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- Jerrold E. Marsden, Lawrence Sirovich, +5 authors Lawrence Perko
- 2010

A collection of methods is presented to adapt a pre-existing time-stepping code to perform various bifurcation-theoretic tasks. It is shown that the implicit linear step of a time-stepping code canâ€¦ (More)

h = 9000. The discretisation is performed using a spanwise periodic spectral/hp element method. The inlet flow has turbulent velocity and pressure fields that are formed by a regenerating channelâ€¦ (More)

- Kerstin Avila, David Moxey, Alberto de Lozar, Marc Avila, Dwight Barkley, BjÃ¶rn Hof
- Science
- 2011

Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even forâ€¦ (More)

Methods are described for absolute and convective stabilit y analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to va ry slowly in the streamwiseâ€¦ (More)

- Irina V. Biktasheva, Dwight Barkley, Vadim N. Biktashev, Andrew J. Foulkes
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2010

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave'sâ€¦ (More)

- Dwight Barkley, Ioannis G. Kevrekidis, Andrew M. Stuart
- SIAM J. Applied Dynamical Systems
- 2006

We explore situations in which certain stochastic and highdimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study mo ment maps, maps on spacesâ€¦ (More)

- Dwight Barkley
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2011

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to establishedâ€¦ (More)

- Paul Wheeler, Dwight Barkley
- SIAM J. Applied Dynamical Systems
- 2006

A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius R increases, eigenvalue spectra converge to the absoluteâ€¦ (More)

- Dwight Barkley, Laurette S. Tuckerman
- Physical review letters
- 2005

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal-flow-unit methodology. Computational domains are of minimal size in two directions butâ€¦ (More)