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 with Fabry-Perot modes in photonic crystal slabs

Fabry–Perot(FP)modes are a class of fundamental resonances in photonic crystal(PhC)slabs.Owing to their low quality factors,FP modes are frequently considered as background fields with their resonance nature being neglected.Nevertheless,FP modes can play important roles in some phenomena,as exemplified by their coupling with guided resonance(GR)modes to achieve bound states in the continuum(BIC).Here,we further demonstrate the genuine resonance mode capability of FP modes PhC slabs.Firstly,we utilize temporal coupled-mode theory to obtain the transmittance of a PhC slab based on the FP modes.Secondly,we construct exceptional points(EPs)in both momentum and parameter spaces through the coupling of FP and GR modes.Furthermore,we identify a Fermi arc connecting two EPs and discuss the far-field polarization topology.This work elucidates that the widespread FPs in PhC slabs can serve as genuine resonant modes,facilitating the realization of desired functionalities through mode coupling.

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.

Effect of toroidal mode coupling on explosive dynamics of m/n=3/1 double tearing mode

The CLT code was used to quantitatively study the impact of toroidal mode coupling on the explosive dynamics of the m/n=3/1 double tearing mode.The focus of this study was on explosive reconnection processes,in which the energy bursts and the main mode no longer dominates when the separation between two rational surfaces is relatively large in the medium range.The development of higher m and n modes is facilitated by a relatively large separation between two rational surfaces,a small q_(min)(the minimum value of the safety factor),or low resistivity.The relationships between the higher m and n mode development,explosive reconnection rate,and position exchange of 3/1 islands are summarized for the first time.Separation plays a more important role than q_(min)in enhancing the development of higher m and n modes.At a relatively large separation,the good development of higher m and n modes greatly reduces the reconnection rate and suppresses the development of the main mode,resulting in the main mode not being able to develop sufficiently large to generate the position changes of 3/1 islands.

Effects of high modes on the wind-induced response of super high-rise buildings

For super high-rise buildings, the vibration period of the basic mode is several seconds, and it is very close to the period of the fluctuating wind. The damping of super high-rise buildings is low, so super high-rise buildings are very sensitive to fluctuating wind. The wind load is one of the key loads in the design of super high-rise buildings. It is known that only the basic mode is needed in the wind-response analysis of tall buildings. However, for super high-rise buildings, especially for the acceleration response, because of the frequency amplification of the high modes, the high modes and the mode coupling may need to be considered. Three typical super high-rise projects with the SMPSS in wind tunnel tests and the random vibration theory method were used to analyze the effect of high modes on the wind-induced response. The conclusions can be drawn as follows. First, for the displacement response, the basic mode is dominant, and the high modes can be neglected. Second, for the acceleration response, the high modes and the mode coupling should be considered. Lastly, the strain energy of modes can only give the vibration energy distribution of the high-rise building, and it cannot describe the local wind-induced vibration of high-rise buildings, especially for the top acceleration response.

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.

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

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.

VIBRATION ANALYSIS OF TURBINE BASED ON FLUID-STRUCTURE COUPLING

The vibration of a Francis turbine is analyzed with the additional quality matrix method based on fluid-structure coupling （FSC）. Firstly, the vibration frequency and mode of blade and runner in air and water are calculated. Secondly, the influences to runner frequency domain by large flow, small flow and design flow working conditions are compared. Finally the influences to runner modes by centrifugal forces under three rotating speeds of 400 r/rain, 500 r/min and 600 r/rain are compared. The centrifugal force and small flow working condition have greatly influence on the vibration of small runner. With the increase of centrifugal force, the vibration frequency of the runner is sharply increased. Some order frequencies are even close to the runner natural frequency in the air. Because the low frequency vibration will severely damage the stability of the turbine, low frequency vibration of units should be avoided as soon as possible.

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.

Coupled Modes of Rainfall over China and the Pacific Sea Surface Temperature in Boreal Summertime

In this study,monthly NCEP/NCAR reanalysis data and NOAA ERSST as well as observed precipitation data from 160 stations in China were used to investigate coupled modes affecting the rainfall over China and sea surface temperature （SST） in the Pacific during boreal summertime based on singular value decomposition （SVD） method.The SVD analysis revealed three remarkable coupled modes：rainfall over North China associated with an ENSO-like SST pattern （ENSO-NC）,rainfall over the Yangtze River valley associated with SST anomalies in the western tropical Pacific （WTP-YRV）,and rainfall over the Yellow River loop valley associated with tropical Pacific meridional mode-like SST pattern （TPMM-YRLV）.These coupled SVD modes appear robust and closely correlated with the single field.Furthermore,the covariabilities among of the three coupled modes have different characteristics at the decadal time scale.In addition,the possible atmospheric teleconnections of the coupled rainfall and SST modes were discussed.For the ENSO-NC mode,anomalous low-pressure and high-pressure over the Asian continent induces moisture divergence over North China and reduces summer rainfall there.For the WTP-YRV mode,East Asia-Pacific teleconnection induces moisture convergence over the Yangtze River valley and enhances the summer rainfall there.The TPMM SST and the summer rainfall anomalies over the YRVL are linked by a circumglobal,wave-train-like,atmospheric teleconnection.

Characteristics of High-power GaAs Laser Beams and Their Coupling with Fibers

The beams of 980nm high-power LDs are analyzed, and the reasons that aspect ratio of LD beams is high are explained. It is certified by the test that cylindrical lens can efficiently compress the perpendicular divergence angle of the beam. Some typical and popular lensed fibers were compared and analyzed according to coupling characteristics. The factors which affect the coupling efficiency and tolerance of the wedged-shaped GRIN tipped lensed fiber are pointed out, and some methods to reduce the coupling loss of the lensed fibers are proposed finally.

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.

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.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

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.

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.

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.

Phase Effect on Mode Coupling in Kelvin—Helmholtz Instability for Two-Dimensional Incompressible Fluid

This paper studies the phase effect in mode coupling of Kelvin-Helmholtz instability in two-dimensionalincompressible fluid.It is found that there is an important growth phenomenon of every mode in the mode couplingprocess.The growth changes periodically with phase difference and in the condition of our simulation the period is about0.7π.The period characteristic is apparent in all stage of the mode coupling process,especially in the relatively laterstage.