Wed, July 10, 2019
Public Access Category: All |
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- Time:
- 3:00pm-4:00pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 1.
Speaker: Anisa Chorwadwala.
Affiliation: IISER Pune.
Date and Time: Wednesday 10 July, 3:00 pm - 4:00 pm.
Venue: Room 216, Department of Mathematics.
Title: A Glimpse of Shape Optimization Problems.
Abstract: The following questions arise quite naturally from what we see
around us. Why are soap bubbles that float in air approximately spherical?
Why does a herd of reindeer form a round shape when attacked by wolves? Of
all geometric objects having a certain property, which ones have the
greatest area or volume; and of all objects having a certain property,
which ones have the least perimeter or surface area? These problems have
been stimulating much mathematical thought. Mathematicians have been
trying to answer such questions and this has led to a branch of
mathematical analysis known as “shape optimisation problems”.
A typical shape optimisation problem is, as the name suggests, to find a
shape which is optimal in the sense that it minimises a certain cost
functional while satisfying given constraints. Isoperimetric problems form
a special class of shape optimisation problems. A typical isoperimetric
problem is to enclose a given area with a shortest possible curve. In
many cases, the functional being minimised depends on solution/s of a
given partial differential equation defined on a variable domain.
The plan is to give a glimpse of a few shape optimization problems we have
worked on.
- Time:
- 4:30pm-5:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Mathematics Colloquium Talk 2.
Speaker: Apala Majumdar.
Affiliation: University of Bath.
Date and Time: Wednesday 10 July, 4:30 pm - 5:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Solution Landscapes in the Landau-de Gennes Theory for Nematic
Liquid Crystals.
Abstract: Nematic liquid crystals are quintessential examples of soft
matter, intermediate in character between solids and liquids, with
long-range orientational order. We model spatio-temporal pattern formation
for nematic liquid crystals on two-dimensional polygonal geometries, which
are relevant for applications. We work within the powerful continuum
Landau-de Gennes theory for nematic liquid crystals. We illustrate the
complex solution landscapes on square domains as a function of the square
size, temperature and boundary conditions, reporting a novel Well Order
Reconstruction Solution on nnao-scale geometries. We discuss
generalizations to arbitrary 2D polygons, using symmetry-based and
variational techniques to study stable patterns in distinguished
asymptotic limits. We conclude by reviewing recent work on stabilization
of interior vortices by magneto-nematic coupling in ferronematics, which
leads to new possibilities for magneto-mechanical effects in nematic-based
materials. This is joint work with researchers in Peking University,
Shanghai Jiao Tong, IIT Delhi, IIT Bombay, Illinois Technological
University and University of Verona.