Research
Research
Interests
and Publications
I received my Ph.D. from the Engineering
Sciences and Applied Mathematics (ESAM) Department at Northwestern
University in 2000 under the direction of my advisor, Professor Hermann
Riecke. My research involves pattern formation and localized
structures in nonlinear systems.
Publications
C. Crawford, H. Riecke, Tunable front
interaction and localization of periodically forced waves, Phys. Rev. E 65 066307 (2002)
Within
the framework of coupled Ginzburg-Landau equations, periodic forcing
leads to a new mechanism for localizing traveling waves. The
results are expected to be relevant for both pulses observed
binary-mixture convection and localized "worms" seen in
electroconvection of nematic liquid crystals.
C. Crawford, H. Riecke, Oscillon-type
structures and their interaction in a Swift-Hohenberg model, Physica D 129 83 (1999)
Motivated by
oscillons observed in vertically-vibrated granular materials [P.
Umbanhowar, et al, Nature 382
(1996) 793], we
investigate the existence and interaction of oscillon structures using
a Swift-Hohenberg equation.
For parameters in which the bifurcation to square patterns is
sufficiently subcritical, we find that oscillon structures also exist,
due to nonadiabatic locking -- or pinning to the underlying
pattern.
In-Progress
Modulation of
localized waves coupled to an additional mode
A
mathematical model has been previously proposed [H. Riecke, G.
D. Granzow, Phys. Rev. Lett. 81,
(1998) 333] to explain
the existence of localized worms observed in electroconvection of
nematic liquid crystals [M. Dennin, et al, Phys. Rev. Lett. 77
2475 (1996)].
The current investigation introduces periodic forcing to the model to
see how the worms respond in simulations. The results can be used
to compare with experiments and test the validity of the
model.
Dr.
Crawford's Home page
Elmhurst College
Mathematics Home Page
Elmhurst
College Mathematics Faculty Page
Last modified:
January 31, 2002