Abstract We study the three-dimensional (3D) magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor–Couette velocity field and zero magnetic field. Combining a recent linear instability result for the magnetic field with the framework of Friedlander et al (2006 Commun. Math. Phys. 264 335–47), we prove nonlinear instability of the solution around this steady state in L p , for any p > 1. In particular, our results are, to the best of our knowledge, the first rigorous instability results for 3D MHD without forcing, in which the instability is produced as a result of the (exponential) growth of the magnetic field. Furthermore, we offer a mathematical proof of the physically conjectured transfer of energy from the velocity field to the magnetic field in the MHD system.
Kepler Concordia, a new scientific and musical instrument enabling players to explore the solar system and other data within immersive extended-reality (XR) platforms, is being designed by a diverse team of musicians, artists, scientists and engineers using audio-first principles. The core instrument modules will be launched in 2019 for the 400th anniversary of Johannes Kepler's Harmonies of the World, in which he laid out a framework for the harmony of geometric form as well as the three laws of planetary motion. Kepler's own experimental process can be understood as audio-first because he employed his understanding of Western Classical music theory to investigate and discover the heliocentric, elliptical behaviour of planetary orbits. Indeed, principles of harmonic motion govern much of our physical world and show up at all scales in mathematics and physics. Few physical systems, however, offer such rich harmonic complexity and beauty as our own solar system. Concordia is a musical instrument that is modular, extensible and designed to allow players to generate and explore transparent sonifications of planetary movements rooted in the musical and mathematical concepts of Johannes Kepler as well as researchers who have extended Kepler's work, such as Hartmut Warm. Its primary function is to emphasise the auditory experience by encouraging musical explorations using sonification of geometric and relational information of scientifically accurate planetary ephemeris and astrodynamics. Concordia highlights harmonic relationships of the solar system through interactive sonic immersion. This article explains how we prioritise data sonification and then add visualisations and gamification to create a new type of experience and creative distributed-ledger powered ecosystem. Kepler Concordia facilitates the perception of music while presenting the celestial harmonies through multiple senses, with an emphasis on hearing, so that, as Kepler wrote, ‘the mind can seize upon the patterns’.
Forecasting and assessing the risk of heat waves is a crucial public policy stake. Evaluate the probability of heat waves and their severity can be possible by knowing the temperature in continuous time. However, daily extremes (maxima and minima) might be the only available data. The Ornstein-Uhlenbeck process is commonly used to model temperature dynamic. An estimation of the process parameters using only daily observed suprema of temperatures is proposed here. This new approach is based on a least square minimization using the cumulative distribution function of the supremum. Risk measures related to heat waves are then obtained numerically. In order to calculate explicitly those risk measures, it can be useful to have the joint law of the Ornstein-Uhlenbeck process and its supremum. The study is _rst limited to the joint density / distribution of the endpoint and supremum of the Ornstein-Uhlenbeck process. This probability admits a density, solution of the Fokker-Planck equation and explicitly obtained as an expansion involving parabolic cylinder functions. The proof of the density expression relies on a decomposition on a Hilbert basis of the space via a spectral method. We also study the oscillating Ornstein-Uhlenbeck process, which drift parameter is piecewise constant depending on the sign of the process. The Laplace transform of this process hitting time is determined and we also calculate the probability for the process to be positive on a fixed time.
Daniel Michelson, Anders Henja, Sander Ernes, Günther Haase · 9 authors
BALTRAD software exchanges weather-radar data internationally, operationally, and in real-time, and it processes the data using a common toolbox of algorithms available to every node in the decentralized radar network. This approach enables each node to access and process its own and international data to meet its local needs. The software system is developed collaboratively by the BALTRAD partnership, mostly comprising the national Meteorological and Hydrological institutes in the European Union’s Baltic Sea Region. The most important sub-systems are for data exchange, data management, scheduling and event handling, and data processing. C, Java, and Python languages are used depending on the sub-system, and sub-systems communicate using well-defined interfaces. Software is available from a dedicated Git server. BALTRAD software has been deployed throughout Europe and more recently in Canada. Funding statement: From 2009–2014, the BALTRAD and BALTRAD+ projects were part-financed by the European Union (European Regional Development Fund and European Neighbourhood and Partnership Instrument), with project numbers #009 and #101, respectively.