Singularities of bi-Hamiltonian systems

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Panta Rhei benchmark dataset: socio-hydrological data of paired events of floods and droughts

As the adverse impacts of hydrological extremes increase in many regions of the world, a better understanding of the drivers of changes in risk and impacts is essential for effective flood and drought risk management and climate adaptation. However, there is currently a lack of comprehensive, empirical data about the processes, interactions and feedbacks in complex human-water systems leading to flood and drought impacts. Here we present a benchmark dataset containing socio-hydrological data of paired events, i.e., two floods or two droughts that occurred in the same area. The 45 paired events occurred in 42 different study areas and cover a wide range of socio-economic and hydro-climatic conditions. The dataset is unique in covering both floods and droughts, in the number of cases assessed, and in the quantity of socio-hydrological data. The benchmark dataset comprises: 1) detailed review style reports about the events and key processes between the two events of a pair; 2) the key data table containing variables that assess the indicators which characterise management shortcomings, hazard, exposure, vulnerability and impacts of all events; 3) a table of the indicators-of-change that indicate the differences between the first and second event of a pair. The advantages of the dataset are that it enables comparative analyses across all the paired events based on the indicators-of-change and allows for detailed context- and location-specific assessments based on the extensive data and reports of the individual study areas. The dataset can be used by the scientific community for exploratory data analyses e.g. focused on causal links between risk management, changes in hazard, exposure and vulnerability and flood or drought impacts. The data can also be used for the development, calibration and validation of socio-hydrological models. The dataset is available to the public through the GFZ Data Services (Kreibich et al. 2023, link for review: https://dataservices.gfz-potsdam.de/panmetaworks/review/923c14519deb04f83815ce108b48dd2581d57b90ce069bec9c948361028b8c85/).</p