on the development of reading and writing skills?’. The review covers research relevant to the teaching of 5-16 year olds in England, but also draws on research within Europe, the USA, Australia and the Caribbean. The results suggest that curricula have marginalized language variation; that the impact of regional accent and dialect on writing is relatively minor; that young people are adept at style-shifting between standard and non-standard forms; and that inappropriate pedagogical responses to regional variation can have detrimental effects on children’s educational achievement

Civilising the natives? Liberal studies in further education revisited

This paper uses Basil Bernstein’s work on pedagogic discourses to examine a largely neglected facet of the history of vocational education – the liberal studies movement in English further education (FE) colleges. Initially, the paper discusses some of the competing conceptions of education, work and society which underpinned the rise and fall of the liberal studies movement – if indeed it can be described as such. It then draws on data from interviews with former liberal and general studies (LS/GS) lecturers to focus on the ways in which different variants of liberal studies were, over time, implicated in inculcating certain forms of knowledge in vocational learners. Whilst it is acknowledged that LS/GS always represented contested territory and that it was highly variable both in terms of content and quality, the paper argues that, at least and under certain circumstances, liberal studies provided young working-class people with the opportunity to locate their experiences of vocational learning within a critical framework which is largely absent from FE today. This, it is argued, can be conceptualised as an engagement with what Bernstein described as ‘powerful knowledge’

Surveillance, performativity and normalised practice: the use and impact of graded lesson observations in Further Education colleges

In little over a decade, the observation of teaching and learning (OTL) has become the cornerstone of Further Education (FE) colleges’ quality systems for assuring and improving the professional skills and knowledge base of tutors. Yet OTL remains an under-researched area of inquiry with little known about the impact of its use on the professional identity, learning and development of FE tutors. This paper examines the specific practice of graded OTL and in so doing discusses findings from a mixed-methods study conducted in 10 colleges situated across the West Midlands region of England. Data from a questionnaire survey and semi-structured interviews were analysed within a theoretical framework that drew largely on aspects of Foucauldian theory as well as the twin phenomena of new managerialism and performativity. This analysis revealed how OTL has become normalised as a performative tool of managerialist systems designed to assure and improve standards, performance and accountability in teaching and learning. It is argued that FE has now outgrown graded OTL and it is time for a moratorium on its use. Colleges and tutors need to be given greater professional autonomy with regard to OTL and be allowed to develop their own systems that place professional learning and development at the forefront, rather than the requirements of performance management systems