501 research outputs found
Turing Instability in a Boundary-fed System
The formation of localized structures in the chlorine dioxide-idodine-malonic
acid (CDIMA) reaction-diffusion system is investigated numerically using a
realistic model of this system. We analyze the one-dimensional patterns formed
along the gradients imposed by boundary feeds, and study their linear stability
to symmetry-breaking perturbations (Turing instability) in the plane transverse
to these gradients. We establish that an often-invoked simple local linear
analysis which neglects longitudinal diffusion is inappropriate for predicting
the linear stability of these patterns. Using a fully nonuniform analysis, we
investigate the structure of the patterns formed along the gradients and their
stability to transverse Turing pattern formation as a function of the values of
two control parameters: the malonic acid feed concentration and the size of the
reactor in the dimension along the gradients. The results from this
investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review
Cross-Newell equations for hexagons and triangles
The Cross-Newell equations for hexagons and triangles are derived for general
real gradient systems, and are found to be in flux-divergence form. Specific
examples of complex governing equations that give rise to hexagons and
triangles and which have Lyapunov functionals are also considered, and explicit
forms of the Cross-Newell equations are found in these cases. The general
nongradient case is also discussed; in contrast with the gradient case, the
equations are not flux-divergent. In all cases, the phase stability boundaries
and modes of instability for general distorted hexagons and triangles can be
recovered from the Cross-Newell equations.Comment: 24 pages, 1 figur
Amplitude equations near pattern forming instabilities for strongly driven ferromagnets
A transversally driven isotropic ferromagnet being under the influence of a
static external and an uniaxial internal anisotropy field is studied. We
consider the dissipative Landau-Lifshitz equation as the fundamental equation
of motion and treat it in ~dimensions. The stability of the spatially
homogeneous magnetizations against inhomogeneous perturbations is analyzed.
Subsequently the dynamics above threshold is described via amplitude equations
and the dependence of their coefficients on the physical parameters of the
system is determined explicitly. We find soft- and hard-mode instabilities,
transitions between sub- and supercritical behaviour, various bifurcations of
higher codimension, and present a series of explicit bifurcation diagrams. The
analysis of the codimension-2 point where the soft- and hard-mode instabilities
coincide leads to a system of two coupled Ginzburg-Landau equations.Comment: LATeX, 25 pages, submitted to Z.Phys.B figures available via
[email protected] in /pub/publications/frank/zpb_95
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