Running and Tumbling Localized Structures: A Non-Brownian Motion.

Macroscopic systems present particle-type solutions. Spontaneous symmetry-breaking can cause these solutions to travel in different directions, and the inclusion of random fluctuations can induce them to run and tumble. We investigate the running and tumbling of localized structures observed on a prototype model of one-dimensional pattern formation with noise.

Nonreciprocal feedback induces migrating oblique and horizontal banded vegetation patterns in hyperarid landscapes.

In hyperarid environments, vegetation is highly fragmented, with plant populations exhibiting non-random biphasic structures where regions of high biomass density are separated by bare soil. In the Atacama Desert of northern Chile, rainfall is virtually nonexistent, but fog pushed in from the interior sustains patches of vegetation in a barren environment. Tillandsia landbeckii, a plant with no functional roots, survives entirely on fog corridors as a water source.

Topological defects law for migrating banded vegetation patterns in arid climates.

Self-organization and pattern formation are ubiquitous processes in nature. We study the properties of migrating banded vegetation patterns in arid landscapes, usually presenting dislocation topological defects. Vegetation patterns with dislocations are investigated in three different ecosystems.

Effect of heterogeneous environmental conditions on labyrinthine vegetation patterns.

Self-organization is a ubiquitous phenomenon in Nature due to the permanent balance between injection and dissipation of energy. The wavelength selection process is the main issue of pattern formation. Stripe, hexagon, square, and labyrinthine patterns are observed in homogeneous conditions.

Dancing vortices in a driven nematic liquid crystal cell: Theory and experiment.

The interaction of light beams with helical defects in optical materials generates optical vortices. Understanding and manipulating the dynamics of helical defects allows for the creation of versatile sources of optical vortex beams. Using a magnetic ring on a nematic liquid crystal cell, we trapped helical defects identified as matter vortices.

Controlled Transport Based on Multiorbital Aharonov-Bohm Photonic Caging.

The induction of synthetic magnetic fields on lattice structures allows an effective control of their localization and transport properties. In this Letter, we generate effective π magnetic fluxes on a multiorbital diamond lattice, where first-order (S) and second-order (P) modes effectively interact. We implement a z-scan method on femtosecond-laser-written photonic lattices and experimentally observe Aharonov-Bohm caging for S and P modes, as a consequence of a band transformation and the emergence of a spectrum composed of three degenerated flat bands.

Finger front propagation in smectic-A Fréedericksz transition.

Systems with multistability are characterized by exhibiting complex nonlinear waves between equilibria. Experimentally, near the smectic-A to chiral nematic transition in a liquid crystal mixture cell with planar anchoring, we observe finger fronts emerge in the smectic-A phase when applying an electric field, a reorientation transition. Finger fronts propagate in the direction orthogonal to the anchoring.

Gold nanoparticle-decorated earth-abundant clay nanotubes as catalyst for the degradation of phenothiazine dyes and reduction of 4-(4-nitrophenyl)morpholine.

In the present work, halloysite nanotubes modified with gold nanoparticles (AuNPs-HNT) are successfully prepared by wet chemical method for the catalytic degradation of phenothiazine dyes (azure B (AZB) and toluidine blue O (TBO)) and also cleaner reduction of 4-(4-nitrophenyl)morpholine (4NM) in the sodium borohydride (NaBH) media. The catalyst is formulated by modifying the HNT support with a 0.964% metal loading using the HNT supports modified with 3-aminopropyl-trimethoxysilane (APTMS) coupling agent to facilitate the anchoring sites to trap the AuNPs and to prevent their agglomeration/aggregation.

Localized states with nontrivial 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 nontrivial symmetries such as labyrinthine patterns are observed in different physical contexts.

Localized standing waves induced by spatiotemporal forcing.

Particle-type solutions are observed in out-of-equilibrium systems. These states can be motionless, oscillatory, or propagative depending on the injection and dissipation of energy. We investigate a family of localized standing waves based on a liquid-crystal light valve with spatiotemporal modulated optical feedback.

Localised labyrinthine patterns in ecosystems.

Self-organisation is a ubiquitous phenomenon in ecosystems. These systems can experience transitions from a uniform cover towards the formation of vegetation patterns as a result of symmetry-breaking instability. They can be either periodic or localised in space.

Nonreciprocal Coupling Induced Self-Assembled Localized Structures.

Chains of coupled oscillators exhibit energy propagation by means of waves, pulses, and fronts. Nonreciprocal coupling radically modifies the wave dynamics of chains. Based on a prototype model of nonlinear chains with nonreciprocal coupling to nearest neighbors, we study nonlinear wave dynamics.

Introduction to Focus Issue: Instabilities and nonequilibrium structures.

This Focus Issue on instabilities and nonequilibrium structures includes invited contributions from leading researchers across many different fields. The issue was inspired in part by the "VII Instabilities and Nonequilibrium Structures 2019" conference that took place at the Pontifica Universidad Católica de Valparaiso, Chile in December 2019. The conference, which is devoted to nonlinear science, is one of the oldest conferences in South America (since December 1985).

Topological transitions 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.

Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model.

We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density.

Deterministic Generation of Large Fock States.

We present a protocol to deterministically prepare the electromagnetic field in a large photon number state. The field starts in a coherent state and, through resonant interaction with one or few two-level systems, it evolves into a coherently displaced Fock state without any postselection. We show the feasibility of the scheme under realistic parameters.

Pulse propagation in a 1D array of excitable semiconductor lasers.

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers.

Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure.

A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato-Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures.

Colorimetry characterization of molecular reorientation transition in thin nematic cells.

The characterization of equilibria and their transition is fundamental in dynamic systems. Experimentally, the characterization of transitions is complex due to time scales separation, the effect of thermal fluctuations, and inherent experimental imperfections. Liquid crystal devices are derived from the manipulation of the molecular reorientation and transition between them by employing external electrical and magnetic fields.

Transition from nonradiative to radiative oscillons in parametrically driven systems.

Nonequilibrium systems exhibit particle-type solutions. Oscillons are one of the best-known localized states of systems with time-dependent forcing or parametrically driven systems. We investigate the transition from nonradiative to radiative oscillons in the parametrically driven sine-Gordon model in two spatial dimensions.

Front propagation steered by a high-wavenumber modulation: Theory and experiments.

Homogeneously driven dynamical systems exhibit multistability. Depending on the initial conditions, fronts present a rich dynamical behavior between equilibria. Qualitatively, this phenomenology is persistent under spatially modulated forcing.

Chaotic motion of localized structures.

Mobility properties of spatially localized structures arising from chaotic but deterministic forcing of the bistable Swift-Hohenberg equation are studied and compared with the corresponding results when the chaotic forcing is replaced by white noise. Short structures are shown to possess greater mobility, resulting in larger root-mean-square speeds but shorter displacements than longer structures. Averaged over realizations, the displacement of the structure is ballistic at short times but diffusive at larger times.

Weak signal enhancement by nonlinear 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 experimentally and theoretically a significant 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.