## MAP-PDMA

**Roman Chertovskih**

*Research Center for Systems and Technologies (SYSTEC), Engineering Faculty, University of Porto*

**Abstract ::** We will discuss the dynamo problem [1] – magnetic field generation by flows of an electrically conducting fluid. We will survey the magnetic activity in the Universe: magnetic fields of planets, stars and galaxies [2], and consider an important engineering application – magnetic fields in liquid metals cooling a reactor. To simulate such magnetic phenomena, the governing equations will be introduced and the basics of magnetohydrodynamics [3] will be discussed. We also plan to overview the mathematical methods used in the analysis of such problems: ranging from the dynamical systems theory [4] andthe equivariant bifurcation theory [5] to the numerical spectral methods [6]. Finally, the use of high performance computers for the considered problems will be addressed.

[1] Moffatt K., Dormy E. Self-Exciting Fluid Dynamos. Cambridge Texts in Applied Mathematics, Cambridge University Press, 2019.

[2] Rudiger G., Hollerbach R. The Magnetic Universe: Geophysical and Astrophysical Dynamo Theory. Wiley, 2004.

[3] Molokov S., Moreau R., Moffatt K. Magnetohydrodynamics: Historical Evolution andfTrends. Springer, 2007.

[4] Bohr T., Jensen M.H., Paladin G., Vulpiani A. Dynamical Systems Approach to Turbulence. Cambridge Nonlinear Science Series, Cambridge University Press, 2005.

[5] Chossat P., Lauterbach R. Methods in Equivariant Bifurcations and Dynamical Systems. Advanced Series in Nonlinear Dynamics, World Scientific, 2000.

[6] Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A. Spectral Methods: Fundamentals in Single Domains. Scientific Computation series, Springer, 2006.

Seminar Room of DMat-UMinho (3.08), and via zoom at

https://videoconf-colibri.zoom.us/j/94769148463?pwd=YWRVYjEzMkk2bmtMY2Q2OEhFM0hUdz09

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)