The high-aspect-ratio wing,which is widely utilized in aircraft to achieve superior aerodynamic efficiency,frequently experiences large deformations such as bending and torsion during its service life.This work focuse...The high-aspect-ratio wing,which is widely utilized in aircraft to achieve superior aerodynamic efficiency,frequently experiences large deformations such as bending and torsion during its service life.This work focuses on the topology optimization of the high-aspect-ratio wing using multiple materials with bending and torsion controls considering geometric nonlinearity.A novel approach is proposed for achieving a spar-ribs material layout by independently controlling the directional maximum length scale of the void phase.The bending control based on the wing-tip nodal displacement and torsion control based on the deformation difference of the wing-tip nodes are proposed,respectively.Afterwards,the optimization formulations are given and the sensitivity analysis of the optimization responses is derived based on the increment of nodal displacement.The optimized results reveal that the spar-ribs structural layout is successfully attained through directional length scale control.Moreover,the optimized configurations with bending and torsion precisely controlled can be achieved.It also has been demonstrated that considering bending and torsion controls is highly profitable when assessing the trade-off between end compliance in wing optimization.展开更多
Previous studies have explored the possible impact of joint El Niño–Southern Oscillation(ENSO)–Quasi-Biennial Oscillation(QBO)forcings on the northern winter stratospheric circulation.This study continues to in...Previous studies have explored the possible impact of joint El Niño–Southern Oscillation(ENSO)–Quasi-Biennial Oscillation(QBO)forcings on the northern winter stratospheric circulation.This study continues to investigate the relative contributions of the nonlinearity and linearity of joint ENSO–QBO forcings in the total circulation anomaly.The possible interference of ENSO(QBO)signals within QBO(ENSO)is removed before the pure QBO(ENSO)signals in the circulation are calculated.A linear superposition of the pure QBO+ENSO signals is compared with the joint ENSO–QBO composite patterns.It is revealed that the combined ENSO–QBO effect is nearly a linear summation of the pure ENSO+QBO signals in the stratosphere,displaying strong linearity.This linearity decreases slightly from the stratosphere to the troposphere,and the nonlinearity of the joint ENSO–QBO impact increases in regional tropospheric circulation.The linearity and nonlinearity of the joint ENSO–QBO impact in the troposphere are nonuniformly distributed:Lower-to-mid latitude circulation changes associated with configured ENSO–QBO forcings are nearly a linear combination of pure ENSO and QBO signals,while nonlinearity soon dominates the total circulation anomaly pattern at high latitudes,with the ENSO signals overwhelming the QBO signals,especially for the El Niño–EQBO(QBO easterly phase)configurations.This study provides evidence that linearity of the joint ENSO–QBO impact prevails in the stratosphere and tropical troposphere,while nonlinearity exists in the Arctic troposphere.展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and Iαforα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and Iαforα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
This paper introduces a novel analytical technique called the "Variable Coefficient Second Degree Generalized Abel equation Method"(VCSDGAE),designed to tackle the complex Ginzburg-Landau equation.Unlike con...This paper introduces a novel analytical technique called the "Variable Coefficient Second Degree Generalized Abel equation Method"(VCSDGAE),designed to tackle the complex Ginzburg-Landau equation.Unlike conventional methods that depend on constant coefficient ordinary differential equations(ODEs) and auxiliary ODEs,our approach employs variable coefficient ODEs within a sub-equation framework.We demonstrate the versatility of this method by successfully applying it to the complex Ginzburg-Landau equation.Through the presentation of analytical solutions,we showcase the method's effectiveness and efficiency,positioning it as a valuable resource for addressing complex nonlinear partial differential equations in fields such as fluid dynamics and wave propagation.The stability of the obtained soliton solutions is established through a linear stability analysis,confirming their robustness against small perturbations.This research not only broadens the spectrum of available analytical techniques but also contributes significantly to the advancement of solutions for various mathematical physics models.展开更多
In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve ...In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators.Firstly,based on Hamilton's principle and the Galerkin method,the control equations for the coupled system are established.The theoretical band gap boundary is then derived with the modal analysis method.The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor,distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics.Then,the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation,and are verified by the theoretical results.Furthermore,parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region.Finally,a prototype of the meta-beam is fabricated and assembled,and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.展开更多
We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We s...We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.展开更多
We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system...We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system comprises an optical cavity, a two-level atomic ensemble and a mechanical resonator that possesses Duffing nonlinearity. The interaction between these components is mediated by the cavity mode, which is driven by an external laser. Our findings indicate that optimizing the coupling strengths between photons and phonons, as well as between atoms and the cavity,leads to maximal entanglement and EPR steering. The amplitude of the driving laser plays a pivotal role in enhancing the coupling between photons and phonons, and the system maintains robust entanglement and EPR steering even under high dissipation, thereby mitigating the constraints on initial conditions and parameter precision. Remarkably, the Duffing nonlinearity enhances the system's resistance to thermal noise, ensuring its stability and entanglement protection. Our analysis of EPR steering conditions reveals that the party with lower dissipation exhibits superior stability and a propensity to steer the party with higher dissipation. These discoveries offer novel perspectives for advancing quantum information processing and communication technologies.展开更多
In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantita...In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantitative results of traditional methods,such as partial least squares regression(PLS),which can be used to construct linear models.The problem was addressed in this study by using deep learning(DL).We employed three different DL models:a one-dimensional convolutional neural network(1D CNN),a deep neural network(DNN),and a stacked autoencoder with feedforward neural networks(SAE-FNNs).By carefully selecting and tuning the architectures and parameters of these models,we were able to find the most suitable model for dealing with such nonlinear relationships.Our experimental findings reveal that both the DNN and the SAE-FNN models excel in addressing the nonlinear issues of pectin concentration in tobacco,surpassing the performance of the classic linear model(PLS).Specifically,the DNN model stands out for its low average root mean squared error of prediction(RMSEP)value and small standard deviation(SD)of RMSEPs,leading to a tighter and more centered distribution of residuals in the prediction set.These DL models not only proficiently identify complex patterns within NIR data but also boast high prediction accuracy and fast implementation,demonstrating their effectiveness in analytical applications.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is c...Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is carried out in the present study. To obtain the Structural nonlinear response and ultimate resistance capacity, material and geometrical nonlinear analysis of circular concrete-filled steel tube is performed with a three-dimensional degenerated beam ele- ment. Then we investigate the reliability of concrete-filled steel tube using the first-order reliability method combined with nonlinear finite element analysis. The influences of such parameters as material strength, slenderness, initial geo- metrical imperfection, etc. on the reliability of circular concrete-filled steel tube column are studied. It can be con- cluded that inevitable random fluctuation of those parameters has significant influence on structural reliability, and that stochastic or reliability methods can provide a more rational and subjective evaluation on the safety of CFT structures than a deterministic approach.展开更多
This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to re...This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to reflect the structural response and the joint load distribution under large deformation.To avoid a failure of fastener joints,topology optimization is then carried out to minimize the structural end compliance in the equilibrium state while controlling joint loads intensities over fasteners.During nonlinear analysis and optimization,a novel implementation of adjoint vector sensitivity analysis along with super element condensation is introduced to address numerical instability issues.The degrees of freedom of weak regions are condensed so that their influences are excluded from the iterative Newton-Raphson(NR)solution.Numerical examples are presented to validate the efficiency and robustness of the proposed method.The effects of joint load constraints and geometrical nonlinearity are highlighted by comparing numerical optimization results.展开更多
A grating eddy current displacement sensor(GECDS) can be used in a watertight electronic transducer to realize long range displacement or position measurement with high accuracy in difficult industry conditions.The pa...A grating eddy current displacement sensor(GECDS) can be used in a watertight electronic transducer to realize long range displacement or position measurement with high accuracy in difficult industry conditions.The parameters optimization of the sensor is essential for economic and efficient production.This paper proposes a method to combine an artificial neural network(ANN) and a genetic algorithm(GA) for the sensor parameters optimization.A neural network model is developed to map the complex relationship between design parameters and the nonlinearity error of the GECDS,and then a GA is used in the optimization process to determine the design parameter values,resulting in a desired minimal nonlinearity error of about 0.11%.The calculated nonlinearity error is 0.25%.These results show that the proposed method performs well for the parameters optimization of the GECDS.展开更多
Magnetorheological(MR)dampers show superior performance in reducing rotor vibration,but their high nonlinearity will cause nonsynchronous response,resulting in fatigue and instability of rotors.Herein,we are devoted t...Magnetorheological(MR)dampers show superior performance in reducing rotor vibration,but their high nonlinearity will cause nonsynchronous response,resulting in fatigue and instability of rotors.Herein,we are devoted to the investigation of the nonlinear characteristics of MR damper mounted on a flexible rotor.First,Reynolds equations with bilinear constitutive equations of MR fluid are employed to derive nonlinear oil film forces.Then,the Finite Element(FE)model of rotor system is developed,where the local nonlinear support forces produced by MR damper and its coupling effects with the rotor are considered.A hybrid numerical method is proposed to solve the nonlinear FE motion equations of the MR damper-rotor system.To validate the proposed model,a rotor test bench with two dual-coil MR dampers is constructed,upon which experimental studies on the dynamic characteristics of MR damper-rotor system are carried out.The effects of different system parameters,including rotational speed,excitation current and amount of unbalance,on nonlinear dynamic behaviors of MR damper-rotor system are evaluated.The results show that the system may appear chaos,jumping,and other complex nonlinear phenomena,and the level of the nonlinearity can be effectively alleviated by applying suitable excitation current and oil supply pressure.展开更多
We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements, cross-Kerr n...We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements, cross-Kerr nonlinearity, and homodyne measurement, therefore it is feasible with current experimental technology, The success probability of our protocol is optimal, this property makes our protocol more efficient than others in the applications of quantum communication.展开更多
In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solu...In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM),Cosine-function method (CFM).We show that the solutions by using ISM and CFM are equal.Finally,we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).展开更多
A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high bire- fringence and nonlinearity at a wavelength of 1.55 μm. The full vector finite element method was ...A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high bire- fringence and nonlinearity at a wavelength of 1.55 μm. The full vector finite element method was adopted to investigate its characteristics, including birefringence, nonlinearity, and dispersion. The PCF exhibited a very high birefringence of 2.89x10-2 and very high nonlinear coefficient of 102.69 W-1 .km 1. In particular, there were two zero-dispersion wave- lengths (ZDWs) in the visible (X: 640-720 nm and Y: 730-760 nm) and near-infrared regions (X: 1050-1606 nm and Y: 850-1500 nm). The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum, with potential applications in nonlinear optics.展开更多
Passive inter-modulation (PIM) is a form of nonlinear distortion caused by the inherent nonlinearities of the passive devices and components in RF/microwave system. It will degenerate the performance of communicatio...Passive inter-modulation (PIM) is a form of nonlinear distortion caused by the inherent nonlinearities of the passive devices and components in RF/microwave system. It will degenerate the performance of communication system with broad-band channel and high-sensitivity receiver. Therefore, it is necessary to construct a model to simulate this process in order to predict the level of PIM. This paper is aimed at constructing some plate models with one-dimensional and two-dimensional contact nonlinearity sections illuminated by two-tone waves, and calculating the scattered field at a fixed-point in space using time-domain physical optics method. By taking fast Fourier transform (FFT), we get the spectrum of the scattered field and then analyze the generated PIM products. At the end of this paper, some numerical examples are presented to show the influence rules of the relative factors on PIM. The results indicate the variation of the level of PIM with the number of the nonlinear regions, the nonlinear spacing, and the incident power levels.展开更多
A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-...A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-sulfoxande,dioxane,ethanol,and methanol,etc.The nonlinear refractive index for the solvents at femtosecond time scale was measured.展开更多
Limit cycle oscillations (LCOs) as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of ...Limit cycle oscillations (LCOs) as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance (HB) method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB (HB3) method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.展开更多
The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attenti...The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12172294).
摘要The high-aspect-ratio wing,which is widely utilized in aircraft to achieve superior aerodynamic efficiency,frequently experiences large deformations such as bending and torsion during its service life.This work focuses on the topology optimization of the high-aspect-ratio wing using multiple materials with bending and torsion controls considering geometric nonlinearity.A novel approach is proposed for achieving a spar-ribs material layout by independently controlling the directional maximum length scale of the void phase.The bending control based on the wing-tip nodal displacement and torsion control based on the deformation difference of the wing-tip nodes are proposed,respectively.Afterwards,the optimization formulations are given and the sensitivity analysis of the optimization responses is derived based on the increment of nodal displacement.The optimized results reveal that the spar-ribs structural layout is successfully attained through directional length scale control.Moreover,the optimized configurations with bending and torsion precisely controlled can be achieved.It also has been demonstrated that considering bending and torsion controls is highly profitable when assessing the trade-off between end compliance in wing optimization.
基金financially supported by the National Natural Science Foundation of China[grant numbers 42175069,42322503,and 42361144843]the Qinglan Project of Jiangsu of China.
摘要Previous studies have explored the possible impact of joint El Niño–Southern Oscillation(ENSO)–Quasi-Biennial Oscillation(QBO)forcings on the northern winter stratospheric circulation.This study continues to investigate the relative contributions of the nonlinearity and linearity of joint ENSO–QBO forcings in the total circulation anomaly.The possible interference of ENSO(QBO)signals within QBO(ENSO)is removed before the pure QBO(ENSO)signals in the circulation are calculated.A linear superposition of the pure QBO+ENSO signals is compared with the joint ENSO–QBO composite patterns.It is revealed that the combined ENSO–QBO effect is nearly a linear summation of the pure ENSO+QBO signals in the stratosphere,displaying strong linearity.This linearity decreases slightly from the stratosphere to the troposphere,and the nonlinearity of the joint ENSO–QBO impact increases in regional tropospheric circulation.The linearity and nonlinearity of the joint ENSO–QBO impact in the troposphere are nonuniformly distributed:Lower-to-mid latitude circulation changes associated with configured ENSO–QBO forcings are nearly a linear combination of pure ENSO and QBO signals,while nonlinearity soon dominates the total circulation anomaly pattern at high latitudes,with the ENSO signals overwhelming the QBO signals,especially for the El Niño–EQBO(QBO easterly phase)configurations.This study provides evidence that linearity of the joint ENSO–QBO impact prevails in the stratosphere and tropical troposphere,while nonlinearity exists in the Arctic troposphere.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
摘要We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and Iαforα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
摘要This paper introduces a novel analytical technique called the "Variable Coefficient Second Degree Generalized Abel equation Method"(VCSDGAE),designed to tackle the complex Ginzburg-Landau equation.Unlike conventional methods that depend on constant coefficient ordinary differential equations(ODEs) and auxiliary ODEs,our approach employs variable coefficient ODEs within a sub-equation framework.We demonstrate the versatility of this method by successfully applying it to the complex Ginzburg-Landau equation.Through the presentation of analytical solutions,we showcase the method's effectiveness and efficiency,positioning it as a valuable resource for addressing complex nonlinear partial differential equations in fields such as fluid dynamics and wave propagation.The stability of the obtained soliton solutions is established through a linear stability analysis,confirming their robustness against small perturbations.This research not only broadens the spectrum of available analytical techniques but also contributes significantly to the advancement of solutions for various mathematical physics models.
基金supported by the National Natural Science Foundation of China(Nos.12172014,U224126412332001)。
摘要In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators.Firstly,based on Hamilton's principle and the Galerkin method,the control equations for the coupled system are established.The theoretical band gap boundary is then derived with the modal analysis method.The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor,distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics.Then,the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation,and are verified by the theoretical results.Furthermore,parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region.Finally,a prototype of the meta-beam is fabricated and assembled,and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.
基金partially supported by the National Natural Science Foundation of China(Grant No.12201417)the Project funded by the China Postdoctoral Science Foundation(Grant No.2023M733173)partially supported by the National Natural Science Foundation of China(Grant No.12375006)。
摘要We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12204440)Fundamental Research Program of Shanxi Province (Grant Nos. 20210302123063 and 202103021223184)。
摘要We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system comprises an optical cavity, a two-level atomic ensemble and a mechanical resonator that possesses Duffing nonlinearity. The interaction between these components is mediated by the cavity mode, which is driven by an external laser. Our findings indicate that optimizing the coupling strengths between photons and phonons, as well as between atoms and the cavity,leads to maximal entanglement and EPR steering. The amplitude of the driving laser plays a pivotal role in enhancing the coupling between photons and phonons, and the system maintains robust entanglement and EPR steering even under high dissipation, thereby mitigating the constraints on initial conditions and parameter precision. Remarkably, the Duffing nonlinearity enhances the system's resistance to thermal noise, ensuring its stability and entanglement protection. Our analysis of EPR steering conditions reveals that the party with lower dissipation exhibits superior stability and a propensity to steer the party with higher dissipation. These discoveries offer novel perspectives for advancing quantum information processing and communication technologies.
基金supported by a joint project with SINOPEC(Dalian)Research Institute of Petroleum and Petrochemicals Co.,Ltd.(Contract No.323061).
摘要In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantitative results of traditional methods,such as partial least squares regression(PLS),which can be used to construct linear models.The problem was addressed in this study by using deep learning(DL).We employed three different DL models:a one-dimensional convolutional neural network(1D CNN),a deep neural network(DNN),and a stacked autoencoder with feedforward neural networks(SAE-FNNs).By carefully selecting and tuning the architectures and parameters of these models,we were able to find the most suitable model for dealing with such nonlinear relationships.Our experimental findings reveal that both the DNN and the SAE-FNN models excel in addressing the nonlinear issues of pectin concentration in tobacco,surpassing the performance of the classic linear model(PLS).Specifically,the DNN model stands out for its low average root mean squared error of prediction(RMSEP)value and small standard deviation(SD)of RMSEPs,leading to a tighter and more centered distribution of residuals in the prediction set.These DL models not only proficiently identify complex patterns within NIR data but also boast high prediction accuracy and fast implementation,demonstrating their effectiveness in analytical applications.
摘要In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金supported by the Fundamental Research Funds for the Central Universities (SWJTU09CX012 and SWJTU11BR006)the Doctoral Fund for Youth Scholars of Ministry of Educationof China (No. 20110184120010)
摘要Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is carried out in the present study. To obtain the Structural nonlinear response and ultimate resistance capacity, material and geometrical nonlinear analysis of circular concrete-filled steel tube is performed with a three-dimensional degenerated beam ele- ment. Then we investigate the reliability of concrete-filled steel tube using the first-order reliability method combined with nonlinear finite element analysis. The influences of such parameters as material strength, slenderness, initial geo- metrical imperfection, etc. on the reliability of circular concrete-filled steel tube column are studied. It can be con- cluded that inevitable random fluctuation of those parameters has significant influence on structural reliability, and that stochastic or reliability methods can provide a more rational and subjective evaluation on the safety of CFT structures than a deterministic approach.
基金co-supported by National Key Research and Development Program(No.2017YFB1102800)NSFC for Excellent Young Scholars(No.11722219)Key Project of NSFC(Nos.51790171,5171101743,51735005,11620101002,and 11432011).
摘要This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to reflect the structural response and the joint load distribution under large deformation.To avoid a failure of fastener joints,topology optimization is then carried out to minimize the structural end compliance in the equilibrium state while controlling joint loads intensities over fasteners.During nonlinear analysis and optimization,a novel implementation of adjoint vector sensitivity analysis along with super element condensation is introduced to address numerical instability issues.The degrees of freedom of weak regions are condensed so that their influences are excluded from the iterative Newton-Raphson(NR)solution.Numerical examples are presented to validate the efficiency and robustness of the proposed method.The effects of joint load constraints and geometrical nonlinearity are highlighted by comparing numerical optimization results.
摘要A grating eddy current displacement sensor(GECDS) can be used in a watertight electronic transducer to realize long range displacement or position measurement with high accuracy in difficult industry conditions.The parameters optimization of the sensor is essential for economic and efficient production.This paper proposes a method to combine an artificial neural network(ANN) and a genetic algorithm(GA) for the sensor parameters optimization.A neural network model is developed to map the complex relationship between design parameters and the nonlinearity error of the GECDS,and then a GA is used in the optimization process to determine the design parameter values,resulting in a desired minimal nonlinearity error of about 0.11%.The calculated nonlinearity error is 0.25%.These results show that the proposed method performs well for the parameters optimization of the GECDS.
基金supports from National Natural Science Foundation of China(No.11972204)Natural Science Foundation of Tianjin,China(No.19JCQNJC02500)。
摘要Magnetorheological(MR)dampers show superior performance in reducing rotor vibration,but their high nonlinearity will cause nonsynchronous response,resulting in fatigue and instability of rotors.Herein,we are devoted to the investigation of the nonlinear characteristics of MR damper mounted on a flexible rotor.First,Reynolds equations with bilinear constitutive equations of MR fluid are employed to derive nonlinear oil film forces.Then,the Finite Element(FE)model of rotor system is developed,where the local nonlinear support forces produced by MR damper and its coupling effects with the rotor are considered.A hybrid numerical method is proposed to solve the nonlinear FE motion equations of the MR damper-rotor system.To validate the proposed model,a rotor test bench with two dual-coil MR dampers is constructed,upon which experimental studies on the dynamic characteristics of MR damper-rotor system are carried out.The effects of different system parameters,including rotational speed,excitation current and amount of unbalance,on nonlinear dynamic behaviors of MR damper-rotor system are evaluated.The results show that the system may appear chaos,jumping,and other complex nonlinear phenomena,and the level of the nonlinearity can be effectively alleviated by applying suitable excitation current and oil supply pressure.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61068001 and 11064016)
摘要We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements, cross-Kerr nonlinearity, and homodyne measurement, therefore it is feasible with current experimental technology, The success probability of our protocol is optimal, this property makes our protocol more efficient than others in the applications of quantum communication.
基金Supported by the Research Foundation of Education Bureau of Hunan Province under Grant No.11C0628Foundation of Hunan Institute of Science and Technology under Grant No.2011Y49
摘要In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM),Cosine-function method (CFM).We show that the solutions by using ISM and CFM are equal.Finally,we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).
基金Project supported by the National Natural Science Foundation of China(Grant No.61475029)
摘要A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high bire- fringence and nonlinearity at a wavelength of 1.55 μm. The full vector finite element method was adopted to investigate its characteristics, including birefringence, nonlinearity, and dispersion. The PCF exhibited a very high birefringence of 2.89x10-2 and very high nonlinear coefficient of 102.69 W-1 .km 1. In particular, there were two zero-dispersion wave- lengths (ZDWs) in the visible (X: 640-720 nm and Y: 730-760 nm) and near-infrared regions (X: 1050-1606 nm and Y: 850-1500 nm). The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum, with potential applications in nonlinear optics.
摘要Passive inter-modulation (PIM) is a form of nonlinear distortion caused by the inherent nonlinearities of the passive devices and components in RF/microwave system. It will degenerate the performance of communication system with broad-band channel and high-sensitivity receiver. Therefore, it is necessary to construct a model to simulate this process in order to predict the level of PIM. This paper is aimed at constructing some plate models with one-dimensional and two-dimensional contact nonlinearity sections illuminated by two-tone waves, and calculating the scattered field at a fixed-point in space using time-domain physical optics method. By taking fast Fourier transform (FFT), we get the spectrum of the scattered field and then analyze the generated PIM products. At the end of this paper, some numerical examples are presented to show the influence rules of the relative factors on PIM. The results indicate the variation of the level of PIM with the number of the nonlinear regions, the nonlinear spacing, and the incident power levels.
基金Supported by the National Natural Science Foundation of China under Grant No.19525412National Science and Technology Commission of China。
摘要A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-sulfoxande,dioxane,ethanol,and methanol,etc.The nonlinear refractive index for the solvents at femtosecond time scale was measured.
摘要Limit cycle oscillations (LCOs) as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance (HB) method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB (HB3) method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872141)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060056005)the National Basic Research Program of China (GrantNo. 007CB714000)
摘要The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.