Nonlinear Coupling Strength Research Articles

Free-energy-based lattice Boltzmann model for emulsions with soluble surfactant

We propose a diffuse interface model to simulate a system of two immiscible liquids with surfactant. This model is based on a modified Ginzburg-Landau free energy functional to account for non-ionic soluble surfactants and couples the Navier-Stokes equations with two Cahn-Hilliard transport equations to represent immiscible fluids and surfactant concentration. The governing equations are solved using a lattice Boltzmann framework. The proposed model is validated for Langmuir and Frumkin adsorption isotherms when applied to simulate a planar interface and a spherical drop equilibration. The model ensures numerical stability and accurate results for low and high surfactant concentrations, and the diffuse interface thickness remains constant even for high surfactant loads. The model also allows achieving a surface tension reduction of 45-50% compared to the clean system, even at low surfactant concentrations. The appropriate surfactant mobility and solubility values are recommended for different values of the strength of nonlinear surfactant coupling.

Resonant Mode Coupling in δ Scuti Stars

Delta Scuti (δ Sct) variables are intermediate-mass stars that lie at the intersection of the main sequence and the instability strip on the Hertzsprung–Russell diagram. Various lines of evidence indicate that nonlinear mode interactions shape their oscillation spectra, including the particularly compelling detection of resonantly interacting mode triplets in the δ Sct star KIC 8054146. Motivated by these observations, we use the theory of three-mode coupling to study the strength and prevalence of nonlinear mode interactions in 14 δ Sct models that span the instability strip. For each model, we calculate the frequency detunings and nonlinear coupling strengths of ∼104 unique combinations of mode triplets. We find that all the models contain at least ∼100 well-coupled triplets whose detunings and coupling strengths are consistent with the triplets identified in KIC 8054146. Our results suggest that resonant mode interactions can be significant in δ Sct stars and may explain why many exhibit rapid changes in amplitude and oscillation period.

Third-harmonic-assisted four-wave mixing in a chip-based microresonator frequency comb generation.

Microcombs generated in photonic integrated circuits can provide broadband and coherent optical frequency combs with a high repetition rate from microwave to terahertz. Coherent microcombs formed in normal group velocity dispersion microresonators usually have a flat-top temporal profile, called platicon. Here, we propose a novel scheme to generate platicon in Si3N4 microresonator with the assistance of third-harmonic generation. The nonlinear coupling between the fundamental and the third-harmonic waves that draws support from third-order sum/difference frequency generation provides a new mechanism to achieve the phase matching of four-wave mixing in normal dispersion microresonators. We show that single or multiple platicons can be obtained by changing the third-harmonic nonlinear coupling strength and phase matching condition for third-order sum/difference frequency generation. Our work provides a promising solution to facilitate coherent and visible microcomb generation in a pure χ(3) microresonator, which is potential for self-referencing combs and optical clock stabilization.

Adaptive synchronization control for stochastic complex networks with derivative coupling

In this paper, the problem of the adaptive synchronization control is studied for a class of stochastic complex networks with unknown nonlinear coupling strength and derivative coupling. First, in order to deal with the unknown nonlinear coupling strength, Takagi–Sugeno (T–S) fuzzy method is used to transform the network model into a T–S fuzzy complex network model. Then,a fuzzy adaptive controller and the corresponding adaptive parameter update rate are designed. Subsequently, a new Lyapunov function is constructed, which is related to the derivative coupling. By employing the stochastic analysis technique and Lyapunov stability theory, a sufficient condition is given for exponential stabilization in mean square of the synchronization error system. Finally, the effectiveness of the obtained theoretical results is verified through a simulation.

Nanoscale optical parametric amplification through super-nonlinearity induction

Optical parametric amplification (OPA) is a nonlinear process through which a low-power input wave is amplified by extracting energy from an interaction medium that is energized by a high-intensity pump wave. For a significant amplification of an input wave, a sufficiently long interaction medium is required, which is usually on the order of a few centimeters. Therefore, in the small scale, OPA is considered unfeasible, and this prevents it from being employed in micro and nanoscale devices. There have been recent studies that proposed microscale OPA through the use of micro-resonators. However, there is currently no study that has suggested high-gain nanoscale OPA, which could be quite useful for implementing nanoscale optical devices. This study aims to show that nanoscale OPA is feasible through the concurrent maximization of the pump wave induced electric energy density and the polarization density (nonlinear coupling strength) within the interaction medium, which enables a very high amount of energy to be transferred to the input wave that is sufficient to amplify the input wave with a gain factor that is comparable to those provided by centimeter scale nonlinear crystals. The computational results of our OPA model match with the experimental ones in the context of sum-harmonic generation, which is the wave-mixing process that gives rise to OPA, with an accuracy of 97.6%. The study aims to make room for further investigation of nanoscale OPA through adaptive optics and/or nonlinear programming algorithms for the enhancement of the process.

Disturbance rejections and synchronization of fractional-order fuzzy complex networks

This paper deals with the problem of disturbance rejection and synchronization of fractional-order complex dynamical networks subject to nonlinear coupling strength and discontinuous nonlinear functions. Notably, the nonlinear coupling strength is linearised by using a well-known Takagi-Sugeno fuzzy approach. The considered system is transformed into a nominal form by employing the uncertainty and disturbance estimator-based control approach, which simplifies the control objective and improves the system performance. Second, the uncertainty and disturbance estimator is incorporated into the traditional feedback control scheme to reject the unknown disturbance and uncertainty. Then, the required synchronization conditions for both the discontinuous and continuous fractional-order systems are obtained by using Lyapunov stability and fractional calculus theories. Last, numerical examples are provided to illustrate the efficiency of the proposed control strategy, wherein it is shown that the system yields better satisfactory tracking performance and high robustness against possible disturbance and uncertainties and finite set of jump discontinuous nonlinear functions. Moreover, the selection of appropriate filter design is discussed for various kinds of disturbance signals.

Universal model of strong coupling at the nonlinear resonance in open cavity-QED systems

Many molecular, quantum-dot, and optomechanical nanocavity-QED systems demonstrate strong nonlinear interactions between electrons, photons, and phonon (vibrational) modes. We show that such systems can be described by a universal model in the vicinity of the nonlinear resonance involving all three degrees of freedom. We solve the nonperturbative quantum dynamics in the strong-coupling regime of the nonlinear resonance, taking into account quantization, dissipation, and fluctuations of all fields. We find analytic solutions for quantum states in the rotating-wave approximation which demonstrate tripartite quantum entanglement once the strong-coupling regime is reached. We show how the strong coupling at the nonlinear resonance modifies photon emission and vibrational spectra, and how the observed spectra can be used to extract information about relaxation rates and the nonlinear coupling strength in specific systems.

Dynamics and Synchronization of Complex-Valued Ring Networks

Networks of coupled oscillators have been used to model various real-world self-organizing systems. However, the dynamics, especially chaos and bifurcation, of complex-valued networks are rarely investigated. In this paper, a ring network of interacting complex-valued van der Pol oscillators is studied to model the formation of ring dynamics. Although there are only stable limit cycles in a complex-valued van der Pol oscillator, chaos, hyperchaos, and coexisting chaotic attractors are observed from the ring network, which are analyzed by using the Lyapunov exponent spectrum, bifurcation diagram and 0–1 test. In addition, complexity analysis on nonlinear coefficients and coupling strengths illustrates that the range of parameters within the chaotic (hyperchaotic) region has positive correlation with the number of oscillators. It is shown that the chaotic bifurcation path is highly robust against the size variation of the ring network, which always evolves to chaos directly from period-1 and quasi-periodic states, respectively. Moreover, it is demonstrated that complete synchronization and phase synchronization of oscillations are stable in a large-scale ring network, while chaotic phase synchronization is unstable in a small-scale network.

The photon blockade effect of a complete Buck-Sukumar model

The Buck-Sukumar (BS) model, with a nonlinear coupling between the atom and the light field, is well defined only when its coupling strength is lower than a critical coupling. Its energy collapses at a critical coupling and is unbounded beyond that value. In other words, the BS model is incomplete. We introduce a simple and a complete BS model by adding a nonlinear photon term into the initial BS model. Considering the rotating wave approximation, this complete BS model conserves the excited number and the parity. By expanding it in the subspace of the product state between the atom and the field, we solve the time-independent SchrÖdinger equation to obtain the eigenenergy and eigenstate. Furthermore, we explore the influence of the nonlinear photon term on the energy spectrum and the photon blockade effect for the complete BS model by calculating the excited number and second-order correlation function. Our study shows that, the nonlinear photon term not only eliminates the energy spectral collapse but also makes it well-defined and complete in all the coupling regime. When at the resonance between the atomic and the field frequency, the nonlinear photon term breaks the harmonicity of the energy spectrum and produces a ladder of the excited number in the ground state. Because the larger nonlinear photon term inhibits the photon transition from an energy level to the higher one, it produces the single-photon projection state in the larger coupling region. Accordingly, we find that the nonlinear photon term promotes photon blockade by calculating the second-order correlation function. When at the non-resonant region, the nonlinear photon term enlarges the originally anharmonic energy ladder. For a complete BS model with the fixed nonlinear photon coupling strength and the fixed detuning, the energy level for the positive detuning is lower than that with the negative detuning, and more energy is required to overcome the absorption of a photon. Therefore, the positive detuning promotes the photon blockade. For the negative detuning, the system is more likely to absorb a photon and jump to a higher energy level, and therefore, suppresses the photon blockade.

The photon blockade effect of a complete Buck-Sukumar model

<sec>The Buck-Sukumar (BS) model, with a nonlinear coupling between the atom and the light field, is well defined only when its coupling strength is lower than a critical coupling. Its energy collapses at a critical coupling and is unbounded beyond that value. In other words, the BS model is incomplete. We introduce a simple and complete BS model by adding a nonlinear photon term into the initial BS model. Considering the rotating wave approximation, this complete BS model conserves the excited number and the parity. By expanding it in the subspace of the product state between the atom and the field, we solve the time-independent Schrödinger equation to obtain the eigenenergy and eigenstate. Furthermore, we explore the influence of the nonlinear photon term on the energy spectrum and the photon blockade effect for the complete BS model by calculating the excited number and second-order correlation function.</sec><sec>Our study shows that, the nonlinear photon term not only eliminates the energy spectral collapse but also makes it well-defined and complete in all the coupling regime. When at the resonance between the atomic and the field frequency, the nonlinear photon term breaks the harmonicity of the energy spectrum and produces a ladder of the excited number in the ground state. Because the larger nonlinear photon term inhibits the photon transition from an energy level to the higher one, it produces the single-photon projection state in the larger coupling region. Accordingly, we find that the nonlinear photon term promotes photon blockade by calculating the second-order correlation function. When at the non-resonant region, the nonlinear photon term enlarges the originally anharmonic energy ladder. For a complete BS model with the fixed nonlinear photon coupling strength and the fixed detuning, the energy level for the positive detuning is lower than that with the negative detuning, and more energy is required to overcome the absorption of a photon. Therefore, the positive detuning promotes the photon blockade. For the negative detuning, the system is more likely to absorb a photon and jump to a higher energy level, and therefore, suppresses the photon blockade.</sec>

Collapse of superradiant phase and Dicke phase transition at finite temperature in a hybrid optical-mechanical system

In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.

弯曲限模对大模场光纤横模不稳定效应的影响

The effect of transverse mode instability has gradually become the primary problem that causes laser beam quality degradation and limits power scaling of high-power fiber lasers. This paper conducts a series of study on the transverse mode instability (TMI) in large mode area (LMA) fiber based on a co-pumped all-fiberized narrow linewidth high power amplification platform. According to the calculation results of the coupled mode equations, the nonlinear coupling strength between the LP01 and LP11 modes of the LMA fiber 25/400 μm is the largest, which directly induces the TMI. In order to suppress the generation and amplification of the LP11 mode at the main amplifier, the fiber coiling method was used as an operational mode filtering technique to achieve mode control. The threshold of TMI increased from 1000 W to 1600 W while reducing the bending radius of the main amplifier gain fiber from 6 cm to 5 cm, and the other output performance of the fiber laser was hardly affected. This provides a powerful experimental reference for us to build an actual narrow linewidth, high power, all-fiberized laser system.

Wideband two-process frequency conversion under stimulated Raman adiabatic passage via a continuum of dark intermediate states

In this paper, we propose a novel hybrid planar-channel waveguide configuration in which the channel waveguide is submerged within the planar region, with an aim to study two simultaneous three-wave mixing processes under stimulated Raman adiabatic passage. In our study, an input frequency is converted to an output frequency lying very close to or very far from the input frequency via an intermediate frequency. This frequency is in the form of a continuum of modes in the planar region, while all other frequencies propagate as guided modes of the channel waveguide. The continuum of modes at the intermediate frequency allows the simultaneous phase matching to be satisfied over a wide range of wavelengths. As a consequence, this leads to a wideband and efficient conversion from the input to the output frequency without any significant power accumulation at the intermediate stage, which is ensured through the counterintuitive and adiabatic variation in the nonlinear coupling strengths.

The Cardiorespiratory Network in Healthy First-Degree Relatives of Schizophrenic Patients.

Impaired heart rate- and respiratory regulatory processes as a sign of an autonomic dysfunction seems to be obviously present in patients suffering from schizophrenia. Since the linear and non-linear couplings within the cardiorespiratory system with respiration as an important homeostatic control mechanism are only partially investigated so far for those subjects, we aimed to characterize instantaneous cardiorespiratory couplings by quantifying the casual interaction between heart rate (HR) and respiration (RESP). Therefore, we investigated causal linear and non-linear cardiorespiratory couplings of 23 patients suffering from schizophrenia (SZO), 20 healthy first-degree relatives (REL) and 23 healthy subjects, who were age-gender matched (CON). From all participants’ heart rate (HR) and respirations (respiratory frequency, RESP) were investigated for 30 min under resting conditions. The results revealed highly significant increased HR, reduced HR variability, increased respiration rates and impaired cardiorespiratory couplings in SZO in comparison to CON. SZO were revealed bidirectional couplings, with respiration as the driver (RESP → HR), and with weaker linear and non-linear coupling strengths when RESP influencing HR (RESP → HR) and with stronger linear and non-linear coupling strengths when HR influencing RESP (HR → RESP). For REL we found only significant increased HR and only slightly reduced cardiorespiratory couplings compared to CON. These findings clearly pointing to an underlying disease-inherent genetic component of the cardiac system for SZO and REL, and those respiratory alterations are only clearly present in SZO seem to be connected to their mental emotional states.

Intermuscular coupling based on wavelet packet-cross frequency coherence

Human motion control system has a high degree of nonlinear characteristics. Through quantitative evaluation of the nonlinear coupling strength between surface electromyogram (sEMG) signals, we can get the functional state of the muscles related to the movement, and then explore the mechanism of human motion control. In this paper, wavelet packet decomposition and n: m coherence analysis are combined to construct an intermuscular cross-frequency coupling analysis model based on wavelet packet- n: m coherence. In the elbow flexion and extension state with 30% maximum voluntary contraction force (MVC), sEMG signals of 20 healthy adults were collected. Firstly, the subband components were obtained based on wavelet packet decomposition, and then the n: m coherence of subband signals was calculated to analyze the coupling characteristics between muscles. The results show that the linear coupling strength (frequency ratio 1:1) of the cooperative and antagonistic pairs is higher than that of the nonlinear coupling (frequency ratio 1:2, 2:1 and 1:3, 3:1) under the elbow flexion motion of 30% MVC; the coupling strength decreases with the increase of frequency ratio for the intermuscular nonlinear coupling, and there is no significant difference between the frequency ratio n: m and m: n. The intermuscular coupling in beta and gamma bands is mainly reflected in the linear coupling (1:1), nonlinear coupling of low frequency ratio (1:2, 2:1) between synergetic pair and the linear coupling between antagonistic pairs. The results show that the wavelet packet- n: m coherence method can qualitatively describe the nonlinear coupling strength between muscles, which provides a theoretical reference for further revealing the mechanism of human motion control and the rehabilitation evaluation of patients with motor dysfunction.

Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control

This paper considers the finite-time synchronization of dynamic networks with nonlinear coupling strength and stochastic perturbations by using intermittent control. Since it is difficult to estimate the settling-time due to the uncertain intermittent intervals, a novel lemma is established. Then, two quantized intermittent controllers without chattering are designed, which can reduce the control cost and save channel resources. T-S fuzzy method is utilized to deal with the nonlinear coupling strength. By using Lyapunov direct method, sufficient conditions formulated by linear matrix inequalities (LMIs) are derived to ensure that the considered system can realize finite-time synchronization. Moreover, the control gains are designed. Two numerical simulations are given to show the merits of theoretical analysis.

Bose-Einstein condensate confined in a one-dimensional ring stirred with a rotating delta link.

We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.

Nonlinear normal modes in the [formula omitted]-Fermi-Pasta–Ulam-Tsingou chain

Nonlinear normal mode solutions of the β-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths. Solutions for the N-body chain are found for the case of purely nonlinear couplings. Three distinct solution types are presented: a linear analogue, a chaotic amplitude mapping, and a localized nonlinear mode. The relaxation of perturbed modes are also explored using l1-regularized least squares regression to estimate the free energy functional near the nonlinear normal mode solution. The perturbed modes are observed to decay sigmoidally towards a quasi-equilibrium state and a logarithmic relationship between the perturbation strength and mode lifetime is found.

Quantum Rabi–Stark model: solutions and exotic energy spectra

The quantum Rabi–Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestingly, a first-order quantum phase transition indicated by level crossing of the ground state and the first excited state is induced by the positive nonlinear Stark-like coupling, which is however absent in any previous isotropic quantum Rabi models. When the absolute value of the nonlinear coupling strength is equal to twice the cavity frequency, this model can be reduced to an effective quantum harmonic oscillator, and solutions are then obtained analytically. The spectra collapse phenomenon is observed at a critical coupling, while below this critical coupling, infinite discrete spectra accumulate into a finite energy from below.

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States**Supported by the National Science Foundation of China under Grant Nos. 11674285 and 11834005

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.