John Gibson

ASSOCIATE PROFESSOR
Phone: (603) 862-2681
Office: Mathematics & Statistics, Kingsbury Hall Rm N309 E, Durham, NH 03824
John Gibson

My primary research interest is understanding turbulence through dynamical systems theory. The key idea is to compute unstable invariant solutions of the Navier-Stokes equations (steady states, traveling waves, and periodic orbits) and describe turbulent dynamics as a chaotic walk between these unstable solutions along the low-dimensional network of their unstable manifolds. Additional interests include numerical methods, scientific computing, open-source software, the Julia programming language, and open education.

Education

  • Ph.D., Theoretical & Applied Mechanics, Cornell University
  • B.A., Liberal Arts, St. John's College

Research Interests

  • Applied Mathematics
  • Computational Mathematics
  • Fluid Dynamics
  • Nonlinear Dynamics

Courses Taught

  • IAM 950: Spatiotemp. & Turb. Dynamics
  • IAM 961: Numerical Linear Algebra
  • INCO 790: Adv Rsrch Exp/Mathematics
  • MATH 445: Mathematics and Apps in MATLAB
  • MATH 527: Diff Equation w/Linear Algebra
  • MATH 753: Intro to Numerical Methods I

Selected Publications

Brand, E., & Gibson, J. F. (2014). A doubly localized equilibrium solution of plane Couette flow. Journal of Fluid Mechanics, 750. doi:10.1017/jfm.2014.285

GIBSON, J. F., HALCROW, J., & CVITANOVIĆ, P. (2008). Visualizing the geometry of state space in plane Couette flow. Journal of Fluid Mechanics, 611, 107-130. doi:10.1017/s002211200800267x

Schneider, T. M., Gibson, J. F., & Burke, J. (n.d.). Snakes and Ladders: Localized Solutions of Plane Couette Flow. Physical Review Letters, 104(10). doi:10.1103/physrevlett.104.104501