## Publications of Anne Catlla

%% Papers Published
@article{fds43577,
Author = {A. Catlla and J. Porter and M. Silber},
Title = {Weakly nonlinear analysis of impulsively-forced Faraday
waves},
Journal = {Physical Review E},
Volume = {72},
Number = {5},
Pages = {056212},
Year = {2005},
Month = {November},
Abstract = {Parametrically-excited surface waves, forced by a repeating
sequence of N delta-function impulses, are considered within
the framework of the Zhang-Viñals model [W. Zhang and J.
Viñals, J. Fluid Mech. 336, 301 (1997)]. With impulsive
forcing, the linear stability analysis can be carried out
exactly and leads to an implicit equation for the neutral
stability curves. As noted previously [J. Bechhoefer and B.
Johnson, Am. J. Phys. 64, 1482 (1996)], in the simplest case
of N=2 equally-spaced impulses per period (which alternate
up and down) there are only subharmonic modes of
instability. The familiar situation of alternating
subharmonic and harmonic resonance tongues emerges only if
an asymmetry in the spacing between the impulses is
introduced. We extend the linear analysis for N=2 impulses
per period to the weakly nonlinear regime, where we
determine the leading order nonlinear saturation of
one-dimensional standing waves as a function of forcing
strength. Specifically, an analytic expression for the cubic
Landau coefficient in the bifurcation equation is derived as
a function of the dimensionless spacing between the two
impulses and the fluid parameters that appear in the
Zhang-Viñals model. As the capillary parameter is varied,
one finds a parameter regime of wave amplitude suppression,
which is due to a familiar 1:2 spatiotemporal resonance
between the subharmonic mode of instability and a damped
harmonic mode. This resonance occurs for impulsive forcing
even when harmonic resonance tongues are absent from the
neutral stability curves. The strength of this resonance
feature can be tuned by varying the spacing between the
impulses. This finding is interpreted in terms of a recent
symmetry-based analysis of multifrequency forced Faraday
waves [J. Porter, C. M. Topaz, and M. Silber, Phys. Lett.
93, 034502 (2004); C. M. Topaz, J. Porter, and M. Silber,
Phys. Rev. E 70, 066206 (2004)].},
Key = {fds43577}
}
%% Papers Accepted
@article{fds139217,
Author = {A. Catlla and D. Schaeffer and T. Witelski and E. Monson and A.
Lin},
Title = {On Spiking Models of Synaptic Activity and Impulsive
Differential Equations},
Journal = {SIAM Review},
Year = {2007},
Key = {fds139217}
}