Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Mode coupling in nonlinear Kelvin-Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.

Effects of mode coupling between low-mode radiation flux asymmetry and intermediate-mode ablator roughness on ignition capsule implosions

The low-mode shell asymmetry and high-mode hot spot mixing appear to be the main reasons for the performance degradation of the National Ignition Facility(NIF)implosion experiments.The effects of the mode coupling between low-mode P2 radiation flux asymmetry and intermediate-mode L=24 capsule roughness on the implosion performance of ignition capsule are investigated by two-dimensional radiation hydrodynamic simulations.It is shown that the amplitudes of new modes generated by the mode coupling are in good agreement with the second-order mode coupling equation during the acceleration phase.The later flow field not only shows large areal density P2 asymmetry in the main fuel,but also generates large-amplitude spikes and bubbles.In the deceleration phase,the increasing mode coupling generates more new modes,and the perturbation spectrum on the hot spot boundary is mainly from the strong mode interactions rather than the initial perturbation conditions.The combination of the low-mode and high-mode perturbations breaks up the capsule shell,resulting in a significant reduction of the hot spot temperature and implosion performance.

Comparison of heating mechanisms of argon helicon plasma in different wave modes with and without blue core

In this work,we investigated the discharge characteristics and heating mechanisms of argon helicon plasma in different wave coupled modes with and without blue core.Spatially resolved spectroscopy and emission intensity of argon atom and ion lines were measured via local optical emission spectroscopy,and electron density was measured experimentally by an RFcompensated Langmuir probe.The relation between the emission intensity and the electron density was obtained and the wavenumbers of helicon and’Trivelpiece-Gould’(TG)waves were calculated by solving the dispersion relation in wave modes.The results show that at least two distinct wave coupled modes appear in argon helicon plasma at increasing RF power,i.e.blue core(or BC)mode with a significant bright core of blue lights and a normal wave(NW)mode without blue core.The emission intensity of atom line 750.5 nm(lArⅠ750.5nm)is related to the electron density and tends to be saturated in wave coupled modes due to the neutral depletion,while the intensity of ion line 480.6 nm(IArⅡ480.6nm)is a function of the electron density and temperature,and increases dramatically as the RF power is increased.Theoretical analysis shows that TG waves are strongly damped at the plasma edge in NW and/or BC modes,while helicon waves are the dominant mechanism of power deposition or central heating of electrons in both modes.The formation of BC column mainly depends on the enhanced central electron heating by helicon waves rather than TG waves since the excitation of TG waves would be suppressed in this special anti-resonance region.

Calculation of the Coupling Coefficient of Twin-Core Fiber Based on the Supermode Theory with Finite Element Method

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.

The Coupling Structure Features Between (2,1) NTM and (1,1) Internal Mode in EAST Tokamak

In the discharge of EAST tokamak, it is observed that （2, 1） neoclassical tearing mode （NTM） is triggered by mode coupling with a （1, 1） internal mode. Using singular value decomposition （SVD） method for soft X-ray emission and for electron cyclotron emission （ECE）, the coupling spatial structures and coupling process between these two modes are analyzed in detail. The results of SVD for ECE reveal that the phase difference between these two modes equals to zero. This is consistent with the perfect coupling condition. Finally, performing statistical analysis of r1/1, ξ1/1 and w2/1, we find that r1/1 more accurately represents the coupling strength than ξ1/1, and r1/1 is also strongly related to the （2, 1） NTM triggering, where r1/1 is the width of （1, 1） internal mode, ξ1/1 is the perturbed amplitude of （1, 1） internal mode, and w2/1 denotes the magnetic island width of （2, 1） NTM.

Coupling of Cutoff Modes in a Chain of Nonlinear Metallic Nanorods

We study the coupling of cutoff modes in a chain of metallic nanorods embedded in a Kerr nonlinear optical medium with strong near-field interactions analytically. Based on a quasidiscreteness approach, we derive a system of two coupled nonlinear Schrbdinger equations governing the evolution of the envelopes of these modes. It is shown that this system supports a variety of subwavelength plasmonic lattice vector solitons of the bright- bright, bright-dark, dark-bright, and dark-dark type through a cross-phase modulation. It is also shown that the existence of different solitons depends strongly on the gap width scaled for the rod radius and the type of nonlinearity of the embedded medium.

Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.

Mueller matrix analysis for all optical fiber co-existence of birefringence-polarization dependent gain-mode coupling at a single wavelength

Birefringence （polarization-related phase-shift）, polarization dependent gain （PDG） and mode coupling are three factors that may synchronously influence the transmission of single-wavelength polarized light in optical fibers. This paper obtains a new Mueller matrix analysis, which can be used under conditions that all these three factors are existing and changing. According to our transmission model, the state of polarization （SOP） changes along an optical mierostructure fiber with co-existence of birefringence-PDG-mode coupling were simulated. The simulated results, which show the phenomena of SOP constringency, are in good agreement with previous theoretical analyses.

Single-mode antiresonant terahertz fiber based on mode coupling between core and cladding

Based on the index-induced mode coupling between the higher-order mode in core and the fundamental mode in cladding tubes,the single-mode operation can be realized in any antiresonant fibers(ARFs)when satisfying that the area ratio of cladding tube and core is about 0.46:1,and this area ratio also should be modified according to the shape and the number of cladding tubes.In the ARF with nodal core boundary,the mode in core also can couple with the mode in the wall of core boundary,which can further enhance the suppression of high-order mode.Accordingly,an ARF with conjoint semi-elliptical cladding tubes realizes a loss of higher-order mode larger than 30 dB/m;simultaneously,a loss of fundamental mode loss less than 0.4 dB/m.

Acoustic longitudinal mode coupling in w-shaped Al/Ge Co-doped fibre

This paper proposes a novel fibre structure aiming at distributed temperature and strain sensing. Utilizing Al2O3 and CeO2 as dopants to form a w-shaped acoustic waveguide, it realizes modal coupling between longitudinal acoustic modes of its inner and outer core layers, leading to a dual-peak or multi-peak Brillouin gain spectrum. The relationship between the acoustic mode coupling properties and the fibre materials, doping concentrations and structural parameters are investigated, showing that the positions of mode coupling points in acoustic dispersion curves and the coupling intensities can be designed flexibly. A specific fibre design for the discriminative sensing of temperature and strain under a pump wavelength of 1.55 μm is given. The responses of its Brillouin gain properties on temperature and strain are analysed theoretically, demonstrating its potential for distributed fibre Brillouin sensing.

Theoretical analysis of the mode coupling induced by heat of large-pitch micro-structured fibers

In this paper,a theoretical model to analyze the mode coupling induced by heat,when the fiber amplifier works at high power configuration,is proposed.The model mainly takes into consideration the mode field change due to the thermally induced refractive index change and the coupling between modes.A method to predict the largest average output power of fiber is also proposed according to the mode coupling theory.The largest average output power of a large pitch fiber with a core diameter of 190 μm and an available pulse energy of 100 mJ is predicted to be 540 W,which is the highest in large mode field fibers.

Temperature dependence of mode coupling effect in piezoelectric vibrator made of[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT ternary single crystals with high electromechanical coupling factor

The influence of temperature on mode coupling effect in piezoelectric vibrators remains unclear.In this work,we discuss the influence of temperature on two-dimensional(2D)mode coupling effect and electromechanical coupling coefficient of cylindrical[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT piezoelectric single-crystal vibrator with an arbitrary configuration ratio.The electromechanical coupling coefficient kt decreases with temperature increasing,whereas k33 is largely invariant in a temperature range of 25℃-55℃.With the increase of temperature,the shift in the‘mode dividing point’increases the scale of the poling direction of the piezoelectric vibrator.The temperature has little effect on coupling constantΓ.At a given temperature,the coupling constantΓof the cylindrical vibrator is slightly greater than that of the rectangular vibrator.When the temperature changes,the applicability index(M)values of the two piezoelectric vibrators are close to 1,indicating that the coupling theory can be applied to piezoelectric vibrators made of late-model piezoelectric single crystals.

Effects of transverse mode coupling and optical confinement factor on gallium-nitride based laser diode

We have investigated the transverse mode pattern and the optical field confinement factor of gallium nitride （GaN） laser diodes （LDs） theoretically. For the particular LD structure, composed of approximate 4 μm thick n-GaN substrate layer, the maximum optical confinement factor was found to be corresponding to the 5^th order transverse mode, the so-called lasing mode. Moreover, the value of the maximum confinement factor varies periodically when increasing the n-side GaN layer thickness, which simultaneously changes and increases the oscillation mode order of the GaN LD caused by the effects of mode coupling. The effects of the thickness and the average composition of Al in the AlGaN/GaN superlat.tice on the optical confinement factor are also presented. Finally, the mode coupling and optimization of the layers in the GaN-based LD are discussed.

Study of Mode Coupling on Coaxial Resonators

A study of mode coupling phenomenon of coaxial resonators has been conducted with theories. Through establishing the source-free transmission line equation, boundary conditions of the coaxial resonators with a corrugated inner conductor are analyzed. In the end, calculations are performed in a wide range of corrugation parameters for the resonator of the Karlsruhe Institute of Technology （KIT） relevant coaxial gyrotron.

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.

Mode coupling in solar spicule oscillations

In a real medium which has oscillations, the perturbations can cause an energy transfer between different modes. A perturbation, which is interpreted as an interaction between the modes, is inferred to be mode coupling. The mode coupling process in an inhomogeneous medium such as solar spicules may lead to the coupling of kink waves to local Alfven waves. This coupling occurs in practically any conditions when there is smooth variation in density in the radial direction. This process is seen as the decay of transverse kink waves in the medium. To study the damping of kink waves due to mode coupling, a 2.5-dimensional numerical simulation of the initial wave is considered in spicules. The initial perturbation is assumed to be in a plane perpendicular to the spicule axis. The considered kink wave is a standing wave which shows an exponential damping in the inhomogeneous layer after the mode coupling occurs.

An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

FUZZY STABILITY ANALYSIS OF MODE COUPLING CHATTER ON CUTTING PROCESS

The influence of fuzzy uncertainty factors is considered on the analysis of chatter occurring during machine tool cutting process. Using fuzzy mathematics analysis methods, a detailed discussion over fuzzy stability analysis problems is presented related to the mode coupling chatter with respect to intrinsic structure fuzzy factors, and the possibility distribution of the fuzzy stability cutting range and the confidence level expressions of the fuzzy stability cutting width are given.

City-Bus-Route Demand-based Efficient Coupling Driving Control for Parallel Plug-in Hybrid Electric Bus

Recently,plug?in hybrid electric bus has been one of the energy?e cient solutions for urban transportation. However,the current vehicle e ciency is far from optimum,because the unpredicted external driving conditions are di cult to be obtained in advance. How to further explore its fuel?saving potential under the complicated city bus driving cycles through an e cient control strategy is still a hot research issue in both academic and engineering area. To realize an e cient coupling driving operation of the hybrid powertrain,a novel coupling driving control strategy for plug?in hybrid electric bus is presented. Combined with the typical feature of a city?bus?route,the fuzzy logic inference is employed to quantify the driving intention,and then to determine the coupling driving mode and the gear?shifting strategy. Considering the response deviation problem in the execution layer,an adaptive robust controller for electric machine is designed to respond to the transient torque demand,and instantaneously compensate the response delay and the engine torque fluctuation. The simulations and hard?in?loop tests with the actual data of two typical driving conditions from the real?world city?bus?route are carried out,and the results demonstrate that the pro?posed method could guarantee the hybrid powertrain to track the actual torque demand with 10.4% fuel economy improvement. The optimal fuel economy can be obtained through the optimal combination of working modes. The fuel economy of plug?in hybrid electric bus can be significantly improved by the proposed control scheme without loss of drivability.