arXiv subjects

Marcel G. Clerc

Publications and source records attributed to Marcel G. Clerc.

At least 19 recordsLinked to original sources

arXiv2025

Energy minimizers in a periodic phase transition model of light-matter interaction in nematic liquid crystals

In this paper we complete the study of global minimizers of a forced, non autonomous, one dimensional, phase transition model, initiated in [8]. Motivated by the recent findings in [9], revealing new configurations of topological structures in light, we consider a forcing term having two periods. We show that depending on the strength of the forcing, at most two thresholds that determine the structure of the minimizers (kinks) are attained. These kinks are now a combination of the previous types encountered in [8], and they may have at most three zeros. The existence of these complex types of phase transition follows from a periodic one dimensional model of matter-light interaction in nematic liquid crystal based on a thin sample limit of the Oseen-Frank energy. We show that the qualitative behaviour of global minimizers is consistent with the original model.

math.AP↗

arXiv2025

Quasi-reversible parametric instability in presence of noise

We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the inclusion of fluctuations. Experimentally, we observe the modification of the bifurcation diagram of parametrically amplified surface waves as spatiotemporal fluctuations stemming from an underlying vortex flow are included. Theoretically, we characterize the noise-dependent effective dynamics in a model system, the parametrically driven nonlinear Schrödinger equation, subjected to noise which allows us to rationalize the effect of the underlying vortex flow on the surface waves

nlin.PS↗

arXiv2024

Noise-induced nonreciprocal topological dissipative solitons in directionally coupled chains and lattices

Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear convective instabilities in nonlinear systems that drive topological dissipative solitons in a single direction, producing a lossless information transmission. Considering fluctuations, which are intrinsic to every macroscopic dynamical system, noise-sustained structures emerge permanently in time. Here, we study arrays of nonreciprocally coupled bistable systems exhibiting noise-sustained topological phase wall (or soliton) dynamics. The bifurcations between different steady states are analytically addressed, and the properties of the noise-sustained states are unveiled as a function of the reciprocal and nonreciprocal coupling parameters. Furthermore, we study critical points where the structures' characteristic size diverges with different power law exponents. Our numerical results agree with the theoretical findings.

nlin.PS↗

arXiv2021

Localized states with non-trivial symmetries: localized labyrinthine patterns

The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial symmetries such as labyrinthine patterns are observed in different physical contexts. Here we report stable localized disordered patterns in spatially extended dissipative systems. These 2D and 3D localized structures consist of an isolated labyrinth embedded in a homogeneous steady state. Their partial bifurcation diagram allows us to explain this phenomenon as a manifestation of a pinning-depinning transition. We illustrate our findings on Swift-Hohenberg type of equations and other well-established models for plant ecology, nonlinear optics, and reaction-diffusion systems.

nlin.PS↗

arXiv2021

A quasi-periodic route to chaos in a parametrically driven nonlinear medium

Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped nonlinear oscillators, we investigate a route to spatiotemporal chaos emerging from standing waves. The route from the stationary to the chaotic state proceeds through quasiperiodic dynamics. The standing wave undergoes the onset of oscillatory instability, which subsequently exhibits a different critical frequency, from which the complexity originates. A suitable amplitude equation, valid close to the parametric resonance, makes it possible to produce universe results. The respective phase-space structure and bifurcation diagrams are produced in a numerical form. We characterize the relevant dynamical regimes by means of the largest Lyapunov exponent, the power spectrum, and the evolution of the total intensity of the wave field.

nlin.CD↗

arXiv2020

Exotic states of matter in an oscillatory driven liquid crystal cell

Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose- Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. Here we investigate topological states of matter in a system with injection and dissipation of energy. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from non-vortex state to a state in which vortices persist. Depending on the period and the type of the forcing, the vortices self-organise forming square lattices, glassy states, and disordered vortex structures. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states.

cond-mat.soft↗

arXiv2019

Engineered discreteness enables observation and control of chimera-like states in a system with local coupling

Chimera states -- named after the mythical beast with a lion's head, a goat's body, and a dragon's tail -- correspond to spatiotemporal patterns characterised by the coexistence of coherent and incoherent domains in coupled systems. They were first identified in 2002 in theoretical studies of spatially extended networks of Stuart-Landau oscillators, and have been subject to extensive theoretical and experimental research ever since. While initially considered peculiar to networks with weak nonlocal coupling, recent theoretical studies have predicted that chimera-like states can emerge even in systems with purely local coupling. Here we report on the first experimental observations of chimera-like states in a system with local coupling -- a coherently-driven Kerr nonlinear optical resonator. We show that artificially engineered discreteness -- realised by suitably modulating the coherent driving field -- allows for the nonlinear localisation of spatiotemporal complexity, and we demonstrate unprecedented control over the existence, characteristics, and dynamics of the resulting chimera-like states. Moreover, using ultrafast time lens imaging, we resolve the chimeras' picosecond-scale internal structure in real time.

physics.optics↗

arXiv2019

Weak signal enhancement by non-linear resonance control in a forced nano-electromechanical resonator

Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance whereby a weak low-frequency signal applied to a bistable resonator can be amplified by driving the non-linear oscillator with another appropriately-adjusted non-resonant high-frequency field. Here we demonstrate the resonant enhancement of a weak signal by use of a vibrational force yet in a monostable system consisting of a driven nano-electromechanical nonlinear resonator. The oscillator is subjected to a strong quasi-resonant drive and to two additional tones: a weak signal at lower frequency and a non-resonant driving at an intermediate frequency. We show experimentally and theoretically a significant enhancement of the weak signal thanks to the occurence of vibrational resonance enabled by the presence of the intermediate frequency driving. We analyse this phenomenon in terms of coherent nonlinear resonance manipulation. Our results illustrate a general mechanism which may have applications in the fields of radio-frequency signal processing or sensing for instance.

physics.app-ph↗

arXiv2019

The connecting solution of the Painlevé phase transition model

The second Painlevé O.D.E. $y''-xy-2y^3=0$, $x\in \mathbb{R},$ is known to play an important role in the theory of integrable systems, random matrices, Bose-Einstein condensates and other problems. The generalized second Painlevé equation $Δy -x_1 y - 2 y^3=0$, $(x_1,x_2)\in \mathbb{R}^2$, is obtained by multiplying by $-x_1$ the linear term $u$ of the Allen-Cahn equation $Δu =u^3-u$. It involves a non autonomous potential $H(x_1,y)$ which is bistable for every fixed $x_1<0$, and thus describes as the Allen-Cahn equation a phase transition model. The scope of this paper is to construct a solution $y$ connecting along the vertical direction $x_2$, the two branches of minima of $H$ parametrized by $x_1$. This solution plays a similar role that the heteroclinic orbit for the Allen-Cahn equation. It is the the first to our knowledge solution of the Painlevé P.D.E. both relevant from the applications point of view (liquid crystals), and mathematically interesting.

math.AP↗

arXiv2018

Gradient theory of domain walls in thin, nematic liquid crystals films

In this paper we describe domain walls appearing in a thin, nematic liquid crystal sample subject to an external field with intensity close to the Fréedericksz transition threshold. Using the gradient theory of the phase transition adopted to this situation, we show that depending on the parameters of the system, domain walls occur in the bistable region or at the border between the bistable and the monostable region.

math.AP↗

arXiv2018

Phase Stochastic Resonance in a forced nano-electromechanical oscillator

Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced nano-electromechanical membrane by evidencing the enhancement of a weak phase modulated signal thanks to the addition of phase noise. Based on a general forced Duffing oscillator model, we demonstrate experimentally and theoretically that phase noise acts multiplicatively inducing important physical consequences. These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.

physics.optics↗

arXiv2017

Extended patchy ecosystems may increase their total biomass through self-replication

Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as localized structures. Previous findings have shown that such localized structures can self-replicate in a binary fashion, where a single vegetation patch elongates and divides into two new patches. Here, we extend these previous results by considering the more general case, where the plants interact non-locally, this extension adds an extra level of complexity and shrinks the gap between the model and real ecosystems, where it is known that the plant-to-plant competition through roots and above-ground facilitating interactions have non-local effects, i.e. they extend further away than the nearest neighbor distance. Through numerical simulations, we show that for a moderate level of aridity, a transition from a single patch to periodic pattern occurs. Moreover, for large values of the hydric stress, we predict an opposing route to the formation of periodic patterns, where a homogeneous cover of vegetation may decay to spot-like patterns. The evolution of the biomass of vegetation patches can be used as an indicator of the state of an ecosystem, this allows to distinguish if a system is in a self-replicating or decaying dynamics. In an attempt to relate the theoretical predictions to real ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation forms patches of tens of meters in diameter. We show that the properties of the patches together with their spatial distributions are consistent with the self-organization hypothesis. We argue that the characteristics of the observed landscapes may be a consequence of patch self-replication, however, detailed field and temporal data is fundamental to assess the real state of the ecosystems.

nlin.PS↗

arXiv2016

Slanted snaking of localized Faraday waves

We report on an experimental, theoretical and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume, and introduce a universal model based on symmetry arguments, which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.

nlin.PS↗

arXiv2016

Optical textures: characterizing spatiotemporal chaos

Macroscopic systems subjected to injection and dissipation of energy can exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Here, we report a one and two dimensional pattern forming set up, which exhibits a transition from stationary patterns to spatiotemporal chaotic textures, based on a nematic liquid crystal layer with spatially modulated input beam and optical feedback. Using an adequate projection of spatiotemporal diagrams, we determine the largest Lyapunov exponent. Jointly, this exponent and Fourier transform allow us to distinguish between spatiotemporal chaos and amplitude turbulence concepts, which are usually merged.

nlin.PS↗

arXiv2016

Berry phase of light Bragg-reflected by chiral liquid crystal media

Berry phase is revealed for circularly polarized light when it is Bragg-reflected by a chiral liquid crystal medium of the same handedness. By using a chiral nematic layer we demonstrate that if the input plane of the layer is rotated with respect to a fixed reference frame, then, a geometric phase effect occurs for the circularly polarized light reflected by the periodic helical structure of the medium. Theory and numerical simulations are supported by an experimental observation, disclosing novel applications in the field of optical manipulation and fundamental optical phenomena.

physics.optics↗

arXiv2015

Spatiotemporal chaos induces extreme events in an extended microcavity laser

Extreme events such as rogue wave in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme events appearance in a spatially extended semiconductor microcavity laser with intracavity saturable absorber. This system can display deterministic irregular dynamics only thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor.

nlin.CD↗

arXiv2015

Spin-transfer-driven nano-oscillators are equivalent to parametric resonators

The equivalence between different physical systems permits us to transfer knowledge between them and to characterize the universal nature of their dynamics. We demonstrate that a nanopillar driven by a spin-transfer torque is equivalent to a rotating magnetic plate, which permits us to consider the nanopillar as a macroscopic system under a time-modulated injection of energy, that is, a simple parametric resonator. This equivalence allows us to characterize the phases diagram and to predict magnetic states and dynamical behaviors, such as solitons, stationary textures, and oscillatory localized states, among others. Numerical simulations confirm these predictions.

cond-mat.mes-hall↗

arXiv2008

Transversal interface dynamics of a front connecting a stripe pattern to a uniform state

Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical Swift-Hohenberg equation, show that this interface has transversal spatial periodic structures, zigzag dynamics and complex coarsening process. Close to a spatial bifurcation, an amended amplitude equation and a one-dimensional interface model allow us to characterize the dynamics exhibited by this interface.

nlin.PS↗