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M. Tlidi

Publications and source records attributed to M. Tlidi.

25 records · Page 2Linked to original sources

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.

nlin.PS↗

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.

nlin.PS↗

Delayed feedback control of self-mobile cavity solitons

Control of the motion of cavity solitons is one the central problems in nonlinear optical pattern formation. We report on the impact of the phase of the time-delayed optical feedback and carrier lifetime on the self-mobility of localized structures of light in broad area semiconductor cavities. We show both analytically and numerically that the feedback phase strongly affects the drift instability threshold as well as the velocity of cavity soliton motion above this threshold. In addition we demonstrate that non-instantaneous carrier response in the semiconductor medium is responsible for the increase in critical feedback rate corresponding to the drift instability.

nlin.PS↗

Strong interaction between plants induces circular barren patches: fairy circles

Vast landscapes extending from southern Angola, Namibia, and South Africa exhibit localised barren patches of vegetation called fairy circles. They consist of isolated or randomly distributed circular areas devoid of any vegetation. They are surrounded by fringes of tall grasses and are embedded in a sparse grassland on sandy soils. When the aridity increases, the size of the fairy circles increases and can reach diameters up to 10m. Although several hypotheses have been proposed, the origin of this phenomenon remains unsolved. We show that a simple non-local model of plant ecology based on realistic assumptions provides a quantitative explanation of this phenomenon. Fairy circles result from strong interaction between interfaces connecting two uniform covers: the uniform grassland and the bare states, and their stabilisation is attributed to the Lorentzian-like non-local coupling that models the competition between plants. The cause of their formation in thus rather inherent to the vegetation dynamics. Our analysis explain how a circular shape and fringes are formed, and how the aridity level influences the size of the fairy circles. In agreement with field observation, these theoretical findings, provide a link between a strong non-local interaction of plants and the formation of stable fairy circles. Finally, we show that the proposed mechanism is model-independent: indeed, it also applies to the reaction-diffusion type of model that emphasises the influence of water transport on the vegetation dynamics.

nlin.PS↗

Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures

In order to investigate the size limit on spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator containing an additional metamaterial layer in the cavity, allowing the nonlocal response of the material to become the dominating spatial process. In that case, our bifurcation analysis shows that this nonlocality imposes a new limit on the width of localized structures going beyond the traditional diffraction limit.

nlin.PS↗

Hyperbolic Transverse Patterns in Nonlinear Optical Resonators

We consider a nonlinear optical system in general, and a broad aperture laser in particular in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic Maxwell-Bloch equations, where the spatial coupling is provided by the DAlambert operator rather than by the Laplace operator. We show that this system supports hyperbolic transverse patterns residing on hyperbolas in far field domain, and consisting of stretched vortices in near field domain. These structures are described analytically by normal form analysis, and investigated numerically.

physics.optics↗

Bistability between different dissipative solitons in nonlinear optics

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer, and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. Quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The dependence of the phenomena on the other relevant parameters is discussed.

nlin.PS↗