Research
General Research Interests:
  1. Variational Problems
  2. Thin Elastic Sheets
  3. PDEs
  • Current Work on Thin Elastic Sheets
Currently, I am working with Dr. Shankar Venkataramani in colloboration with Dr. Eran Sharon, from The Hebrew University of Jerusalem, and his students on modelling the equilibrium configuration taken by environmentally responsive thin elastic sheets with a specified target metric tensor g. These sheets model the growth processes in leaves and flowers and can be used as a shaping mechanism for elastic structures.

A preliminary draft of this work:
Elastic Energy and Isometric Embeddings of Thin Elastic Discs with a Prescribed Metric.

Graduate Student Brown Bag Presentation:

Elastic Discs and the Ripples in Leaves.

Analysis and its Applications Seminar Presentation:


Inducible Shape Transitions in Thin, Elastic Non-Euclidean, Free Sheets. 


  • Previous Work on Generalizations of the Brachistichrone Problem
When I was an undergraduate at Millersville University of Pennsylvania I worked on an original research project under the directions of Dr. Michael Nolan and Dr. Ron Umble. The project considered extensions of the classical Brachistichrone problem to particles falling along surfaces lying in gravitational fields that are not necessarily uniform.

Preprint:
Generalizations of the Brachistichrone Problem.



Presentation:


Generalizations of the Brachistichrone Problem. (The movie files no longer work).


Poster:


Generalizations of the Brachistichrone Problem.