BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sara Daneri (Gran Sasso Science Institute) DTSTART:20220927T160000Z DTEND:20220927T170000Z DTSTAMP:20260423T035054Z UID:OSGA/108 DESCRIPTION:Title: S ymmetry breaking and pattern formation for functionals with competing inte ractions\nby Sara Daneri (Gran Sasso Science Institute) as part of Onl ine Seminar "Geometric Analysis"\n\n\nAbstract\nIn this talk we will revie w some recent results we obtained on the one-dimensionality of the minimiz ers\nof a family of continuous local/nonlocal interaction functionals in g eneral dimension. Such functionals have a local term\, typically the perim eter or its Modica-Mortola approximation\, which penalizes interfaces\, an d a nonlocal term favouring oscillations which are high in frequency and i n amplitude. The competition between the two terms is expected by experime nts and simulations to give rise to periodic patterns at equilibrium. Func tionals of this type are used  to model pattern formation\, either in mat erial science or in biology. The difficulty in proving the emergence of su ch structures is due to the fact that the functionals are symmetric with r espect to permutation of coordinates\, while in more than one space dimens ions minimizers are one-dimensional\, thus losing the symmetry property of the functionals. We will present new techniques and results showing that for two classes of functionals (used to model generalized anti-ferromagnet ic systems\, respectively  colloidal suspensions)\, both in sharp interfa ce and in diffuse interface models\, minimizers are one-dimensional and pe riodic\, in general dimension and also while imposing a nontrivial volume constraint. The results are contained in a series of joint works with Eris Runa and Alicja Kerschbaum.\n LOCATION:https://researchseminars.org/talk/OSGA/108/ END:VEVENT END:VCALENDAR