[Dottorcomp] Seminari di Matematica Applicata. Martedì 7 settembre, Michele Ruggeri

[Lorenzo Tamellini]

Martedì 7 settembre 2021, alle ore 15 precise, il Dott. Michele Ruggeri (TU
Wien) terrà un seminario dal titolo:

Convergent finite element methods for the Ericksen model of nematic liquid
crystals

Il seminario si terrà in formato *ibrido*, su Zoom al link:

https://us02web.zoom.us/j/85346967892?pwd=dWdBbTZoLzk1aXI3TWswUzZIbkphUT09
Meeting ID: 853 4696 7892
Passcode: seminario

e in presenza *in aula Beltrami* del dipartimento di matematica.

Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/



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* Abstract:* The Ericksen model describes nematic liquid crystals (LCs) in
terms of a unit-length vector field (director) and a scalar function
(degree of orientation).
Compared to the classical Oseen-Frank model, it allows for the description
of a larger class of defects.
Equilibrium states of the LC are given by admissible pairs that minimize an
energy functional,
which consists of the sum of Oseen-Frank-like energies and a double well
potential.
The resulting Euler-Lagrange equations are degenerate for the director,
which poses serious
difficulties to formulate mathematically sound algorithms for their
approximation.
We propose a simple but novel finite element approximation of the problem
that can be
implemented easily within standard finite element packages.
The scheme does not employ a projection to impose the unit-length
constraint on the director
and thus circumvents the use of weakly acute meshes,
which are quite restrictive in 3D but are required by recent algorithms for
convergence.
We show stability and Gamma-convergence properties of the new method in the
presence
of defects. We also discuss an effective nested gradient flow algorithm for
computing minimizers
that controls the violation of the unit-length constraint.
We present several simulations in 2D and 3D that document the performance
of the proposed
scheme and its ability to capture quite intriguing defects.
This is joint work with Ricardo H. Nochetto and Shuo Yang (University of
Maryland).
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