46 research outputs found
Evolution equation for bidirectional surface waves in a convecting fluid
Surface waves in a heated viscous fluid exhibit a long wave oscillatory
instability. The nonlinear evolution of unidirectional waves is known to be
described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the
present work we eliminate the restriction of unidirectional waves and find that
the evolution of the wave is governed by a modified Boussinesq system . A
perturbed Boussinesq equation of the form which includes
instability and dissipation is derived from this system.Comment: 8 pages, no figure
Speed of field driven domain walls in nanowires with large transverse magnetic anisotropy
Recent analytical and numerical work on field driven domain wall propagation
in nanowires has shown that for large transverse anisotropy and sufficiently
large applied fields the Walker profile becomes unstable before the breakdown
field, giving way to a slower stationary domain wall. We perform an asymptotic
expansion of the Landau Lifshitz Gilbert equation for large transverse magnetic
anisotropy and show that the asymptotic dynamics reproduces this behavior. At
low applied field the speed increases linearly with the field and the profile
is the classic Landau profile. Beyond a critical value of the applied field the
domain wall slows down. The appearance of a slower domain wall profile in the
asymptotic dynamics is due to a transition from a pushed to a pulled front of a
reaction diffusion equation.Comment: 8 page
Variational calculation of the period of nonlinear oscillators
The problem of calculating the period of second order nonlinear autonomous
oscillators is formulated as an eigenvalue problem. We show that the period can
be obtained from two integral variational principles dual to each other. Upper
and lower bounds on the period can be obtained to any desired degree of
accuracy. The results are illustrated by an application to the Duffing
equation.Comment: 7 page
Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation
We give an integral variational characterization for the speed of fronts of
the nonlinear diffusion equation with , and
in , which permits, in principle, the calculation of the exact
speed for arbitrary
On the speed of pulled fronts with a cutoff
We study the effect of a small cutoff on the velocity of a pulled
front in one dimension by means of a variational principle. We obtain a lower
bound on the speed dependent on the cutoff, and for which the two leading order
terms correspond to the Brunet Derrida expression. To do so we cast a known
variational principle for the speed of propagation of fronts in new variables
which makes it more suitable for applications.Comment: 12 pages no figure