Exact ground states of spin-2 chains

We use the matrix product approach to construct all optimum ground states of general anisotropic spin-2 chains with nearest neighbour interactions and common symmetries. These states are exact ground states of the model and their properties depend on up to three parameters. We find three different antiferromagnetic Haldane phases, one weak antiferromagnetic and one weak ferromagnetic phase. The antiferromagnetic phases can be described as spin liquids with exponentially decaying correlation functions. The variety of phases found with the matrix product ansatz also gives insight into the behaviour of spin chains with arbitrary higher spins.Comment: 7 pages, 2 figures, to be published in europhysics letters, uses epl.cl

A sensitive optical pyrometer for shock-temperature measurements

A new optical system was used to determine temperatures above 2400 K in shocked materials by measuring the spectral radiance of sub-microsecond pulses of light emitted from initially transparent solid samples in the visible and near infrared (450 to 900 nm). The high sensitivity of this optical pyrometer is attributed to the small number of channels, large aperture (0.03 steradian), the large bandwidth per channel (40 nm), and large photodiode detection area (0.2 sq cm). Improved calibration techniques reduce systematic errors encountered in previous shock-temperature experiments

Jena Soil Model (JSM v1.0; revision 1934): a microbial soil organic carbon model integrated with nitrogen and phosphorus processes

Plant–soil interactions, such as the coupling of plants' below-ground biomass allocation with soil organic matter (SOM) decomposition, nutrient release and plant uptake, are essential to understand the response of carbon (C) cycling to global changes. However, these processes are poorly represented in the current terrestrial biosphere models owing to the simple first-order approach of SOM cycling and the ignorance of variations within a soil profile. While the emerging microbially explicit soil organic C models can better describe C formation and turnover, at present, they lack a full coupling to the nitrogen (N) and phosphorus (P) cycles with the soil profile. Here we present a new SOM model – the Jena Soil Model (JSM) – which is microbially explicit, vertically resolved and integrated with the N and P cycles. To account for the effects of nutrient availability and litter quality on decomposition, JSM includes the representation of enzyme allocation to different depolymerisation sources based on the microbial adaptation approach as well as of nutrient acquisition competition based on the equilibrium chemistry approximation approach. Herein, we present the model structure and basic features of model performance in a beech forest in Germany. The model reproduced the main SOM stocks and microbial biomass as well as their vertical patterns in the soil profile. We further tested the sensitivity of the model to parameterisation and showed that JSM is generally sensitive to changes in microbial stoichiometry and processes

Homotopy Type Theory in Lean

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely quotients and truncations, and the use of cubical methods.Comment: 17 pages, accepted for ITP 201

Higher order forward spin polarizability

As a guideline for future experiments to extract the four (leading) spin polarizabilities of the nucleon, we have constructed the forward amplitude for polarized Compton scattering by dispersion integrals. These integrals have been saturated by recently measured helicity-dependent photoabsorption cross sections as well as predictions for pion photoproduction multipoles from several phenomenological descriptions and chiral perturbation theory. The comparison of these results corroborates the strategy to extract the spin polarizabilities by fitting them to polarized Compton data and fixing all higher order spin effects by dispersion relations based on pion photoproduction multipoles.Comment: 21 pages, 6 figures, 3 Tables; version to appear in Phys. Lett.

Shock temperatures in anorthite glass

Temperatures of CaAl2Si2O8 (anorthite glass) shocked to pressures between 48 and 117 GPa were measured in the range from 2500 to 5600 K, using optical pyrometry techniques. The pressure dependence of the shock temperatures deviates significantly from predictions based on a single high pressure phase. At least three phase transitions, at pressures of about 55, 85, and 100 GPa and with transition energies of about 0.5 MJ/kg each (approximately 1.5 MJ/kg total) are required to explain the shock temperature data. The phase transition at 100 GPa can possibly be identified with the stishovite melting transition. Theoretical models of the time dependence of the thermal radiation from the shocked anorthite based on the geometry of the experiment and the absorptive properties of the shocked material yields good agreement with observations, indicating that it is not necessary to invoke intrinsic time dependences to explain the data in many cases

On upscaling of rain-gauge data for evaluating numerical weather forecasts

Summary: One of the main objectives of numerical weather prediction models is reliable forecasting of heavy rain events. This paper discusses problems and strategies of evaluation of daily rain forecasting with operationally available rain station data. The focus is on spatial upscaling of rain station data to the grid of the direct model output. We show limitations of regression - or smoothing - based upscaling like as done, for example, by Kriging analysis and promote probabilistic upscaling by ensembles of stochastic simulations conditioned to the available observations. These ensembles easily provide uncertainties of daily evaluation and unbiased estimates for second moment comparison statistics. As an evaluation exercise we assess the quality of daily forecasts for Austria (total area: 84,000 km2) with the limited-area model ALADIN (horizontal grid-spacing 10 km). A quasi-operational set-up is compared to a physically enhanced but less well tested and tuned set-up. It is shown that the evaluation uncertainty is large, but with a full year of forecasts available it is possible to conclude that the physically enhanced set-up simulates too much rain and significantly more than the operational version with only small differences in simulated patterns and variabilit

On evaluation of ensemble precipitation forecasts with observation-based ensembles

Spatial interpolation of precipitation data is uncertain. How important is this uncertainty and how can it be considered in evaluation of high-resolution probabilistic precipitation forecasts? These questions are discussed by experimental evaluation of the COSMO consortium's limited-area ensemble prediction system COSMO-LEPS. The applied performance measure is the often used Brier skill score (BSS). The observational references in the evaluation are (a) analyzed rain gauge data by ordinary Kriging and (b) ensembles of interpolated rain gauge data by stochastic simulation. This permits the consideration of either a deterministic reference (the event is observed or not with 100% certainty) or a probabilistic reference that makes allowance for uncertainties in spatial averaging. The evaluation experiments show that the evaluation uncertainties are substantial even for the large area (41 300 km²) of Switzerland with a mean rain gauge distance as good as 7 km: the one- to three-day precipitation forecasts have skill decreasing with forecast lead time but the one- and two-day forecast performances differ not significantly