Statistics of vector Manakov rogue waves.

We present a statistical analysis based on the height and return-time probabilities of high-amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational or semirational solutions, associated with extreme, rogue wave (RW) structures, are the leading high-amplitude events in this system. We define the thresholds for classifying an extreme wave event as a RW. Our results indicate that there is a strong relationship between the type of RW and the mechanism which is responsible for its creation. Initially, high-amplitude events originate from modulation instability. Upon subsequent evolution, the interaction among these events prevails as the mechanism for RW creation. We suggest a strategy for confirming the basic properties of different extreme events. This involves the definition of proper statistical measures at each stage of the RW dynamics. Our results point to the need for redefining criteria for identifying RW events.

Real-time chest-wall-motion tracking by a single optical fibre grating: a prospective method for ventilator triggering.

OBJECTIVE: The ventilators involved in non-invasive mechanical ventilation commonly provide ventilator support via a facemask. The interface of the mask with a patient promotes air leaks that cause errors in the feedback information provided by a pneumatic sensor and hence patient-ventilator asynchrony with multiple negative consequences. Our objective is to test the possibility of using chest-wall motion measured by an optical fibre-grating sensor as a more accurate non-invasive ventilator triggering mechanism. APPROACH: The basic premise of our approach is that the measurement accuracy can be improved by using a triggering signal that precedes pneumatic triggering in the neuro-ventilatory coupling sequence. We propose a technique that uses the measurement of chest-wall curvature by a long-period fibre-grating sensor. The sensor was applied externally to the rib-cage and interrogated in the lateral (edge) filtering scheme. The study was performed on 34 healthy volunteers. Statistical data analysis of the time lag between the fibre-grating sensor and the reference pneumotachograph was preceded by the removal of the unwanted heartbeat signal by wavelet transform processing. MAIN RESULTS: The results show a consistent fibre-grating signal advance with respect to the standard pneumatic signal by (230 ± 100) ms in both the inspiratory and expiratory phases. We further show that heart activity removal yields a tremendous improvement in sensor accuracy by reducing it from 60 ml to 0.3 ml. SIGNIFICANCE: The results indicate that the proposed measurement technique may lead to a more reliable triggering decision. Its imperviousness to air leaks, non-invasiveness, low-cost and ease of implementation offer good prospects for applications in both clinical and homecare ventilation.

Models of spin-orbit-coupled oligomers.

We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.

Influence of disorder on generation and probability of extreme events in Salerno lattices.

Extreme events (EEs) in nonlinear and/or disordered one-dimensional photonic lattice systems described by the Salerno model with on-site disorder are studied. The goal is to explain particular properties of these phenomena, essentially related to localization of light in the presence of nonlinear and/or nonlocal couplings in the considered systems. Combining statistical and nonlinear dynamical methods and measures developed in the framework of the theory of localization phenomena in disordered and nonlinear systems, particularities of EEs are qualitatively clarified. Findings presented here indicate that the best environment for EEs' creation are disordered near-integrable Salerno lattices. In addition, it is been shown that the leading role in the generation and dynamical properties of EEs in the considered model is played by modulation instability, i.e., by nonlinearities in the system, although EEs can be induced in linear lattices with on-site disorder too.

Soliton nanoantennas in two-dimensional arrays of quantum dots.

We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schrödinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nano-antenna, which is stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.

Rib-cage-movement measurements as a potential new trigger signal in non-invasive mechanical ventilation.

Non-invasive ventilation performed through an oronasal mask is a standard in clinical and homecare mechanical ventilation. Besides all its advantages, inevitable leaks through the mask cause errors in the feedback information provided by the airflow sensor and, hence, patient-ventilator asynchrony with multiple negative consequences. Here we investigate a new way to provide a trigger to the ventilator. The method is based on the measurement of rib cage movement at the onset of inspiration and during breathing by fibre-optic sensors. In a series of simultaneous measurements by a long-period fibre grating sensor and pneumotachograph we provide the statistical evidence of the 200 ms lag of the pneumo with respect the fibre-optic signal. The lag is registered consistently across three independent delay metrics. Further, we discuss exceptions from this trend and identify the needed improvements to the proposed fibre-sensing scheme.

Non-invasive respiratory monitoring using long-period fiber grating sensors.

In non-invasive ventilation, continuous monitoring of respiratory volumes is essential. Here, we present a method for the measurement of respiratory volumes by a single fiber-grating sensor of bending and provide the proof-of-principle by applying a calibration-test measurement procedure on a set of 18 healthy volunteers. Results establish a linear correlation between a change in lung volume and the corresponding change in a local thorax curvature. They also show good sensor accuracy in measurements of tidal and minute respiratory volumes for different types of breathing. The proposed technique does not rely on the air flow through an oronasal mask or the observation of chest movement by a clinician, which distinguishes it from the current clinical practice.

Interface solitons in locally linked two-dimensional lattices.

Existence, stability, and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel two-dimensional (2D) lattices, are investigated. The system with the onsite cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schrödinger equations linearly coupled at the single site. Symmetric, antisymmetric, and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.

Extreme events in discrete nonlinear lattices.

We perform statistical analysis on discrete nonlinear waves generated through modulational instability in the context of the Salerno model that interpolates between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrödinger equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.

Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation.

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce "model 1" (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. "Model 2," which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

Left-handed metamaterials with saturable nonlinearity.

The left-handed properties of metamaterials with saturable nonlinearity are analyzed with respect to their electromagnetic response as a function of externally varying parameters. We demonstrate that the response of the medium is strongly affected by the saturation of the nonlinear effects. The last can be exploited to modulate the amplitude or tune the frequency of the response. Moreover, the existence of bistability regions in large parts of the external parameter space allows for switching between different magnetization states, with either positive or negative response. The stability issue of multiple possible states is addressed through modulational instability analysis of plane wave envelopes in each of those states.