124 research outputs found
Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
Localised structures in dissipative appears in various fields of natural
science such as biology, chemistry, plant ecology, optics and laser physics.
The proposed theme issue is to gather specialists from various fields of
non-linear science toward a cross-fertilisation among active areas of research.
This is a cross-disciplinary area of research dominated by the nonlinear optics
due to potential applications for all-optical control of light, optical
storage, and information processing. This theme issue contains contributions
from 18 active groups involved in localized structures field and have all made
significant contributions in recent years.Comment: 14 pages, 0 figure, submitted to Phi. Trasaction Royal Societ
Plant clonal morphologies and spatial patterns as self-organized responses to resource-limited environments
We propose here to interpret and model peculiar plant morphologies (cushions,
tussocks) observed in the Andean altiplano as localized structures. Such
structures resulting in a patchy, aperiodic aspect of the vegetation cover are
hypothesized to self-organize thanks to the interplay between facilitation and
competition processes occurring at the scale of basic plant components
biologically referred to as 'ramets'. (Ramets are often of clonal origin.) To
verify this interpretation, we applied a simple, fairly generic model (one
integro-differential equation) emphasizing via Gaussian kernels non-local
facilitative and competitive feedbacks of the vegetation biomass density on its
own dynamics. We show that under realistic assumptions and parameter values
relating to ramet scale, the model can reproduce some macroscopic features of
the observed systems of patches and predict values for the inter-patch distance
that match the distances encountered in the reference area (Sajama National
Park in Bolivia). Prediction of the model can be confronted in the future to
data on vegetation patterns along environmental gradients as to anticipate the
possible effect of global change on those vegetation systems experiencing
constraining environmental conditions.Comment: 14 pages, 6figure
Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion
In the limit of large diffusivity ratio, spot-like solutions in the
two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are
studied. It is shown analytically that such spots undergo an instability as the
diffusivity ratio is decreased. An instability threshold is derived. For spots
of small radius, it is shown that this instability leads to a spot splitting
into precisely two spots. For larger spots, it leads to deformation, fingering
patterns and space-filling curves. Numerical simulations are shown to be in
close agreement with the analytical predictions.Comment: To appear, PR
Homoclinic snaking in bounded domains
Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of how this occurs depend critically on the choice of boundary conditions. With periodic boundary conditions the snaking branches terminate on a branch of spatially periodic states. However, with non-Neumann boundary conditions they turn continuously into a large amplitude filling state that replaces the periodic state. This behavior, shown here in detail for the Swift-Hohenberg equation, explains the phenomenon of “snaking without bistability”, recently observed in simulations of binary fluid convection by Mercader, Batiste, Alonso and Knobloch (preprint)
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