Spin - or, actually: Spin and Quantum Statistics

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli's theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin

A tailored multi-model ensemble for air traffic management: Demonstration and evaluation for the Eyjafjallajökull eruption in May 2010

High quality volcanic ash forecasts are crucial to minimize the economic impact of volcanic hazards on air traffic. Decision-making is usually based on numerical dispersion modeling with only one model realization. Given the inherent uncertainty of such approach, a multi-model multi-source term ensemble has been designed and evaluated for the Eyjafjallaj&ouml;kull eruption in May 2010. Its use for air traffic management is discussed. Two multi-model ensembles were built: the first is based on the output of four dispersion models and their own implementation of ash ejection. All a priori model source terms were constrained by observational evidence of the volcanic ash cloud top as a function of time. The second ensemble is based on the same four dispersion models, which were run with three additional source terms: (i) a source term obtained with background modeling constrained with satellite data (a posteriori source term), (ii) its lower bound estimate, and (iii) its upper bound estimate. The a priori ensemble gives valuable information about the probability of ash dispersion during the early phase of the eruption, when observational evidence is limited. However, its evaluation with observational data reveals lower quality compared to the second ensemble. While the second ensemble ash column load and ash horizontal location compare well to satellite observations, 3D ash concentrations are negatively biased. This might be caused by the vertical distribution of ash, which is too much diluted in all model runs, probably due to defaults in the a posteriori source term and vertical transport and/or diffusion processes in all models. Relevant products for the air traffic management are horizontal maps of ash concentration quantiles (median, 75 %, 99 %) at a fine-resolved flight level grid. These maps can be used for route optimization in the areas where ash does not pose a direct and urgent threat to aviation. Cost-optimized consideration of such hazards will result in much less impact on flight cancellations, reroutings, and traffic flow congestions.</p

An ensemble of state-of-the-art ash dispersion models: towards probabilistic forecasts to increase the resilience of air traffic against volcanic eruptions

High-quality volcanic ash forecasts are crucial to minimize the economic impact of volcanic hazards on air traffic. Decision-making is usually based on numerical dispersion modelling with only one model realization. Given the inherent uncertainty of such an approach, a multi-model multi-source term ensemble has been designed and evaluated for the Eyjafjallajökull eruption in May 2010. Its use for flight planning is discussed. Two multi-model ensembles were built: the first is based on the output of four dispersion models and their own implementation of ash ejection