CTMS Adventures in Theory Lectures, Spring_2015
https://services.math.duke.edu/mcal?listgroup-30
CTMS Adventures in Theory Lectures Upcoming Seminarsen-us2024-03-29T03:01:46-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyEnergy on the edge - a mathematical view
https://services.math.duke.edu/mcal?abstract-9039
Waves in free-space diffractively spread, while waves
in a spatially non-homogeneous medium undergo a combination of
scattering and localization.
<br/>
In many applications, e.g. photonic and quantum systems, one is interested in
controlled localization of wave energy.
Edge states are a type of localization along a line-defect, the interface
between different media.
<br/>
Topologically protected edge states are a class of edge states which are
robust to strong local distortions of the edge.
They are therefore potential vehicles for robust energy-transfer
in the presence of defects and random imperfections.
These states arise, for example, in graphene and its photonic analogues.
<br/>
We first review the mathematics of dispersive waves in periodic media
and discuss examples of wave localization by a defect.
<br/>
We then specialize to the case of honeycomb structures (such as grapheme)
and discuss their novel properties.
Finally we introduce and discuss a rich family of continuum partial differential equation
(Schroedinger) models, admitting edge states
which are topologically protected and those which are not.<a href="http://www.columbia.edu/~miw2103/">Michael I. Weinstein</a> (Columbia University)2015-03-17T16:30:00-04:009039CTMS Adventures in Theory LecturesCTMS Adventures In Theory LecturesTue, 17 Mar 2015 16:30:00 EDTSpring, 2015Tue, 17 Mar 2015 17:30:00 EDTTuesday, March 17, 2015, 4:30pm128 PhysicsNumerical methods for first-principle molecular simulation
https://services.math.duke.edu/mcal?abstract-9092
First-principle molecular simulation based on electronic structure calculation has become an essential tool in chemistry, condensed matter physics, molecular biology, materials science, and nanosciences. It is also an inexhaustible source of exciting mathematical and numerical problems.
In this talk, I will focus on Density Functional Theory and the Kohn-Sham model, which is to date the most widely used approach in electronic structure calculation, as it provides the best compromise between accuracy and computational efficiency. I will present some recent progress made in the mathematical understanding and the numerical analysis of this model, which pave the road to high-fidelity numerical simulations (with a posteriori error bounds) of the electronic structure of large molecular systems. I will then discuss the difficult issue of coupling the Kohn-Sham model with coarser models in view of simulating even larger molecular systems, such as drug-protein complexes in solution.<a href="http://cermics.enpc.fr/~cances/home.html">Eric Cances</a> (Ecole des Ponts ParisTech)2015-04-21T16:30:00-04:009092CTMS Adventures in Theory LecturesCTMS Adventures In Theory LecturesLSRC B101Tue, 21 Apr 2015 17:30:00 EDTTuesday, April 21, 2015, 4:30pmSpring, 2015Tue, 21 Apr 2015 16:30:00 EDT