BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:‪Giuseppe Tomassetti‬ (Università Roma Tre) DTSTART:20201130T144000Z DTEND:20201130T161000Z DTSTAMP:20260405T174413Z UID:NSCM/8 DESCRIPTION:Title: Sha pe programming of a magnetic elastica\nby ‪Giuseppe Tomassetti‬ (U niversità Roma Tre) as part of Nečas Seminar on Continuum Mechanics\n\n \nAbstract\nWe consider a cantilever beam which possesses a possibly non-u niform permanent magnetization\, and whose shape is controlled by an appli ed magnetic field. We model the beam as a plane elastic curve and we suppo se that the magnetic field acts upon the beam by means of a distributed co uple that pulls the magnetization towards its direction. Given a list of t arget shapes\, we look for a design of the magnetization profile and for a list of controls such that the shapes assumed by the beam when acted upon by the controls are as close as possible to the targets\, in an averaged sense. To this effect\, we formulate and solve an optimal design and contr ol problem leading to the minimization of a functional which we study by b oth direct and indirect methods. In particular\, we prove that minimizers exist\, solve the associated Lagrange-multiplier formulation (besides non- generic cases)\, and are unique at least for sufficiently low intensities of the controlling magnetic fields. To achieve the latter result\, we use two nested fixed-point arguments relying on the Lagrange-multiplier formul ation of the problem\, a method which also suggests a numerical scheme. Va rious relevant open question are also discussed.\n LOCATION:https://researchseminars.org/talk/NSCM/8/ END:VEVENT END:VCALENDAR