Q.M. Wargnier (Lockheed Martin Solar and Astrophysics Laboratory and Baeri)
Advanced Time-Adaptive PIROCK Method with Error Control for Magnetic Reconnection Simulations in Chromospheric Environments abstract
Abstract:
Understanding the heating mechanism of the Sun\'s chromosphere remains a central challenge in solar physics, with magnetic reconnection (MR) playing a pivotal role in its heating and dynamics. Recent observations have highlighted the significance of ion-neutral interactions, which current models struggle to fully incorporate. In this presentation, we will introduce a numerical simulation with a Multi-Fluid Multi-Species (MFMS) model to investigate MR in upper chromospheric environments, accounting for multi-fluid/multi-species interactions, including helium and hydrogen species.The MFMS model is a multi-scale temporal model presenting challenges for temporal integration with classical integration methods. The model comprises stiff source terms from collisional or reactive effects, coupled with diffusion terms, and an increased number of equations due to the duplication for each fluid considered, complicating the time integration process. Therefore, our approach employs the second-order Partitioned Implicit-Explicit Runge-Kutta (PIROCK) method, renowned for its ability to handle complex convective-diffusive-reactive systems of equations like the MFMS model. Comparative analyses with alternative integration methods, including third-order explicit Runge-Kutta time integration and another method based on a first-order Lie splitting approach, underscore the superior computational efficiency and accuracy of PIROCK. Our findings underscore the vital role of particle decoupling in facilitating efficient heating mechanisms within the chromosphere, with implications for phenomena such as helium enrichment observed in switchbacks and coronal mass ejections.
14:00 • Université de Genève, Conseil Général 7-9, conference room, 8th floor (unusual room!)
Nicolas Ressayre (Lyon)
On the Belkale-Kumar cohomology of G/P abstract
Abstract:
Horn\'s conjecture provides an answer to the question: what can be said about the spectrum of the sum of two Hermitian matrices knowing the spectra of the summands? This problem concerns representations of the unitary group or the complex linear group. It can be generalised directly to any reductive group G.In 2006, Belkale and Kumar introduced a new product on the cohomology of projective homogeneous spaces and showed that it governs the geometry of the Horn problem for G.In this talk, we shall present the Belkale-Kumar product and discuss its connection with Horn. We will present one of the speaker\'s conjectures about it. Finally, we will explain two partial results on this conjecture, obtained independently, with Pierre-Emmanuel Chaput and Luca Francone.
15:00 • Université de Genève, Conseil Général 7-9, Room 1-07