Publications of Anne Catlla

%% Papers Published   
   Author = {A. Catlla and J. Porter and M. Silber},
   Title = {Weakly nonlinear analysis of impulsively-forced Faraday
   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   
   Author = {A. Catlla and D. Schaeffer and T. Witelski and E. Monson and A.
   Title = {On Spiking Models of Synaptic Activity and Impulsive
             Differential Equations},
   Journal = {SIAM Review},
   Year = {2007},
   Key = {fds139217}