Speaker
Scott
MacLachlan
| Department
of
Mathematics
and
Statistics, Memorial
University
of
Newfoundland
https://www.math.mun.ca/~smaclachlan/
Title
Finite-Element Modeling of Liquid Crystal Equilibria
Abstract
Numerical
simulation
tools
for
fluid
and
solid
mechanics
are
often based
on
the
discretisation
of
coupled
systems
of
partial
differential equations,
which
can
easily
be
identified
in
terms
of
physical conservation
laws.
In
contrast,
equilibrium
configurations
of
many liquid
crystal
phases
are
more
naturally
described
by
the
first-order optimality
conditions
of
constrained
free-energy
functionals.
In this
talk,
I
will
present
a
variational
finite-element
approach
for computing
liquid
crystal
equilibria,
and
demonstrate
its
use
for
both nematic
(rod-like)
and
smectic
(soap-like)
liquid
crystals.
As
the
main
scientific
and
engineering
interest
in
liquid
crystals
comes
from their
ability
to
exhibit
multiple
distinct
stable
equilibrium
states, I
will
discuss
the
combination
of
this
framework
with
a
nonlinear deflation
technique
that
allows
discovery
of
the
energy
landscapes
for these
problems.