Research
John Gemmer

General Research Interests:
1. Calculus of Variations
2. Mulitiple Scale Analysis
3. Nonlinear Elasiticity
4. Nonlinear Partial Differential Equations		 5.  Riemannian Geometry
6.  Pattern Formation
7.  Differential Game Theory
8.  Nonlinear Dynamical Control Theory
Research Statement (.pdf)
Specific Projects
  • Non-Euclidean Model of Differential Growth 
      

My dissertation research, under the supervision of Shankar Venkataramani, focuses on studying the equilibrium configuration of non-Euclidean plates with constant negative Gaussian curvature. These sheets model the complex patterns formed by swelling thin elastic sheets. This work is in collaboration with physicist Eran Sharon and has been supported by the National Science Foundation and the United States – Israel Binational Science Foundation.


Video of a presentation given at the IMA

Publications:
  1. Defects and boundary layers in non-Euclidean plates. (preprint on arxiv)
  2. Shape selection in non-Euclidean plates, (with S. Venkataramani), Physica D: Nonlinear Phenomena, 240(19) (2011) pp. 1536-1552
  3. Shape selection in the non-euclidean model of elasticity (.pdf of dissertation)
Selected Presentations:
  1. Introduction to Nonlinear Elasticity and Non-Euclidean Plates.
  2. Periodic Shapes in Swelling Thin Elastic Sheets.
  3. Modelling Swelling Thin Elastic Sheets.
Posters:
  1. Differential Growth and Ripples in Thin Elastic Sheets.
  2. Shape Selection in Swelling Thin Elastic Sheets.

  • Dynamical Control Theory
In my second semester of graduate school I did a short project on nonlinear differential control theory. In the future I intend to continue research in the areas of optimal control theory and differential game theory.

Termpaper:

  1. Geometric Nonlinear Differential Control Theory

Selected Presentations:
  1. Nonlinear Dynamical Control and Parallel Parking a Car
  2. How to Control a Front-Wheel-Drive Bike
  • Generalizations of the Brachistochrone 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.

Publications:

  1. Generalizations of the brachistochrone problem, (with M. Nolan and R. Umble), Pi Mu Epislon Journal, 13 (4) (2011), pp. 207-218

Poster:
  1. The General Brachistochrone Problem.