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

On localized vegetation patterns, fairy circles and localized patches in arid landscapes

We investigate the formation of localized structures with a varying width in one and two-dimensional systems. The mechanism of stabilization is attributed to strong nonlocal coupling mediated by a Lorentzian type of Kernel. We show that, in addition to stable dips found recently [see, e.g., C. Fernandez-Oto, M. G. Clerc, D. Escaff, and M. Tlidi, Phys. Rev. Lett. {\bf{110}}, 174101 (2013)], exist stable localized peaks which appear as a result of strong nonlocal coupling, i.e. mediated by a coupling that decays with the distance slower than an exponential. We applied this mechanism to arid ecosystems by considering a prototype model of a Nagumo type. In one-dimension, we study the front that connects the stable uniformly vegetated state with the bare one under the effect of strong nonlocal coupling. We show that strong nonlocal coupling stabilizes both---dip and peak---localized structures. We show analytically and numerically that the width of localized dip, which we interpret as fairy circle, increases strongly with the aridity parameter. This prediction is in agreement with filed observations. In addition, we predict that the width of localized patch decreases with the degree of aridity. Numerical results are in close agreement with analytical predictions

Bouncing localized structures in a liquid-crystal light-valve experiment

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported.Comment: 4 page

Extreme events prediction from nonlocal partial information in a spatiotemporally chaotic microcavity laser

The forecasting of high-dimensional, spatiotemporal nonlinear systems has made tremendous progress with the advent of model-free machine learning techniques. However, in real systems it is not always possible to have all the information needed; only partial information is available for learning and forecasting. This can be due to insufficient temporal or spatial samplings, to inaccessible variables or to noisy training data. Here, we show that it is nevertheless possible to forecast extreme events occurrence in incomplete experimental recordings from a spatiotemporally chaotic microcavity laser using reservoir computing. Selecting regions of maximum transfer entropy, we show that it is possible to get higher forecasting accuracy using nonlocal data vs local data thus allowing greater warning times, at least twice the time horizon predicted from the nonlinear local Lyapunov exponent

Dielectric resonances of lattice animals and other fractal structures

Electrical and optical properties of binary inhomogeneous media are currently modelled by a random network of metallic bonds (conductance $\sigma_0$, concentration $p$) and dielectric bonds (conductance $\sigma_1$, concentration $1-p$). The macroscopic conductivity of this model is analytic in the complex plane of the dimensionless ratio $h=\sigma_1/\sigma_0$ of the conductances of both phases, cut along the negative real axis. This cut originates in the accumulation of the resonances of clusters with any size and shape. We demonstrate that the dielectric response of an isolated cluster, or a finite set of clusters, is characterised by a finite spectrum of resonances, occurring at well-defined negative real values of $h$, and we define the cross-section which gives a measure of the strength of each resonance. These resonances show up as narrow peaks with Lorentzian line shapes, e.g. in the weak-dissipation regime of the $RL-C$ model. The resonance frequencies and the corresponding cross-sections only depend on the underlying lattice, on the geometry of the clusters, and on their relative positions. Our approach allows an exact determination of these characteristics. It is applied to several examples of clusters drawn on the square lattice. Scaling laws are derived analytically, and checked numerically, for the resonance spectra of linear clusters, of lattice animals, and of several examples of self-similar fractals.Comment: 25 pages, plain TeX. Figures (hard copies) available upon request, to appear in the Journal of Physics

Long-term effects of rotational wetland mowing on breeding birds: evidence from a 30-year experiment

Wetlands are amongst the richest, yet most threatened types of habitats on Earth. One major threat is the modification of water regime for human activities, which disrupts normal ecosystem equilibrium. In lacustrine wetlands, reduced flooding allows shrubs to take over, ultimately leading to a shift towards woody communities. To counter this, wetland managers have initiated a variety of measures, including mowing, burning, and pasturing. Because of the short time frames of previous studies on the subject, little is known on their potential negative side effects on the ecosystem. Here, we evaluate the long-term effect of mowing on breeding populations of the five most abundant species in our central European study area (the reed warbler Acrocephalus scirpaceus, the common reed bunting Emberiza schoeniclus, Savi’s warbler Locustella luscinioides, the water rail Rallus aquaticus, and the bearded reedling Panurus biarmicus). This study, of an unprecedented time scale (30 years), shows that rotational mowing has no long-term detrimental effects on birds. However, optimal mowing regime for the birds might often be less frequent than what is usually applied. We recommend that mowing be spaced every 3 years at least, and ideally every 6 years or more. We discuss additional measures that could be implemented to complement mowing. Because of the widespread distribution of the target habitat and species, our study provides readily applicable information for wetland managers in Europe and worldwide