Primitive axial algebras of Jordan type

An axial algebra over the field $\mathbb F$ is a commutative algebra generated by idempotents whose adjoint action has multiplicity-free minimal polynomial. For semisimple associative algebras this leads to sums of copies of $\mathbb F$. Here we consider the first nonassociative case, where adjoint minimal polynomials divide $(x-1)x(x-\eta)$ for fixed $0\neq\eta\neq 1$. Jordan algebras arise when $\eta=\frac{1}{2}$, but our motivating examples are certain Griess algebras of vertex operator algebras and the related Majorana algebras. We study a class of algebras, including these, for which axial automorphisms like those defined by Miyamoto exist, and there classify the $2$-generated examples. For $\eta \neq \frac{1}{2}$ this implies that the Miyamoto involutions are $3$-transpositions, leading to a classification.Comment: 41 pages; comments welcom

Condensate splitting in an asymmetric double well for atom chip based sensors

We report on the adiabatic splitting of a BEC of $^{87}$Rb atoms by an asymmetric double-well potential located above the edge of a perpendicularly magnetized TbGdFeCo film atom chip. By controlling the barrier height and double-well asymmetry the sensitivity of the axial splitting process is investigated through observation of the fractional atom distribution between the left and right wells. This process constitutes a novel sensor for which we infer a single shot sensitivity to gravity fields of $\delta g/g\approx2\times10^{-4}$. From a simple analytic model we propose improvements to chip-based gravity detectors using this demonstrated methodology.Comment: 4 pages, 5 figure

Cluster-assisted accretion for massive stars

Gravitational interactions in very young high-density stellar clusters can to some degree change the angular momentum in the circumstellar discs surrounding initially the majority of stars. However, for most stars the cluster environment alters the angular momentum only slightly. For example, in simulations of the Orion Nebula cluster (ONC) encounters reduce the angular momentum of the discs on average at most by 3-5% and in the higher density region of the Trapezium %where encounters are more likely, the disc angular momentum is on average lowered by 15-20% - still a minor loss process. However, in this paper it is demonstrated that the situation is very different if one considers high-mass stars (M* > 10 M(solar) only. Assuming an age of 2 Myr for the ONC, their discs have on average a 50-90% lower angular momentum than primordially. This enormous loss in angular momentum in the disc should result in an equivalent increase in accretion, implying that the cluster environment boosts accretion for high-mass stars, thus %in the cluster center, making them even more massive.Comment: 10 pages including 2 figures, accepted for publication in ApJ

Designing a web-application to support home-based care of childhood CKD stages 3-5: Qualitative study of family and professional preferences

Background: There is a lack of online, evidence-based information and resources to support home-based care of childhood CKD stages 3-5. Methods. Qualitative interviews were undertaken with parents, patients and professionals to explore their views on content of the proposed online parent information and support (OPIS) web-application. Data were analysed using Framework Analysis, guided by the concept of Self-efficacy. Results: 32 parents, 26 patients and 12 professionals were interviewed. All groups wanted an application that explains, demonstrates, and enables parental clinical care-giving, with condition-specific, continously available, reliable, accessible material and a closed communication system to enable contact between families living with CKD. Professionals advocated a regularly updated application to empower parents to make informed health-care decisions. To address these requirements, key web-application components were defined as: (i) Clinical care-giving support (information on treatment regimens, video-learning tools, condition-specific cartoons/puzzles, and a question and answer area) and (ii) Psychosocial support for care-giving (social-networking, case studies, managing stress, and enhancing families' health-care experiences). Conclusions: Developing a web-application that meets parents' information and support needs will maximise its utility, thereby augmenting parents' self-efficacy for CKD caregiving, and optimising outcomes. Self-efficacy theory provides a schema for how parents' self-efficacy beliefs about management of their child's CKD could potentially be promoted by OPIS. © 2014 Swallow et al.; licensee BioMed Central Ltd

An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

Scalar and vector bosons in the background of one-dimensional nonminimal vector linear plus inversely linear potentials are explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. The problem is mapped into a Sturm-Liouville problem with an effective singular oscillator. With boundary conditions emerging from the problem, exact bound-state solutions in the spin-0 sector are found in closed form and it is shown that the spectrum exhibits degeneracy. It is shown that, depending on the potential parameters, there may or may not exist bound-state solutions in the spin-1 sector.Comment: 1 figure. arXiv admin note: substantial text overlap with arXiv:1009.159

Effect of Magnetization Inhomogeneity on Magnetic Microtraps for Atoms

We report on the origin of fragmentation of ultracold atoms observed on a permanent magnetic film atom chip. A novel technique is used to characterize small spatial variations of the magnetic field near the film surface using radio frequency spectroscopy of the trapped atoms. Direct observations indicate the fragmentation is due to a corrugation of the magnetic potential caused by long range inhomogeneity in the film magnetization. A model which takes into account two-dimensional variations of the film magnetization is consistent with the observations.Comment: 4 pages, 4 figure