Την Δευτέρα 2 Ιουνίου θα δοθούν δύο ομιλίες από τον Καθηγητή Renzo L. RICCA του Παν/μίου του Μιλάνου-Μπικόκα, οι οποίες θα πραγματοποιηθούν στην Αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ και ώρες 16:00-17:00 & 17:00-18:00.
Ακολουθούν οι τίτλοι και οι περιλήψεις των ομιλιών.
Talk 1: Helicity conservation and its topological interpretation
Talk 2: Twist-fold processes and energy relaxation in nature
ABSTRACT of Talk 1
Ηelicity is a fundamental conserved quantity of ideal fluid mechanics; its conservation was discovered in the context of magnetic fields by Woltjer in 1958, and in the context of the Euler equations by Moreau in 1961. But it was only in 1968, with the original work of Moffatt, that helicity acquired a topological meaning establishing a deep connection between the continuous deformation of an ideal fluid and the topology of flow maps [1]. Here we review this progress focussing on some of the key features of these advances in relation to open problems of current research [2], and in the light of the modern trends in topological fluid dynamics [3].
[1] Moffatt, H.K. 2014 Helicity and singular structures in fluid dynamics. PNAS USA 111, 3663-3670.
[2] Ricca, R.L 2025 Topological fluid dynamics and knotted fields. In Encyclopedia of Mathematical Physics (ed. R. Szabo & M. Bojowald) 4, pp. 245-255. Academic Press (2nd edition).
[3] Ricca, R.L. & Liu, X. (Eds.) 2024 Knotted Fields. Lecture Notes in Mathematics 2344. Springer-Nature, Switzerland.
ABSTRACT of Talk 2
Twist-fold processes are ubiquitous in nature and are often governed by energy relaxation mechanisms. In this talk we show how the Reidemeister twist move associated with an inflexional instability of a physical knot leads to an energy change of the system, sometimes with dramatic effects. Three different cases are considered: when magnetic energy is released, when elastic energy is stored, and when tension energy is re-distributed through the topological re-organisation of a soap film.
[1] Ricca, R.L. 2005 Inflexional disequilibrium of magnetic flux tubes. Fluid Dyn. Res. 36, 319-332.
[2] Ricca, R.L. & Maggioni, F. 2008 Multiple folding and packing in DNA modeling. Comp. & Math. with Appl. 55, 1044-1053.
[3] Goldstein, R.E., Moffatt, H.K., Pesci, A.I. & Ricca, R.L. 2010 A soap film Möbius strip changes topology with a twist singularity. PNAS USA 107, 21979-21984.
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