[Dottorcomp] Seminari di Matematica Applicata. Martedì 13 Giugno. Ricardo Nochetto. Giovanni Leoni.

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 13 giugno 2023, alle ore 15.00 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Ricardo H. Nochetto (University of Maryland, USA)

terrà un seminario dal titolo:

Liquid Crystal Polymeric Networks: Modeling, Approximation and Computation

e alle ore 16.00 precise,

Giovanni Leoni (Carnegie Mellon University),

terrà un seminario dal titolo:

On Gagliardo-Nirenberg Inequalities.

I seminari verranno anche trasmessi in diretta su zoom.

Link Zoom:
https://us02web.zoom.us/j/87518137128?pwd=eHg2eG9QZUdydFJEU1NESWN5a1lPQT09


Abstract (Nochetto). Liquid crystal polymeric networks (LCNs) are materials
where a nematic liquid crystal is coupled with a rubbery material. When
actuated with heat or light, the interaction of the liquid crystal with the
rubber creates complex shapes. Thin bodies of LCNs are natural candidates
for soft robotics applications. Starting from the classical 3D trace energy
formula of Bladon, Warner and Terentjev (1994), we derive a 2D membrane
energy as the formal asymptotic limit of the 3D energy and characterize the
zero energy deformations. The membrane energy lacks convexity properties,
which lead to challenges for the design of a sound numerical method. We
discretize the problem with conforming piecewise linear finite elements and
add a higher order bending energy regularization to address the lack of
convexity. We prove that minimizers of the discrete energy converge to zero
energy states of the membrane energy in the spirit of Gamma convergence;
this includes the presence of creases. We solve the discrete minimization
problem via an energy stable gradient flow scheme. We present computations
showing the geometric effects that arise from liquid crystal defects as
well as computations of nonisometric origami, both within and beyond
theory. This work is joint with L. Bouck and S. Yang.


Abstract (Leoni). This talk presents a simple approach to
Gagliardo-Nirenberg’s inequalities in fractional Sobolev spaces.


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