Strong Linear Coupling Research Articles

Model reduction for an internally damped n-particle chain in a potential well under polyharmonic excitation

The study focuses on the model reduction of an internally damped chain of particles confined within a weakening potential well subjected to polyharmonic excitation to investigate the chain’s escape dynamics. The chain features strong linear coupling between particles and nonnegligible viscous damping forces arising from their relative motion. The potential well is modeled to have no energy dissipation, which means that damping arises solely from the internal interactions among particles and not from their motion through a resisting medium. Polyharmonic excitation frequencies are chosen to excite both the center of mass of the chain and at least one of the internally resonant frequencies, which are significantly higher than the linearized angular eigenfrequency of the center of mass within the well. The relative motion of the particles quickly reaches a steady state because of the non-small internal damping, allowing for the derivation of an efficient force field for the center of mass. Eliminating fast dynamics reduces the system’s degrees of freedom to one, employing a probabilistic approach based on the relative motion’s probability density function. The reduced 1 DoF model is appropriate for further investigation using various methods established in the literature.

Linear magnetoelectric coupling and type-II multiferroic order in NiMn2O4

We report an unexplored type-II multiferroic order in NiMn2O4, exhibiting strong linear magnetoelectric coupling above liquid-nitrogen (LN) temperature. The compound becomes ferroelectric at ∼100 K, coinciding with ferrimagnetic ordering, with a polarization value of ∼535 μC/m2 for a poling field of 5 kV/cm. At LN temperature, the polarization value increases linearly (∼21%) with a magnetic field up to 30 kOe. Rietveld refinement of neutron diffraction patterns reveals a ferrimagnetic model with antiparallel moments at tetrahedral and octahedral sites, as well as a canting of octahedral moment persisting up to ∼100 K. Low-temperature synchrotron diffraction confirms a step-like oxygen displacement during multiferroic ordering, suggesting that the Dzyaloshinskii–Moriya interaction polarizes the intervening oxygen atoms through magnetostriction, providing a microscopic mechanism for spontaneous electric polarization in this linear magnetoelectric multiferroic compound.

The 0:1 resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcation

We consider the non-semisimple 0:1 resonance (i.e., the unperturbed equilibrium has two purely imaginary eigenvalues ( and ) and a non-semisimple double-zero one) Hamiltonian bifurcation with one distinguished parameter, which corresponds to the supercritical Hamiltonian pitchfork bifurcation. Based on BCKV singularity theory established by Broer et al. (Z. Angew. Math. Phys. 44:389-432, 1993), this bifurcation essentially triggered by the reversible universal unfolding with respect to BCKV-restricted morphisms of the planar non-semisimple singularity (the is regarded as distinguished parameter with respect to the external parameter λ). We first give the plane bifurcation diagram of the integrable Hamiltonian on each level of integral in detail, which is related to the usual supercritical Hamiltonian pitchfork bifurcation. Then, we use the -symmetry generated by the additional pair of imaginary eigenvalues to reconstruct the above plane bifurcation phenomenon caused by the zero eigenvalue pair into the case with two degrees of freedom. Finally, we prove the persistence of typical bifurcation scenarios (e.g., 2-dimensional invariant tori and the symmetric homoclinic orbit) under the small Hamiltonian perturbations, as proposed by Broer et al. (Z Angew Math Phys 44: 389-432, 1993). An example system (the coupled Duffing oscillator) with strong linear coupling and weak local nonlinearity is given for this bifurcation.

A model framework to investigate the role of anomalous land surface processes in the amplification of summer drought across Ireland during 2018

AbstractDue to its latitude and ample year‐round rainfall, Ireland is typically an energy‐limited regime in the context of soil moisture availability and evapotranspiration. However, during the summer of 2018, regions within the country displayed significant soil moisture deficits, associated with anomalous atmospheric forcing conditions, with consequent impacts on the surface energy balance. Here, we explore the utility of a physically based land surface scheme coupled with observational, global gridded reanalysis and satellite‐derived data products to analyse the spatial and temporal evolution of the 2018 summer drought event in Ireland over grassland, which represents the dominant agricultural land‐cover. While the surface–air energy exchanges were initially dominated by atmospheric anomalies, soil moisture constraints became increasingly important in regulating these exchanges, as the accumulated rainfall deficit increased throughout the summer months. This was particularly evident over the freer draining soils in the east and southeast of the country. From late June 2018, we identify a strong linear coupling between soil moisture and both evapotranspiration and vegetation response, suggesting a shift from an energy‐limited evapotranspiration regime into a dry or soil water‐limited regime. Applying segmented regression models, the study quantifies a critical soil moisture threshold as a key determinant of the transition from wet to dry evaporative regimes. These findings are important to understand the soil moisture context under which land–atmosphere couplings are strongest in water‐limited regimes across the country and should help improve the treatment of soil parameters in weather prediction models, required for subseasonal and seasonal forecasts, consequently enhancing early warning systems of summer climate extremes in the future.

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators.

We analytically and numerically show that the Hillery-Zubairy’s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

Emergence of strong tunable linear Rashba spin-orbit coupling in two-dimensional hole gases in semiconductor quantum wells

Two-dimensional hole gases (2DHGs) in semiconductor quantum wells are promising platforms for spintronics and quantum computation, but suffer from the lack of the $\mathbf{k}$-linear term in the Rashba spin-orbit coupling (SOC), which is essential for spin manipulations without magnetism. The Rashba SOC in 2DHGs is commonly believed to be a $\mathbf{k}$-cubic term as the lowest order. Here, contrary to conventional wisdom, we taking Ge/Si system as an example uncover a strong and tunable $\mathbf{k}$-linear Rashba SOC in 2DHGs of semiconductor quantum wells (QWs) by performing atomistic pseudopotential calculations in conjunction with theoretical analysis based on the effective model Hamiltonian approach. We illustrate that this emergent $\mathbf{k}$-linear Rashba SOC is a first-order direct Rashba effect, originating from a combination of heavy-hole-light-hole mixing and direct dipolar coupling to the external electric field. The enhanced interband mixing renders [110]-oriented Ge/Si QWs a much stronger linear Rashba SOC than [001]-oriented counterpart with the maximal strength exceeding 120 meV\AA{}, comparable to the highest values reported in two-dimensional electron gases made by narrow band-gap III-V semiconductors, which suffers from short spin lifetime due to the presence of nuclear spin. These findings confirm Ge-based 2DHGs to be an excellent platform for large-scale quantum computation.

Digital Back Propagation via Sub-Band Processing in Spatial Multiplexing Systems

An advanced digital backward-propagation (DBP) method using a separate-channels approach (SCA) is investigated for the compensation of inter-channel nonlinearities in spatial- and wavelength-multiplexed systems. Compared to the conventional DBP, intra-, and inter-mode cross-phase modulation can be efficiently compensated by including the effect of the inter-channel walk-off in the nonlinear step of the split-step Fourier method. We found that the SCA-DBP relaxes the step size requirements by a factor of 10, while improving performance by 0.8 dB for large walk-off and strong linear coupling. For the first time, it is shown that in spatial multiplexed systems transmission performance can be improved by sub-band processing of back propagated channels.

Reconstructing coupled time series in climate systems using three kinds of machine-learning methods

Abstract. Despite the great success of machine learning, its application in climate dynamics has not been well developed. One concern might be how well the trained neural networks could learn a dynamical system and what will be the potential application of this kind of learning. In this paper, three machine-learning methods are used: reservoir computer (RC), backpropagation-based (BP) artificial neural network, and long short-term memory (LSTM) neural network. It shows that the coupling relations or dynamics among variables in linear or nonlinear systems can be inferred by RC and LSTM, which can be further applied to reconstruct one time series from the other. Specifically, we analyzed the climatic toy models to address two questions: (i) what factors significantly influence machine-learning reconstruction and (ii) how do we select suitable explanatory variables for machine-learning reconstruction. The results reveal that both linear and nonlinear coupling relations between variables do influence the reconstruction quality of machine learning. If there is a strong linear coupling between two variables, then the reconstruction can be bidirectional, and both of these two variables can be an explanatory variable for reconstructing the other. When the linear coupling among variables is absent but with the significant nonlinear coupling, the machine-learning reconstruction between two variables is direction dependent, and it may be only unidirectional. Then the convergent cross mapping (CCM) causality index is proposed to determine which variable can be taken as the reconstructed one and which as the explanatory variable. In a real-world example, the Pearson correlation between the average tropical surface air temperature (TSAT) and the average Northern Hemisphere SAT (NHSAT) is weak (0.08), but the CCM index of NHSAT cross mapped with TSAT is large (0.70). And this indicates that TSAT can be well reconstructed from NHSAT through machine learning. All results shown in this study could provide insights into machine-learning approaches for paleoclimate reconstruction, parameterization scheme, and prediction in related climate research.Highlights: i The coupling dynamics learned by machine learning can be used to reconstruct time series. ii Reconstruction quality is direction dependent and variable dependent for nonlinear systems. iii The CCM index is a potential indicator to choose reconstructed and explanatory variables. iv The tropical average SAT can be well reconstructed from the average Northern Hemisphere SAT.

Nonlinear propagation of pulses in multimode fiber with strong linear coupling

Multimode fiber has a richer spatial dimension than single-mode fiber, and is an ideal platform for studying many novel nonlinear effects. We established a strong linear coupling and short-range fiber model to understand the interactive effects of linear coupling and nonlinear effects. We find that strong linear coupling can compensate for the group delay between eigenmodes and cause energy fluctuation between modes which weakens the nonlinear effects. In high energy pulses, the interaction of linear coupling and nonlinear effects can help producing weak dispersion waves when the spectrum is broadened. Since linear coupling in a mode group is common and unavoidable, these results may provide a certain theoretical explanation for multi-mode nonlinear phenomena.

Non-Lagrangian approach for coupled complex Ginzburg-Landau systems with higher order-dispersion

It is known that after a particular distance of evolution in fiber lasers, two (input) asymmetric soliton like pulses emerge as two (output) symmetric pulses having same and constant energy. We report such a compensation technique in dispersion managed fiber lasers by means of a semi-analytical method known as collective variable approach (CVA) with including third-order dispersion (TOD). The minimum length of fiber laser, at which the output symmetric pulses are obtained from the input asymmetric ones, is calculated for each and every pulse parameters numerically by employing Runge-Kutta fourth order method. The impacts of intercore linear coupling, asymmetric nature of initial parameters and TOD on the evolution of pulse parameters and on the minimum length are also investigated. It is found that strong intercore linear coupling and asymmetric nature of input pulse parameters result in the reduction of fiber laser length. Also, the role of TOD tends to increase the width of the pulses as well as their energies. Besides, chaotic patterns and bifurcation points on the minimum length of the fiber owing to the impact of TOD are also reported in a nutshell.

Detection of Sectoral Modes in the Eclipsing Binary KIC 4851217

AbstractKIC 4851217 is a short period eclipsing binary (P = 2.47 days) in the field of the Kepler K1 mission. As well as variability caused by the eclipses, low-amplitude pulsations are also present in the data. A frequency analysis of the residual light-curve revealed δ Sct pulsations in the frequency range from 15–21 d−1 with amplitudes up to 3.5 mmag. Strong linear coupling (fi = fp + kforb) to orbital frequency was found, indicating tidally locked modes. From an analysis of 5 selected groups of frequencies we identified a radial mode on the secondary component, 3 dipole modes (l = |m| = 1), one of them present on the secondary component, and a quadrupole mode (l = |m| = 2), also located on the secondary component.

RISR‐N observations of the IMF By influence on reverse convection during extreme northward IMF

AbstractPrevious studies have demonstrated that the high‐latitude ionospheric convection is strongly influenced by the interplanetary magnetic field (IMF) direction. However, the temporal details of how the convection transitions from one state to another are still not understood completely. In this study, we analyze an interval on 12 September 2014 which provided a rare opportunity to examine dynamic variations in the dayside convection throat as the IMF transitioned from strong By+ to strong Bz+. Between 18:00 and 20:00 UT the northward face of the Resolute Bay Incoherent Scatter Radar (RISR‐N) rotated through the noon sector and directly measured strengthening reverse convection flows in the dayside throat region that peaked at ∼2800 m/s. Near‐simultaneous measurements from DMSP satellites confirm the magnitude of the reverse convection and its proximity to the cusp. Time series comparison of the RISR‐N north‐south flows with the IMF Bz component shows a remarkably high correlation, suggestive of strong linear coupling, with no sign of velocity saturation. Likewise, the east‐west flow variations were highly correlated with the changes in IMF By. However, time‐lagged correlation analysis reveals that the IMF By influence acted on a time scale 10 min shorter than that of the Bz component. As a consequence, the manner in which the convection transitioned from the strong By+ condition to the strong Bz+ condition is inconsistent with either the antiparallel or component reconnection models. Instead, we suggest that these particular observations are consistent with two separate reconnection sites on the magnetopause driven independently by the IMF By and Bz components.

Influence of the linear mode coupling on the nonlinear impairments in few-mode fibers

This paper is focused on the influence of the linear mode coupling caused by the fiber bending on the nonlinear distortions in a mode-division multiplexed system. The system under test utilizes the fundamental Gaussian mode and the conjugated first-order vortex modes propagating in the step-index fiber at the same wavelength. For such kind of system, the nonlinear impairments are caused mainly by the cross-phase and self-phase modulations. Propagation of the modal composition is described by the system of generalized coupled nonlinear Schrödinger equations, which serves as a basis of our simulations. Considering the nonlinear operator analytically, we show that it reaches its maximum value due to the power transfer between mode channels caused by the linear mode coupling. Simulation results for equal initial powers in NRZ-coded mode channels demonstrate that nonlinear signal impairments increase significantly for all mode channels in the case of strong linear mode coupling. In the case of weak linear coupling, the increase of nonlinear impairments was also observed, but this effect was appreciably weaker. Moreover, simulations show that the effect described above is stronger for the first-order modes than for the fundamental mode.

Synchronization of Goodwin's Oscillators under Boundedness and Nonnegativeness Constraints for Solutions

In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction, while the last product inhibits the first reaction in the chain. Goodwin's oscillators are used, in particular, to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this paper we point out that for Goodwin's oscillators, where the individual reactions have nonlinear (e.g. Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear synchronization protocol, where the control inputs are "saturated" by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong.

Going beyond the linear approximation in describing electron-phonon coupling: Relevance for the Holstein model

Using the momentum average approximation we study the importance of adding higher-than-linear terms in the electron-phonon coupling on the properties of single polarons described by a generalized Holstein model. For medium and strong linear coupling, even small quadratic electron-phonon coupling terms are found to lead to very significant quantitative changes in the properties of the polaron, which cannot be captured by a linear Holstein Hamiltonian with renormalized parameters. We argue that the bi-polaron phase diagram is equally sensitive to addition of quadratic coupling terms if the linear coupling is large. These results suggest that the linear approximation is likely to be inappropriate to model systems with strong electron-phonon coupling, at least for low carrier concentrations.

Characterization of affective states by pupillary dynamics and autonomic correlates.

With the recent advent of new recording devices and an easier access to signal processing tools, researchers are increasingly exploring and studying the Pupil Dilation (PD) signal. Recently, numerous studies pointed out the relations between PD dynamics and psychophysiological states. Although it is well known that PD is controlled by the Autonomic Nervous System (ANS), and ANS responses are related to emotional events/stimuli, the relationship between emotional states and PD is still an open issue. The aim of this study is to define the statistical properties of the PD signal, to understand its relation with ANS correlates such as Heart Rate Variability (HRV) and respiration (RESP), and to explore if PD could provide information for the evaluation of the psychophysiological response of ANS to affective triggering events. ECG, RESP, and PD data from 13 normal subjects were recorded during a memory recall paradigm, and processed with spectral and cross-spectral analysis. Our results demonstrate that variability indices extracted from fast PD oscillations, not observable through standard cardiorespiratory identification in the frequency domain, would be able to discern psychophysiological responses elicited by basic emotional stimuli. A strong linear coupling was found between the variables, due to the influence of RESP on both PD and HRV within the High Frequency (HF) band, from 0.15 to 0.45 Hz. Most importantly, our results point at PD features as possible candidates for characterizing basic emotional stimuli.

Reduction of Nonlinear Penalties Due to Linear Coupling in Multicore Optical Fibers

We present a general model for studying nonlinear effects in multicore fibers. Our results show that a strong linear coupling among fiber cores can reduce nonlinear impairments and improve system performance when digital signal processing is used to compensate for all linear degradations.

Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations

We investigate theoretically nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate the case where linear coupling among spatial modes of the fiber is weak and derive new Manakov equations after averaging over random birefringence fluctuations. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms vanish. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We verify the accuracy of new Manakov equations by simulating the transmission of multiple 114-Gb/s bit streams in the PDM-QPSK format over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equations. The agreement is excellent in all cases studied. A major benefit of the new Manakov equations is that they typically reduce the computation time by more than a factor of 10. Our results show that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. The extent of improvement depends on the fiber design and how many spatial modes are used for SDM transmission. We also consider the case where all spatial modes experience strong random linear coupling modeled using a random matrix. We derive new Manakov equations in this regime and show that the impact of some nonlinear effects can be reduced relatively to single-modes fibers. Finally, we extend our analysis to multicore fibers and show that the Manakov equations obtained in the strong- and weak-coupling regimes can still be used depending on the extent of coupling among fiber cores.

Symmetric and asymmetric solitons and vortices in linearly coupled two-dimensional waveguides with the cubic-quintic nonlinearity

It is well known that the two-dimensional (2D) nonlinear Schrödinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are stable for sufficiently large values of the norm. We study stationary localized modes in a symmetric linearly coupled system of two such equations, focusing on asymmetric states. The model may describe “optical bullets” in dual-core nonlinear optical waveguides (including spatiotemporal vortices that have not been discussed before), or a Bose–Einstein condensate (BEC) loaded into a “dual-pancake” trap. Each family of solutions in the single-component model has two different counterparts in the coupled system, one symmetric and one asymmetric. Similarly to the earlier studied coupled 1D system with the CQ nonlinearity, the present model features bifurcation loops, for fundamental and vortex solitons alike: with the increase of the total energy (norm), the symmetric solitons become unstable at a point of the direct bifurcation, which is followed, at larger values of the energy, by the reverse bifurcation restabilizing the symmetric solitons. However, on the contrary to the 1D system, both the direct and reverse bifurcation may be of the subcritical type, at sufficiently small values of the coupling constant, λ . Thus, the system demonstrates a double bistabilityfor the fundamental solitons. The stability of the solitons is investigated via the computation of instability growth rates for small perturbations. Vortex rings, which we study for two values of the “spin”, s = 1 and 2 , may be subject to the azimuthal instability, like in the single-component model. In particular, complete destabilization of asymmetric vortices is demonstrated for a sufficiently strong linear coupling. With the decrease of λ , a region of stable asymmetric vortices appears, and a single region of bistability for the vortices is found. We also develop a quasi-analytical approach to the description of the bifurcations diagrams, based on the variational approximation. Splitting of asymmetric vortices, induced by the azimuthal instability, is studied by means of direct simulations. Interactions between initially quiescent solitons of different types are studied too. In particular, we confirm the prediction of the reversal of the sign of the interaction (attractive/repulsive for in-phase/out-of-phase pairs) for the solitons with the odd spin, s = 1 , in comparison with the even values, s = 0 and 2.

Entanglement Concentration After a Multi-Interactions Channel

Different procedures have been developed in order to recover entanglement after propagation over a noisy channel. Besides a certain amount of noise, entanglement is completely lost and the channel is called entanglement breaking. Here we investigate both theoretically and experimentally an entanglement concentration protocol for a mixed three-qubit state outgoing from a strong linear coupling of two-qubit maximally entangled polarization state with another qubit in a completely mixed state. Thanks to such concentration procedure, the initial entanglement can be probabilistically recovered. Furthermore, we analyse the case of sequential linear couplings with many depolarized photons showing that thanks to the concentration a full recovering of entanglement is still possible.