BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesco Giglio (University of Glasgow) DTSTART:20240312T140000Z DTEND:20240312T145000Z DTSTAMP:20260423T024658Z UID:UEA_mth/5 DESCRIPTION:Title: From Statistical Thermodynamics to (C-)Integrability and back\nby Fran cesco Giglio (University of Glasgow) as part of Fluids and Structures Semi nar @ UEA\n\n\nAbstract\nPhase transitions in macroscopic systems at the e quilibrium have shown to be intimately related to the theory of nonlinear conservation laws. Examples range from simple systems like van der Waals f luids\, (uniaxial) Nematic Liquid Crystal models and spin systems to compl ex systems as Random Matrix models. In such models\, order parameters fulf il suitable nonlinear PDEs with prescribed initial conditions and phase tr ansitions are explained in terms of shock waves travelling in the space of control parameters (e.g. thermodynamic variables). \nRestricting our anal ysis to simple systems\, many paradigmatic models in Statistical Thermodyn amics turn out to be C-Integrable\, that is there exists a nonlinear trans formation which maps a non-linear PDE of hydrodynamic type associated with the physical problem to a linear one. Conversely\, from a C-Integrability ansatz applied to first principles of Thermodynamics one can retrieve fam ilies of models which often generalise known ones\, providing insights of physical relevance. \n\nThe talk aims at discussing the connection between Statistical Thermodynamics and C-Integrability in the context of fluid sy stems\, with a special focus on recent results on biaxial Nematic Liquid C rystals (doi: 10.1098/rspa.2023.0701). We will see that the occurrence of distinct thermodynamic phases in certain degenerate domains of thermodynam ic variables is identified by reductions of the underlying system of conse rvation laws. This highlights the importance of developing solid mathemati cal and theoretical tools to extend simple thermodynamic models and constr uct more general ones.\n LOCATION:https://researchseminars.org/talk/UEA_mth/5/ END:VEVENT END:VCALENDAR