BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alberto Bressan (Penn State University\, USA) DTSTART:20221201T163000Z DTEND:20221201T173000Z DTSTAMP:20260423T040038Z UID:SIAM-PDE/26 DESCRIPTION:Title: On the optimal shape of tree roots and branches\nby Alberto Bressan (Penn State University\, USA) as part of Seminar In the Analysis and Metho ds of PDE (SIAM PDE)\n\n\nAbstract\nFeatured Article: "Optimal Shapes fo r Tree Roots"\, SIAM J. Math. Anal. 54(4) (2022)\, pp. 4757-4784.\n\nFeat ured Article Authors: Alberto Bressan\, Sondre T. Galtung and Qing Su.\n\ n\nLiving organisms come in an immense variety of shapes.\nIn many cases o ne can expect that\, through natural selection\, a ``best possible" shape will have evolved. From a mathematical perspective\, it is thus of interes t to understand whether similar geometric shapes can be recovered as minim izers of suitable functionals.\n\nAs a step in this direction\, we conside r two functionals measuring the efficiency of roots and branches in a tree . Namely: \n(i) a ``sunlight functional"\, modeling the total amount of su nlight captured by the leaves of a tree\, and\n(ii) a ``harvest functional "\, modeling the amount of nutrients collected by the roots.\nThe above fu nctionals must be combined with a ``ramified transportation cost"\, for tr ansporting nutrients from the roots to the base of the trunk\, or from the base of the trunk to the leaves.\n\nThe talk will address the semicontinu ity of these functionals\, and the existence and properties of optimal sol utions\, in a space of measures.\nOpen problems will also be discussed\, i ncluding computational issues and how these optimal shapes may depend on v arious parameters.\n LOCATION:https://researchseminars.org/talk/SIAM-PDE/26/ END:VEVENT END:VCALENDAR