Linear Coupling Research Articles

Linear coupling-related pulse splitting in fiber lasers.

We demonstrate a unique pulse-splitting mechanism dominated by the linear coupling between two vector modes in a mode-locked fiber laser using polarization-maintaining fiber. As the linear coupling strength increases, the pulse experiences larger perturbations and manifests as stronger spectral sidebands. Correspondingly, the temporal pedestals possessing a higher intensity become untrapped and eventually evolve into a stable pulse. Such linear coupling-related pulse splitting is ubiquitous both in normal- and anomalous-dispersion regimes, fundamentally differing from that induced by the excessive nonlinear phase shift. Experimental observations fully sustain numerical results and provide a flexible approach to managing the number and energy of vector solitons.

Exponential synchronization of 2D cellular neural networks with boundary feedback

In this work we propose a new mathematical model of 2D cellular neural networks (CNN) in terms of the lattice FitzHugh-Nagumo equations with boundary feedback. The model features discrete Laplacian operators and periodic boundary feedback instead of the interior-clamped or mean-field feedback. We first prove the globally dissipative dynamics of the solutions through a priori uniform estimates. In the main result we show that the 2D cellular neural networks are exponentially synchronized if the computable threshold condition is satisfied by the synaptic gap signals of pairwise boundary cells of the grid and the system parameters with a linear feedback coupling coefficient tunable in applications.

Cooperative model predictive control for Wave Energy Converter arrays

It is well known that commercial Wave Energy Converters (WECs) are likely to be deployed in arrays, which gives the possibility to enhance the energy harvesting properties of the wave farm as a whole. Advanced control strategies are necessary to exploit the potential and capture as much energy as possible in a limited sea space. Centralized control is a natural benchmark, as it sees the array as a large-scale system, making energy maximization a large plantwide problem. However, centralized control has a high requirement for computational efficiency. In this paper, a cooperative model predictive control (MPC) is proposed to achieve energy maximization while reducing computational cost. A modified array model is constructed to capture the dynamics of interactions in arrays, explicitly showing the linear couplings in the system state, control input, and excitation force of each subsystem. Sensitivity analyses are performed to evaluate the performance for different array layouts, separation distances, and sea states. The results show that cooperative MPC can achieve an energy capture performance that approximates centralized MPC, outperforming decentralized MPC significantly, and is well adapted to sea states. Furthermore, the proposed method has the potential to improve computational efficiency by 14.86%–51.14% for simulations in the study.

A phenomenological model of whole brain dynamics using a network of neural oscillators with power-coupling

We present a general, trainable oscillatory neural network as a large-scale model of brain dynamics. The model has a cascade of two stages - an oscillatory stage and a complex-valued feedforward stage - for modelling the relationship between structural connectivity and functional connectivity from neuroimaging data under resting brain conditions. Earlier works of large-scale brain dynamics that used Hopf oscillators used linear coupling of oscillators. A distinctive feature of the proposed model employs a novel form of coupling known as power coupling. Oscillatory networks based on power coupling can accurately model arbitrary multi-dimensional signals. Training the lateral connections in the oscillator layer is done by a modified form of Hebbian learning, whereas a variation of the complex backpropagation algorithm does training in the second stage. The proposed model can not only model the empirical functional connectivity with remarkable accuracy (correlation coefficient between simulated and empirical functional connectivity- 0.99) but also identify default mode network regions. In addition, we also inspected how structural loss in the brain can cause significant aberration in simulated functional connectivity and functional connectivity dynamics; and how it can be restored with optimized model parameters by an in silico perturbational study.

Solvable limits of a class of generalized vector nonlocal nonlinear schrödinger equation with balanced loss-gain

We consider a class of one dimensional Vector Nonlocal Non-linear Schrödinger equation (VNNLSE) in an external complex potential with time-modulated Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of Schrödinger fields, and space-time dependent nonlinear strength. The system admits Lagrangian and Hamiltonian formulations under certain conditions. It is shown that various dynamical variables like total power, -symmetric Hamiltonian, width of the wave-packet and its speed of growth, etc are real-valued despite the Hamiltonian density being complex-valued. We study the exact solvability of the generic VNNLSE with or without a Hamiltonian formulation. In the first part, we study time-evolution of moments which are analogous to space-integrals of Stokes variables and find condition for existence of solutions which are bounded in time. In the second part, we use a non-unitary transformation followed by a coordinate transformation to map the VNNLSE to various solvable equations. The coordinate transformation is not required at all for the limiting case when non-unitary transformation reduces to pseudo-unitary transformation. The exact solutions are bounded in time for the same condition which is obtained through the study of time-evolution of moments. Various exact solutions of the VNNLSE are presented.

The phenomenology of quadratically coupled ultra light dark matter

We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay. We review the different experiments that can probe such interactions and present the current and expected future bounds on the parameter space. In particular, we discuss the scalar field solution presented in [A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6, 064051], and extend it to theories that capture both the linear and the quadratic couplings of the Dark Matter (DM) field to the Standard Model (SM). Furthermore, we discuss the theoretical aspects and the corresponding challenges for natural models in which the quadratic interactions are of phenomenological importance.

Linear coupling and tune adjustment for the 500 MeV cyclotron

Linear coupling and tune adjustment for the 500 MeV cyclotron

LVC/MM: A Hybrid Linear Vibronic Coupling/Molecular Mechanics Model with Distributed Multipole-Based Electrostatic Embedding for Highly Efficient Surface Hopping Dynamics in Solution.

We present a theoretical framework for a hybrid linear vibronic coupling model electrostatically embedded into a molecular mechanics environment, termed the linear vibronic coupling/molecular mechanics (LVC/MM) method, for the surface hopping including arbitrary coupling (SHARC) molecular dynamics package. Electrostatic embedding is realized through the computation of interactions between environment point charges and distributed multipole expansions (DMEs, up to quadrupoles) that represent each electronic state and transition densities in the diabatic basis. The DME parameters are obtained through a restrained electrostatic potential (RESP) fit, which we extended to yield higher-order multipoles. We also implemented in SHARC a scheme for achieving roto-translational invariance of LVC models as well as a general quantum mechanics/molecular mechanics (QM/MM) interface, an OpenMM interface, and restraining potentials for simulating liquid droplets. Using thioformaldehyde in water as a test case, we demonstrate that LVC/MM can accurately reproduce the solvation structure and energetics of rigid solutes, with errors on the order of 1-2 kcal/mol compared to a BP86/MM reference. The implementation in SHARC is shown to be very efficient, enabling the simulation of trajectories on the nanosecond time scale in a matter of days.

Three distinct scales dominate the role of eolian electric fields in dust turbulent transport

Although previous studies have shown that eolian electric fields significantly alter the lifting and dynamics of dust particles, they are limited to mean fields. The effects of eolian electric fields on the dust turbulent transport have not been reported before. Here, by combing the observational data and wavelet-based spectral analysis, we find that eolian electric fields enhance the vertical turbulent transport of dust particles in the near-surface layer and exhibit three distinct crucial scales. Specifically, the eolian electric fields exhibit a dominant promoting effect at the kilometer-sized synoptic scale, a secondary suppressive effect at the hectometer-sized very-large-scale motion scale, and a negligible effect at the decameter-sized turbulent integral scale. Such scale-dependent electrical effects can be explained by the fact that the linear coupling between vertical eolian electric field and dust concentration is strongest at the synoptic scale, followed by the very-large-scale motion scale, and is weakest at the turbulent integral scale.

Solitons in a coupled system of fractional nonlinear Schrödinger equations

Interest in physical systems with fractional derivatives has exploded in the 21st century. Similarly, interest in the localized excitations of nonlinear dynamical systems continues to grow significantly in recent times. In this work, we demonstrate the existence of localized solutions in the nonlinear system of three coupled Schrödinger equations with fractional dispersion, linear coupling, and cubic nonlinearities. We then check the stability of these localized solutions, i.e., solitons, by utilizing the linear stability analysis method and by propagating the perturbed solutions using the split-step fast-Fourier beam propagation method. We also prove that the solitary solutions can be stabilized in this system, thanks to the confining influence of the cross-phase modulation effect. The system is set with the same cross-phase modulation parameter but different self-phase modulation coefficients. We further find that the Lévy index (LI), the propagation constant, and the cross-phase modulation effect markedly affect the profiles and the stability domains of the solitons in the three-coupled system. Furthermore, the amplitude of the component with the strongest self-phase modulation is the largest among the three components, and the variation of the LI, the propagation constant, or the cross-phase modulation coefficient does not affect much this result. Besides the common perturbed propagation, the propagation with modulated LI is also investigated in this work, displaying increased instability when the LI is modulated suddenly, as opposed to stable propagation when the change in the LI is gradual.

Synchronization transmission of laser signals between networks with arbitrary topology within a finite time based on linear coupling strategy

Two complex networks are constituted by the single-ring erbium-doped fiber lasers (SREDFLs), and the scheme of synchronization transmission of laser signals is designed based on a linear coupling strategy. Furthermore, the signal transmission between the laser networks can be synchronously realized within a finite time. According to the numerical simulation, it is found that each error tends to zero after a short oscillation, implying that the synchronization transmission of the laser signal between corresponding nodes belonging to different networks is achieved in a foreseeable time. Meanwhile, all the coupling coefficients are also fixed to zero while the synchronization transmission between the laser networks is realized. Therefore, the simulation results prove that the control strategy of finite-time synchronization transmission between the laser networks based on a linear coupling technique is feasible and efficient.

Representing the special linear group with block unitriangular matrices.

We prove that every element of the special linear group can be represented as the product of at most six block unitriangular matrices, and that there exist matrices for which six products are necessary, independent of indexing. We present an analogous result for the general linear group. These results serve as general statements regarding the representational power of alternating linear updates. The factorizations and lower bounds of this work immediately imply tight estimates on the expressive power of linear affine coupling blocks in machine learning.

About the nature of luminescent bands in undoped and Eu2+ doped SrAl2O4 phosphors

In this paper we report the luminescence properties of nanosized undoped and Eu2+ (1%) doped SrAl2O4 phosphors. The samples were prepared by combustion method at 600 °C followed by annealing of the resultant combustion ash at 1000 °C in a reductive (Ar + H2) atmosphere. Photo luminescence (PL) and cathodoluminescence (CL) analyses were applied to characterize the phosphors. The qualitative energy level scheme of doped crystal SrAl2O4:Eu2+ and nature of defects in undoped phosphor is proposed and discussed. Within a simplified model of a single vibration and linear vibronic coupling the shape-function of the vibrationally assisted band (Pekarian) is analyzed with the emphasis on the vibrational structure. We propose an approximate approach to pass from the discrete Pekarian distribution to the structureless crystal field spectra taking into account phonon dispersion. This approach is expected to be useful for the description of the shape of the bands when the electronic levels are close to the conduction band of the host crystal.

Generation of Stable Entanglement in an Optomechanical System with Dissipative Environment: Linear-and-Quadratic Couplings

In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom–atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain the interaction Hamiltonian in the interaction picture, and then, by considering some resonance conditions and applying the rotating wave approximation, the effective Hamiltonian, which is independent of time, is derived. In the continuation, the system solution was obtained via solving the Lindblad master equation, which includes atomic, optical and mechanical dissipation effects. Finally, bipartite atom–atom entanglement is quantitatively discussed, by evaluating the negativity, which is a well-known measure of entanglement. Our numerical simulations show that a significant degree of entanglement can be reached via adjusting the system parameters. It is noticeable that the optical and mechanical decay rates play an important role in the quasi-stability and even stability of the obtained atom–atom entanglement.

Nonlinear Energy Transfer of a Spar-Floater System Using the Inerter Pendulum Vibration Absorber

Abstract The inerter pendulum vibration absorber (IPVA) is integrated between a spar and an annulus floater using a ball-screw mechanism to study its wave energy conversion potential. Hydrodynamic stiffness, added mass, and radiation damping effects on the spar-floater system are characterized using the boundary element method. It is found that a 1:2 internal resonance via a period-doubling bifurcation in the system is responsible for nonlinear energy transfer between the spar-floater system and the pendulum vibration absorber. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable due to the 1:2 internal resonance phenomenon. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the first natural frequency of the system. The IPVA system when integrated with the spar-floater system is shown to outperform a linear coupling between the spar and the floater both in terms of the response amplitude operator (RAO) of the spar and one measure of the energy conversion potential of the system. Finally, experiments are performed on the IPVA system integrated with single-degree-of-freedom system (without any hydrodynamic effects) to observe the 1:2 internal resonance phenomenon and the nonlinear energy transfer between the primary mass and the pendulum vibration absorber. It is shown experimentally that the IPVA system outperforms a linear benchmark in terms of vibration suppression due to the energy transfer phenomenon.

Research on Piston Dynamics and Engine Performances of a Free-Piston Engine Linear Generator Coupling with Various Rebound Devices

Free-piston engine linear generators (FPELGs) are an innovative linear power device that exhibits the distinctive dynamics of pistons and performance of free-piston engines. Furthermore, the single-cylinder/single-piston FPELG structure type has more advantages than other FPELG structure types, including a straightforward structure and ease of control. However, when coupled with various rebound devices, the operational characteristics and piston and engine performance of single-cylinder/single-piston FPELGs are quite different. Therefore, this paper aims to quantitatively compare the dynamics of the piston and engine performance of single-cylinder/single-piston FPELGs coupled with various types of rebound device. The results indicate that when the equivalent stiffness of the gas spring is greater than that of the mechanical spring, the operating frequency of the piston of the FPELG coupled with a gas spring will be higher than that when coupled with a mechanical spring. During the compression stroke, the piston velocity of a FPELG coupled with a mechanical spring changes linearly, while the piston velocity of a FPELG coupled with a gas spring changes nonlinearly. FPELGs coupled with gas springs have shorter compression and expansion durations compared to those coupled with mechanical springs. In addition, the indicated powers of FPELGs coupled with ideal gas springs and mechanical springs are 1.5 kW and 1.3 kW, respectively. However, due to leakage, the thermal efficiency of a FPELG coupled with an actual gas spring is reduced by approximately 2.5% compared with the FPELG coupled with the ideal gas spring. Furthermore, the operation frequency of the piston is positively correlated with the stiffness of the mechanical spring. In addition, as the stiffness of the mechanical spring increases, the combustion process of the engine becomes close to an isovolumetric process. The changes in piston dynamics and engine performance when increasing the initial gas pressure of the gas spring are similar to those when increasing the stiffness of the mechanical spring.

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.

Quantum steering in a [formula omitted]-symmetric system of three cavities with a linear coupling between the active and passive cavities

A system of three cavities connected by linear coupling is considered in which the coupling between the active and passive cavities is much weaker than the others. We show the dependence of the phase transition point of PT-symmetry on parameters characterizing our system. The generation of quantum steering is also investigated by using steering parameter calculations that show the steering ability of subsystems. We show that in the unbroken phase of PT-symmetry, quantum steering between subsystems of each pair can be one-way or two-way steering depending on the respective gain and loss of energy in the active and passive cavities. We also point out that the steering abilities of subsystems in our system are dependent on the initial states of the system which are set up with one photon in the active cavity or the passive one.

Emergent Phenomena of Vector Solitons Induced by the Linear Coupling (Laser Photonics Rev. 17(9)/2023)

Emergent Phenomena of Vector Solitons Induced by the Linear Coupling (Laser Photonics Rev. 17(9)/2023)

Physical multi-factor driven nonlinear superposition for machining deformation reconstruction

In recent years, the machining deformation of titanium alloy frame parts has become a major research issue in the field of aviation manufacture. Through the generation mechanism, the machining deformation is divided into three parts including bulk residual stresses, cutting forces and other uncertain factors induced deformation. The nonlinearity of physical multi-factor machining deformation is revealed by the comparison between the purely linear addition and coupling superposition. A novel nonlinear superposition model is proposed for machining deformation reconstruction in this work. With the experimental values as simulation inputs, the physical multi-factor driven simulation is developed to solve the nonlinear parameters of machining components in the superposition model. The posterior information embedded in the measurement is utilized to calibrate the nonlinear superposition model in the form of binary polynomials with five orders. The nonlinear superposition model is validated through four series of machining tasks, with the average model accuracy at 91.09%. To quantitively evaluate the proportion share of deformation components, a dimensionless equivalent machining deformation ratio is developed by the integral operation of the established nonlinear model. The results indicate that the bulk residual stresses, cutting forces and other uncertain factors account for percentages of 24.72%, 65.07%, and 13.21% (the ratio among them around 2:5:1). The proposed nonlinear superposition model and dimensionless equivalent ratio in this work display the potential application prospects in the field of machining deformation prediction and control.