MIT Unit Affiliation:
Lab Affiliation(s):
Sandlab
Post Doc Sponsor / Advisor:
Themis Sapsis
Areas of Expertise:
  • Dynamical Systems
  • Fluid Dynamics
  • Optimization
Date PhD Completed:
September, 2014
Expected End Date of Post Doctoral Position:
August 30, 2016

Mohammad Farazmand

  • Post Doctoral

MIT Unit Affiliation: 

  • Mechanical Engineering

Lab Affiliation(s): 

Sandlab

Post Doc Sponsor / Advisor: 

Themis Sapsis

Date PhD Completed: 

Sep, 2014

Top 3 Areas of Expertise: 

Dynamical Systems
Fluid Dynamics
Optimization

Personal Statement: 

Please visit my webpage at http://www.mfarazmand.com/

Expected End Date of Post Doctoral Position: 

August 30, 2016

CV: 

Research Projects: 

Please visit my webpage at http://www.mfarazmand.com/

Thesis Title: 

A variational approach to coherent structures in unsteady dynamical systems

Thesis Abstract: 

Lagrangian coherent structures (LCSs) are time-evolving surfaces that shape trajectory patterns in non-autonomous dynamical systems, such as turbulent fluid flows. Hyperbolic LCSs (generalized stable-unstable manifolds) are the main drivers of chaotic mixing in the phase space. Elliptic and parabolic LCSs (generalized KAM tori), on the other hand, confine coherent patches with regular dynamics. In many applications, these structures co-exist, partitioning the phase space into regions of distinct dynamics. Hence, knowledge of the location and evolution of LCSs is key to the understanding of the overall dynamics. Here, we show that LCSs are the solutions of suitably defined variational problems. Hyperbolic and parabolic (shearless) LCSs are shown to be the extrema of a Lagrangian shear functional. Elliptic LCSs, on the other hand, extremize a Lagrangian strain functional. Using these variational principles, we develop algorithms for numerical detection of LCSs from models and data sets. The algorithms are tested on several examples. They are then used to study a variety of transport phenomena in fluid flows as well as the stability of mechanical systems with arbitrary time dependence.

Contact Information:
77 Massachusetts Avenue
5-318
Cambridge
MA
02139