Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

Graduate dress code: How undergraduates are planning to use hair, clothes and make-up to smooth their transition to the workplace

This article explores the relationship between students’ identities, their ideas about professional appearance and their anticipated transition to the world of work. It is based on a series of semi-structured interviews with 13 students from a vocationally-focused university in England. It was found that participants viewed clothing and appearance as an important aspect of their transition to the workplace. They believed that, if carefully handled, their appearance could help them to fit in and satisfy the expectations of employers, although some participants anticipated that this process of fitting in might compromise their identity and values. The article addresses students’ anticipated means of handling the tension between adapting to a new environment and ‘being themselves’. It is argued that the way this process is handled is intertwined with wider facets of identity – most notably those associated with gender.The article is based on research funded by the University of Derby. © 2015 IP Publishing Ltd. ((http://www.ippublishing.com). Reproduced by permission

High-pressure phase and transition phenomena in ammonia borane NH3BH3 from X-ray diffraction, Landau theory, and ab initio calculations

Structural evolution of a prospective hydrogen storage material, ammonia borane NH3BH3, has been studied at high pressures up to 12 GPa and at low temperatures by synchrotron powder diffraction. At 293 K and above 1.1 GPa a disordered I4mm structure reversibly transforms into a new ordered phase. Its Cmc21 structure was solved from the diffraction data, the positions of N and B atoms and the orientation of NH3 and BH3 groups were finally assigned with the help of density functional theory calculations. Group-theoretical analysis identifies a single two-component order parameter, combining ordering and atomic displacement mechanisms, which link an orientationally disordered parent phase I4mm with ordered distorted Cmc21, Pmn21 and P21 structures. We propose a generic phase diagram for NH3BH3, mapping three experimentally found and one predicted (P21) phases as a function of temperature and pressure, along with the evolution of the corresponding structural distortions. Ammonia borane belongs to the class of improper ferroelastics and we show that both temperature- and pressure-induced phase transitions can be driven to be of the second order. The role of N-H...H-B dihydrogen bonds and other intermolecular interactions in the stability of NH3BH3 polymorphs is examined.Comment: 23 pages, 7 figure

Enabling participation of Black and Minority Ethnic (BME) and seldom-heard communities in health research: A case study from the SCAMP adolescent cohort study

Our inquiry investigated the barriers to, and facilitators for, the involvement of Black and Minority Ethnic (BME) and ‘seldom-heard’ communities, in a study researching the impact of mobile phone and wireless device usage on adolescents’ cognition, behaviour and mental health. The aim was to co-produce solutions to increase participation, and we used focus groups, telephone interviews, a community event and a public and patient involvement (PPI) café to conduct the inquiry. Five themes emerged from the data: two enablers – the value and benefits of research; and three barriers – concerns about research and about communication, and practical constraints. A central cross-cutting theme, the concept of trust, was evident from the data, and extended across all themes, including across the solutions to nonparticipation. When the data collection and analysis were completed, we ran a symposium for researchers and members of the public to share our findings and to co-produce solutions. The symposium generated ideas about improving participation, including tailoring participant information, engaging with local advocates and involving people in research design and delivery

Finite strain Landau theory of high pressure phase transformations

The properties of materials near structural phase transitions are often successfully described in the framework of Landau theory. While the focus is usually on phase transitions, which are induced by temperature changes approaching a critical temperature T-c, here we will discuss structural phase transformations driven by high hydrostatic pressure, as they are of major importance for understanding processes in the interior of the earth. Since at very high pressures the deformations of a material are generally very large, one needs to apply a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) into account. In particular it is necessary to retune conventional Landau theory to describe such phase transitions. In Troster et al (2002 Phys. Rev. Lett. 88 55503) we constructed a Landau-type free energy based on an order parameter part, an order parameter-(finite) strain coupling and a nonlinear elastic term. This model provides an excellent and efficient framework for the systematic study of phase transformations for a wide range of materials up to ultrahigh pressures

Resourcing Green Technologies through Smart Mineral Enterprise Development: A Case Analysis of Cobalt

Achieving the goals of the Paris Agreement requires the world to adopt ‘green technologies’ such as renewable energies and electric transportation at an unprecedented scale. While many countries have implemented policies to spur the adoption of such technologies, a lack of focus has been placed on the sourcing of minerals that are required as inputs. As a result, there is likely to be a significant deficit that may constrain the adoption of green technologies. In this report, we argue that a neglected area in addressing the mineral scarcity challenge is the private sector’s current trajectory for geological mineral exploration and the lack of innovative initiatives on material efficiency and recycling. We propose a Smart Mineral Enterprise Development (SMED), which entails a partnership between public and private entities to consider pathways whereby public sector data sharing on geology can be coupled with research innovations in the private sector both upstream and downstream of mineral supply. Just as smart energy grids harness efficiencies in electricity supply and demand through a dynamic process of communication, SMED processes can do the same for key technological bottlenecks in mineral supply. We focus on cobalt to highlight the bottlenecks; identify alternative supply sources based on current exploration and recycling technologies; propose ways in which the international legal framework could be adapted to promote investments in critical minerals; and consider ways by which the public sector can assist the private sector in developing a SMED process that would bring forth more efficient and effective entrepreneurial activity to meet our green technology needs

Resourcing Green Technologies through Smart Mineral Enterprise Development: A Case Analysis of Cobalt

Achieving the goals of the Paris Agreement requires the world to adopt ‘green technologies’ such as renewable energies and electric transportation at an unprecedented scale. While many countries have implemented policies to spur the adoption of such technologies, a lack of focus has been placed on the sourcing of minerals that are required as inputs. As a result, there is likely to be a significant deficit that may constrain the adoption of green technologies. In this report, we argue that a neglected area in addressing the mineral scarcity challenge is the private sector’s current trajectory for geological mineral exploration and the lack of innovative initiatives on material efficiency and recycling. We propose a Smart Mineral Enterprise Development (SMED), which entails a partnership between public and private entities to consider pathways whereby public sector data sharing on geology can be coupled with research innovations in the private sector both upstream and downstream of mineral supply. Just as smart energy grids harness efficiencies in electricity supply and demand through a dynamic process of communication, SMED processes can do the same for key technological bottlenecks in mineral supply. We focus on cobalt to highlight the bottlenecks; identify alternative supply sources based on current exploration and recycling technologies; propose ways in which the international legal framework could be adapted to promote investments in critical minerals; and consider ways by which the public sector can assist the private sector in developing a SMED process that would bring forth more efficient and effective entrepreneurial activity to meet our green technology needs

Exact Five-Loop Renormalization Group Functions of ϕ4\phi^4-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to \ep^5

The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal subtraction. The critical exponents $\eta$, $\nu$, and $\omega$ are expanded up to order $\epsilon^5$ for the three nontrivial fixed points O(N)-symmetric, Ising, and cubic. The results suggest the stability of the cubic fixed point for $N\geq3$, implying that the critical exponents seen in the magnetic transition of three-dimensional cubic crystals are of the cubic universality class. This is in contrast to earlier three-loop results which gave $N > 3$, and thus Heisenberg exponents. The numerical differences, however, are less than a percent making an experimental distinction of the universality classes very difficult.Comment: PostScript fil

Observation of a continuous phase transition in a shape-memory alloy

Elastic neutron-scattering, inelastic x-ray scattering, specific-heat, and pressure-dependent electrical transport measurements have been made on single crystals of AuZn and Au_{0.52}Zn_{0.48} above and below their martensitic transition temperatures (T_M=64K and 45K, respectively). In each composition, elastic neutron scattering detects new commensurate Bragg peaks (modulation) appearing at Q = (1.33,0.67,0) at temperatures corresponding to each sample's T_M. Although the new Bragg peaks appear in a discontinuous manner in the Au_{0.52}Zn_{0.48} sample, they appear in a continuous manner in AuZn. Surprising us, the temperature dependence of the AuZn Bragg peak intensity and the specific-heat jump near the transition temperature are in favorable accord with a mean-field approximation. A Landau-theory-based fit to the pressure dependence of the transition temperature suggests the presence of a critical endpoint in the AuZn phase diagram located at T_M*=2.7K and p*=3.1GPa, with a quantum saturation temperature \theta_s=48.3 +/- 3.7K.Comment: 6 figure