Spatial Structure of Ion Beams in an Expanding Plasma

We report spatially resolved perpendicular and parallel, to the magnetic field, ion velocity distribution function (IVDF) measurements in an expanding argon helicon plasma. The parallel IVDFs, obtained through laser induced fluorescence (LIF), show an ion beam with v ≈ 8000 m/s flowing downstream and confined to the center of the discharge. The ion beam is measurable for tens of centimeters along the expansion axis before the LIF signal fades, likely a result of metastable quenching of the beam ions. The parallel ion beam velocity slows in agreement with expectations for the measured parallel electric field. The perpendicular IVDFs show an ion population with a radially outward flow that increases with distance from the plasma axis. Structures aligned to the expanding magnetic field appear in the DC electric field, the electron temperature, and the plasma density in the plasma plume. These measurements demonstrate that at least two-dimensional and perhaps fully three-dimensional models are needed to accurately describe the spontaneous acceleration of ion beams in expanding plasmas

Homological algebra for osp(1/2n)

We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla operator. Based on this cohomology we can derive strong Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules. Then we state the Bott-Borel-Weil theorem which follows immediately from the Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally we calculate the projective dimension of irreducible and Verma modules in the category O

The Shapovalov determinant for the Poisson superalgebras

Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov described irreducible finite dimensional representations of po(0|n) and sh(0|n); we generalize his result for Verma modules: give criteria for irreducibility of the Verma modules over po(0|2k) and sh(0|2k)

The 2020 national seismic hazard model for the United Kingdom

We present updated seismic hazard maps for the United Kingdom (UK) intended for use with the National Annex for the revised edition of Eurocode 8. The last national maps for the UK were produced by Musson and Sargeant (Eurocode 8 seismic hazard zoning maps for the UK. British Geological Survey Report CR/07/125, United Kingdom, 2007). The updated model uses an up-to-date earthquake catalogue for the British Isles, for which the completeness periods have been reassessed, and a modified source model. The hazard model also incorporates some advances in ground motion modelling since 2007, including host-to-target adjustments for the ground motion models selected in the logic tree. For the first time, the new maps are provided for not only peak ground acceleration (PGA) but also spectral acceleration at 0.2 s (SA0.2s) and 1.0 s for 5% damping on rock (time-averaged shear wave velocity for the top 30 m Vs30 ≥ 800 m/s) and four return periods, including 475 and 2475 years. The hazard in most of the UK is generally low and increases slightly in North Wales, the England–Wales border region, and western Scotland. A similar spatial variation is observed for PGA and SA0.2s but the effects are more pronounced for SA0.2s. Hazard curves, uniform hazard spectra, and disaggregation analysis are calculated for selected sites. The new hazard maps are compared with the previous 2007 national maps and the 2013 European hazard maps (Woessner et al. in Bull Earthq Eng 13:3553–3596, 2015). There is a slight increase in PGA from the 2007 maps to this work; whereas the hazard in the updated maps is lower than indicated by the European maps

National seismic hazard maps for the UK: 2020 update

This report is the published product of a study by the British Geological Survey (BGS) to update the national seismic hazard maps for the UK. This is to take account of advances in seismic hazard methodology since the last seismic hazard maps were developed by Musson and Sargeant (2007) and present the results in a format that will be compatible with the future Eurocode 8 revisions

Centre and Representations of U_q(sl(2|1)) at Roots of Unity

Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view since they correspond to relations among quantum expectation values of observables that have to be satisfied on all physical states. In this paper, we establish these relations in the case of the quantum Lie superalgebra U_q(sl(2|1)). In the course of the argument, we find and use a set of representations such that any relation satisfied on all the representations of the set is true in U_q(sl(2|1)). This set is a subset of the set of all the finite dimensional irreducible representations of U_q(sl(2|1)), that we classify and describe explicitly.Comment: Minor corrections, References added. LaTeX2e, 18 pages, also available at http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP583.ps.gz . To appear in J. Phys. A: Math. Ge