Analysis and Numerical Methods in Solid State Physics and Chemistry

Series: 
Dissertation Defense
Thursday, April 27, 2017 - 10:00
2 hours
Location: 
Skiles 005
,  
Georgia Institute of Technology
Organizer: 
We present two distinct problems in the field of dynamical systems.I the first part, we cosider an atomic model of deposition of materials over a quasi-periodic medium, that is, a quasi-periodic version of the well-known Frenkel-Kontorova model. We consider the problem of whether there are quasi-periodic equilibria with a frequency that resonates with the frequencies of the medium. We show that there are always perturbative expansions. We also prove a KAM theorem in a-posteriori form.In the second part, we consider a simple model of chemical reaction and present a numerical method calculating the invariant manifolds and their stable/unstable bundles based on parameterization method.