Which canonical algebras are derived equivalent to incidence algebras of posets?

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr

The structure of fluid trifluoromethane and methylfluoride

We present hard X-ray and neutron diffraction measurements on the polar fluorocarbons HCF3 and H3CF under supercritical conditions and for a range of molecular densities spanning about a factor of ten. The Levesque-Weiss-Reatto inversion scheme has been used to deduce the site-site potentials underlying the measured partial pair distribution functions. The orientational correlations between adjacent fluorocarbon molecules -- which are characterized by quite large dipole moments but no tendency to form hydrogen bonds -- are small compared to a highly polar system like fluid hydrogen chloride. In fact, the orientational correlations in HCF3 and H3CF are found to be nearly as small as those of fluid CF4, a fluorocarbon with no dipole moment.Comment: 11 pages, 9 figure

An electrostatically defined serial triple quantum dot charged with few electrons

A serial triple quantum dot (TQD) electrostatically defined in a GaAs/AlGaAs heterostructure is characterized by using a nearby quantum point contact as charge detector. Ground state stability diagrams demonstrate control in the regime of few electrons charging the TQD. An electrostatic model is developed to determine the ground state charge configurations of the TQD. Numerical calculations are compared with experimental results. In addition, the tunneling conductance through all three quantum dots in series is studied. Quantum cellular automata processes are identified, which are where charge reconfiguration between two dots occurs in response to the addition of an electron in the third dot.Comment: 12 pages, 9 figure

Non-liftable Calabi-Yau spaces

We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and D. van Straten.Comment: 16 pages, 5 tables; v2: minor corrections and addition

Lab::Measurement - A portable and extensible framework for controlling lab equipment and conducting measurements

Lab::Measurement is a framework for test and measurement automatization using Perl 5. While primarily developed with applications in mesoscopic physics in mind, it is widely adaptable. Internally, a layer model is implemented. Communication protocols such as IEEE 488, USB Test & Measurement, or, e.g., VXI-11 are addressed by the connection layer. The wide range of supported connection backends enables unique cross-platform portability. At the instrument layer, objects correspond to equipment connected to the measurement PC (e.g., voltage sources, magnet power supplies, multimeters, etc.). The high-level sweep layer automates the creation of measurement loops, with simultaneous plotting and data logging. An extensive unit testing framework is used to verify functionality even without connected equipment. Lab::Measurement is distributed as free and open source software.Comment: Published version (open access, CC BY 4.0). 7 pages; refers to Lab::Measurement 3.660, see https://www.labmeasurement.de

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

Care leavers in early adulthood: How do they fare in Britain, Finland and Germany?

In this paper we examine the longer term outcomes of young people who experienced out of home care (OHC) as children, in Britain, Germany and Finland, countries characterised by different welfare regimes. While there is some evidence on immediate transitions after leaving care (up to age 21), there is less evidence on experiences around age 30, a phase of early adulthood. Drawing on existing longitudinal data for general population samples we focus on outcomes related to education, employment, family, health and receipt of welfare benefits for those who were ever in care and those who were not. We find evidence for continuing disadvantage regarding education and employment for those who were in care as children, but also indications of subjective wellbeing and commitment to family life – possibly a reflection of “normality” and efforts to “fit in” as parents. Surprisingly, despite variations in welfare system and differences in the scope and quality of available data, trends were similar in each of the countries, suggesting that none provide adequately for the needs of care experienced young adults. The findings point towards the need for a revised conceptualisation of the notion of “independence” which has to take into account the manifold and changing relationships between individuals and the state. Instead of a “cliff edge” approach there should be support for a more gradual shift from “dependence” to “independence” enabling those with care experience to develop their full potential. In interpreting the findings, limitations of the available data have to be acknowledged, pointing to the need for generating harmonised and longitudinal data on vulnerable subpopulations to enable effective monitoring of needs and provision

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

Anomalous relaxations and chemical trends at III-V nitride non-polar surfaces

Relaxations at nonpolar surfaces of III-V compounds result from a competition between dehybridization and charge transfer. First principles calculations for the (110) and (10$\bar{1}$0) faces of zincblende and wurtzite AlN, GaN and InN reveal an anomalous behavior as compared with ordinary III-V semiconductors. Additional calculations for GaAs and ZnO suggest close analogies with the latter. We interpret our results in terms of the larger ionicity (charge asymmetry) and bonding strength (cohesive energy) in the nitrides with respect to other III-V compounds, both essentially due to the strong valence potential and absence of $p$ core states in the lighter anion. The same interpretation applies to Zn II-VI compounds.Comment: RevTeX 7 pages, 8 figures included; also available at http://kalix.dsf.unica.it/preprints/; improved after revie

First principles study of strain/electronic interplay in ZnO; Stress and temperature dependence of the piezoelectric constants

We present a first-principles study of the relationship between stress, temperature and electronic properties in piezoelectric ZnO. Our method is a plane wave pseudopotential implementation of density functional theory and density functional linear response within the local density approximation. We observe marked changes in the piezoelectric and dielectric constants when the material is distorted. This stress dependence is the result of strong, bond length dependent, hybridization between the O $2p$ and Zn $3d$ electrons. Our results indicate that fine tuning of the piezoelectric properties for specific device applications can be achieved by control of the ZnO lattice constant, for example by epitaxial growth on an appropriate substrate.Comment: accepted for publication in Phys. Rev.