In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. Whe...Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. When the electromagnetic frequency is close to the cyclotron one, the linear conductivity increases two orders. Under the resonant frequencies nonlinearity becomes essential at low magnitudes of terahertz electric fields. In absence of a bias magnetic field the nonlinear dependences of the surface electric currents on terahertz electric field are practically the same simulated from kinetics and electron hydrodynamics with nonzero “kinetic” electron effective mass. Graphene possesses higher values of nonlinearity of the resonant conductivity, whereas in absence of a bias magnetic field, the electron nonlinearity is higher in silicene.展开更多
In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use ...In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use the Z1transformation to get the general solutions of some nonlinear partial differential equations for the first time, and use the general solutions to obtain the exact solutions of some typical definite solution problems.展开更多
In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an ast...In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an astonishing effect of light-nucleus interactions.This phenomenon is underpinned by two key factors:(1)the presence of a very low-lying nuclear excited state and(2)a nuclear hyperfine mixing effect that significantly enhances light-nucleus coupling.The resulting highly nonlinear responses facilitate efficient nuclear excitation and enable coherent light emission from the nucleus,resulting in high harmonic generation.229 Th presents a promising platform for advancements in both laser-nuclear physics and nuclear clock development.The pioneering work by Zhang et al.marks a new frontier in light-matter interactions.展开更多
In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order sp...In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.展开更多
Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to...Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to be explored in the existing literature.The shell theory can better simulate the circumferential stress distribution,and thus the Mindlin-Reissner shell theory is used to model the pipeline.In this paper,the continuous pipeline system is combined with clamps through modal expansion for the first time,which realizes the coupling problem between a shell and a clamp.While the Bouc-Wen model is used to simulate the nonlinear external force generated by a clamp,the nonlinear coupling characteristics of the system are effectively captured.Then,the dynamic equation of the clamp-pipeline system is established according to the Lagrange energy equation.Based on the resonance frequency and stress amplitude obtained from the experiment,the nonlinear parameters of the clamp are identified with the semi-analytical method(SAM)and particle swarm optimization(PSO)algorithm.This study provides a theoretical basis for the clamp-pipeline system and an efficient and universal solution for stress prediction and analysis of pipelines in engineering.展开更多
Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.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
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the genera...A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.展开更多
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigatio...In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.展开更多
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study prov...Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates.The inverse hyperbolic shear deformation theory(IHSDT)of plates is employed to characterize the displacement field,with the incorporation of Green-Lagrange nonlinearity.The problem is modeled using the C0finite element method(FEM),and an in-house code is developed in the MATLAB environment to solve it numerically.Various helicoidal layup configurations including helicoidal recursive(HR),helicoidal exponential(HE),helicoidal semi-circular(HS),linear helicoidal(LH),and Fibonacci helicoidal(FH)with different layup sequences and quasi-isotropic configurations are studied.The model is validated,and parametric studies are conducted.These studies investigate the effects of layup configurations,side-to-thickness ratio,modulus ratios,boundary conditions,and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates.The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors.Moreover,this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.展开更多
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches....The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.展开更多
With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymm...With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.展开更多
Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design ...Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.展开更多
The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requ...The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.展开更多
The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant ...The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.展开更多
Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the developm...Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘Resonant linear and nonlinear properties in terahertz range of 2D materials graphene and silicene placed into a bias magnetic field are investigated theoretically on the base of the quasi-classical kinetic theory. When the electromagnetic frequency is close to the cyclotron one, the linear conductivity increases two orders. Under the resonant frequencies nonlinearity becomes essential at low magnitudes of terahertz electric fields. In absence of a bias magnetic field the nonlinear dependences of the surface electric currents on terahertz electric field are practically the same simulated from kinetics and electron hydrodynamics with nonzero “kinetic” electron effective mass. Graphene possesses higher values of nonlinearity of the resonant conductivity, whereas in absence of a bias magnetic field, the electron nonlinearity is higher in silicene.
文摘In previous papers, we proposed the important Ztransformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time. In this paper, we will use the Z1transformation to get the general solutions of some nonlinear partial differential equations for the first time, and use the general solutions to obtain the exact solutions of some typical definite solution problems.
文摘In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an astonishing effect of light-nucleus interactions.This phenomenon is underpinned by two key factors:(1)the presence of a very low-lying nuclear excited state and(2)a nuclear hyperfine mixing effect that significantly enhances light-nucleus coupling.The resulting highly nonlinear responses facilitate efficient nuclear excitation and enable coherent light emission from the nucleus,resulting in high harmonic generation.229 Th presents a promising platform for advancements in both laser-nuclear physics and nuclear clock development.The pioneering work by Zhang et al.marks a new frontier in light-matter interactions.
文摘In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
基金Project supported by the National Science and Technology Major Project(No.J2019-I-0008-0008)the National Natural Science Foundation of China(No.52305096)the Chinese Postdoctoral Science Foundation(No.GZB20230117)。
文摘Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to be explored in the existing literature.The shell theory can better simulate the circumferential stress distribution,and thus the Mindlin-Reissner shell theory is used to model the pipeline.In this paper,the continuous pipeline system is combined with clamps through modal expansion for the first time,which realizes the coupling problem between a shell and a clamp.While the Bouc-Wen model is used to simulate the nonlinear external force generated by a clamp,the nonlinear coupling characteristics of the system are effectively captured.Then,the dynamic equation of the clamp-pipeline system is established according to the Lagrange energy equation.Based on the resonance frequency and stress amplitude obtained from the experiment,the nonlinear parameters of the clamp are identified with the semi-analytical method(SAM)and particle swarm optimization(PSO)algorithm.This study provides a theoretical basis for the clamp-pipeline system and an efficient and universal solution for stress prediction and analysis of pipelines in engineering.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
文摘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 National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB0790000)the Collaborative Innovation Program of Hefei Science Center,CAS(No.2022HSC-CIP008)National Natural Science Foundation of China(Nos.12275236 and 12261131622)。
文摘A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
基金supported by the National Key Research and Development Program of China (2019YFB1803905)the National Natural Science Foundation of China (No.62171022)+2 种基金Beijing Natural Science Foundation (4222009)Guangdong Basic and Applied Basic Research Foundation (2021B1515120057)the Scientific and Technological Innovation Foundation of Shunde Graduate School,USTB (No.BK19AF005)。
文摘In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
文摘Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates.The inverse hyperbolic shear deformation theory(IHSDT)of plates is employed to characterize the displacement field,with the incorporation of Green-Lagrange nonlinearity.The problem is modeled using the C0finite element method(FEM),and an in-house code is developed in the MATLAB environment to solve it numerically.Various helicoidal layup configurations including helicoidal recursive(HR),helicoidal exponential(HE),helicoidal semi-circular(HS),linear helicoidal(LH),and Fibonacci helicoidal(FH)with different layup sequences and quasi-isotropic configurations are studied.The model is validated,and parametric studies are conducted.These studies investigate the effects of layup configurations,side-to-thickness ratio,modulus ratios,boundary conditions,and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates.The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors.Moreover,this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
基金Project supported by the National Science Fund for Distinguished Young Scholars of China(No.12025204)the National Natural Science Foundation of China(No.12202038)。
文摘With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.
基金the China National Funds for Distinguished Young Scholars(No.12025204)。
文摘Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.
基金supported in part by the National Natural Science Foundation of China (62103093)the National Key Research and Development Program of China (2022YFB3305905)+6 种基金the Xingliao Talent Program of Liaoning Province of China (XLYC2203130)the Fundamental Research Funds for the Central Universities of China (N2108003)the Natural Science Foundation of Liaoning Province (2023-MS-087)the BNU Talent Seed Fund,UIC Start-Up Fund (R72021115)the Guangdong Key Laboratory of AI and MM Data Processing (2020KSYS007)the Guangdong Provincial Key Laboratory IRADS for Data Science (2022B1212010006)the Guangdong Higher Education Upgrading Plan 2021–2025 of “Rushing to the Top,Making Up Shortcomings and Strengthening Special Features” with UIC Research,China (R0400001-22,R0400025-21)。
文摘The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.
基金supported by the 2021 Open Project Fund of Science and Technology on Electromechanical Dynamic Control Laboratory,grant number 212-C-J-F-QT-2022-0020China Postdoctoral Science Foundation,grant number 2021M701713+1 种基金Postgraduate Research&Practice Innovation Program of Jiangsu Province,grant number KYCX23_0511the Jiangsu Funding Program for Excellent Postdoctoral Talent,grant number 20220ZB245。
文摘The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.
基金supported by the Australian Research Council(Grant No.DP210101292)the International Technology Center Indo-Pacific (ITC IPAC) via Army Research Office (contract FA520923C0023)。
文摘Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.
