In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.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
Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonli...Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.展开更多
Honeycomb structures of shape memory alloy(SMA)have become one of the most promising materials for flexible skins of morphing aircraft due to their excellent mechanical properties.However,due to the nonlinear material...Honeycomb structures of shape memory alloy(SMA)have become one of the most promising materials for flexible skins of morphing aircraft due to their excellent mechanical properties.However,due to the nonlinear material and geometric large deformation,the SMA honeycomb exhibits significant and complex nonlinearity in the skin and there is a lack of relevant previous research.In this paper,the nonlinear properties of the SMA honeycomb structure with arbitrary geometry are investigated for the first time for large deformation flexible skin applications by theoretical and experimental analysis.Firstly,a novel theoretical model of SMA honeycomb structure considering both material and geometric nonlinearity is proposed,and the corresponding calculation method of nonlinear governing equations is given based upon the shooting method and Runge–Kutta method.Then,the tensile behaviors of four kinds of SMA honeycomb structures,i.e.,U-type,V-type,cosine-type,and trapezoid-type,are analyzed and predicted by the proposed theoretical model and compared with the finite element analysis(FEA)results.Moreover,the tensile experiments were carried out by stretching U-type and V-type honeycomb structures to a global strain of 60%and 40%,respectively,to perform large deformation analysis and verify the theoretical model.Finally,experimental verification and finite element validation show that the curves of the theoretical model results,experimental results,and simulation results are in good agreement,illustrating the generalizability and accuracy of the proposed theoretical model.The theoretical model and experimental investigations in this paper are considered to provide an effective foundation for analyzing and predicting the mechanical behavior of SMA honeycomb flexible skins with large extensional deformations.展开更多
Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of e...Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.展开更多
We present a 3+1 formulation of the light modes in nonlinear electrodynamics described by Plebanski-type Lagrangians,which include post-Maxwellian,Born-Infeld,ModMax,and Heisenberg-Euler-Schwinger QED Lagrangians.In n...We present a 3+1 formulation of the light modes in nonlinear electrodynamics described by Plebanski-type Lagrangians,which include post-Maxwellian,Born-Infeld,ModMax,and Heisenberg-Euler-Schwinger QED Lagrangians.In nonlinear electrodynamics,strong electromagnetic fields modify the vacuum such that it acquires optical properties.Such a field-modified vacuum can possess electric permittivity,magnetic permeability,and a magneto-electric response,inducing novel phenomena such as vacuum birefringence.By exploiting the mathematical structures of Plebanski-type Lagrangians,we establish a streamlined procedure and explicit formulas to determine light modes,i.e.,refractive indices and polarization vectors for a given propagation direction.We also work out the light modes of the various Lagrangians for an arbitrarily strong magnetic field.The 3+1 formulation advanced in this paper has direct applications to the current vacuum birefringence research:terrestrial experiments using permanent magnets/ultra-intense lasers for the subcritical regime and astrophysical observation of X-rays from highly magnetized neutron stars for the near-critical and supercritical regimes.展开更多
In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin...In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin films of the ionic COF material PySQ-iCOF was successfully fabricated using a solid-liquid interface method,meanwhile the building units extracted to be independent small molecule,1-PySA,were synthesized for comparative studies.Compared to 1-PySA,PySQ-iCOF possesses not only a larger conjugated system but also exhibits enhanced polarization and charge transfer capabilities.The NLO properties of PySQ-iCOF and the small molecule 1-PySA were investigated using Z-scan technique at a wavelength of 532 nm,revealing the PySQ-iCOF thin film exhibits outstanding NLO performance.Specifically,it demonstrates saturable absorption under nanosecond(ns)pulse laser irradiation(β=9.59×10^(-6) m/W),while exhibiting reverse saturable absorption under femtosecond(fs)pulse conditions(β=6.91×10^(-8) m/W).Furthermore,the PySQ-iCOF film exhibits strong negative refractive nonlinearity,−6×10^(-12) m^(2)/W for ns and -3.8×10^(-13) m^(2)/W for fs,respectively.Transient absorption spectroscopy studies indicate that the pulse-width-dependent nonlinear absorption char-acteristics of the PySQ-iCOF film originate from the generation of triplet excited states.Both nonlinear absorption coefficient and nonlinear refractive index of the PySQ-iCOF film surpass those of most reported organic materials measured under comparable conditions,which provides huge potential in all-optical manipulating and switching at the nanoscale as outstanding NLO materials.展开更多
This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents differe...This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents different basic INDI variants and their specifics,such as modelbased INDI,sensor-based INDI,and hybrid INDI.Furthermore,it sets these different approaches in context with each other.Later developments of INDI explicitly consider actuator dynamics.Those concepts are summarized and discussed in detail.Subsequently,studies that relate INDI to other control methods are summarized.Finally,an overview of various applications of INDI is given,covering different types of control loops and various types of vehicles and plants.This paper seeks to set these developments into context with each other.The purpose of this paper is twofold.INDI is already well-known in the domain of flight control but less so in other fields.Therefore,the paper is written in a comprehensive tutorial style to provide easy access to readers unfamiliar with the topic.On the other hand,the paper can serve as a reference for readers familiar with the topic.展开更多
This paper develops a residual-based adaptive refinement physics-informed neural networks(RAR-PINNs)method for solving the Gross–Pitaevskii(GP)equation and Hirota equation,two paradigmatic nonlinear partial different...This paper develops a residual-based adaptive refinement physics-informed neural networks(RAR-PINNs)method for solving the Gross–Pitaevskii(GP)equation and Hirota equation,two paradigmatic nonlinear partial differential equations(PDEs)governing quantum condensates and optical rogue waves,respectively.The key innovation lies in the adaptive sampling strategy that dynamically allocates computational resources to regions with large PDE residuals,addressing critical limitations of conventional PINNs in handling:(1)Strong nonlinearities(|u|^(2)u terms)in the GP equation;(2)High-order derivatives(u_(xxx))in the Hirota equation;(3)Multi-scale solution structures.Through rigorous numerical experiments,we demonstrate that RAR-PINNs achieve superior accuracy[relative L^(2)errors of O(10^(−3))]and computational efficiency(faster than standard PINNs)for both equations.The method successfully captures:(1)Bright solitons in the GP equation;(2)First-and second-order rogue waves in the Hirota equation.The RAR adaptive sampling method demonstrates particularly remarkable effectiveness in solving steep gradient problems.Compared with uniform sampling methods,the errors of simulation results are reduced by two orders of magnitude.This study establishes a general framework for data-driven solutions of high-order nonlinear PDEs with complex solution structures.展开更多
When a laser beam is incident on a nonlinear grating with a laterally modulated second-order nonlinear coefficient,nonlinear diffraction of the noncollinear second-harmonic generation(SHG)signal occurs,with Raman–Nat...When a laser beam is incident on a nonlinear grating with a laterally modulated second-order nonlinear coefficient,nonlinear diffraction of the noncollinear second-harmonic generation(SHG)signal occurs,with Raman–Nath nonlinear diffraction(NRND)being a prominent example.As these SHG NRND processes involve coupling between the fundamental-wave pump laser vectorial field and the SHG laser vectorial field through the second-order nonlinearity secondrank tensor of the nonlinear crystal,the nonlinear interaction between light and the nonlinear grating can be manipulated by adjusting the polarization state of the pump laser.In this paper,we derive the relationship between the polarization state of the incident light and the generated nonlinear diffraction signal based on the nonlinear coupled wave equation and experimentally validate the predicted diffraction characteristics.The results show that the optical properties of each order of NRND are highly sensitive to the polarization angle of the incident pump laser beam.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
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.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
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
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
Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based c...Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
基金supported by the National Natural Science Foundation of China(Nos.12172014,U224126412332001)。
文摘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.
文摘Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.
基金supported by the National Key Research and Development Program of China(No.2020YFB1708303)the National Natural Science Foundation of China(Nos.U1808215 and 12072058)the Fundamental Research Funds for the Central Universities of China(DUT20LK02).
文摘Honeycomb structures of shape memory alloy(SMA)have become one of the most promising materials for flexible skins of morphing aircraft due to their excellent mechanical properties.However,due to the nonlinear material and geometric large deformation,the SMA honeycomb exhibits significant and complex nonlinearity in the skin and there is a lack of relevant previous research.In this paper,the nonlinear properties of the SMA honeycomb structure with arbitrary geometry are investigated for the first time for large deformation flexible skin applications by theoretical and experimental analysis.Firstly,a novel theoretical model of SMA honeycomb structure considering both material and geometric nonlinearity is proposed,and the corresponding calculation method of nonlinear governing equations is given based upon the shooting method and Runge–Kutta method.Then,the tensile behaviors of four kinds of SMA honeycomb structures,i.e.,U-type,V-type,cosine-type,and trapezoid-type,are analyzed and predicted by the proposed theoretical model and compared with the finite element analysis(FEA)results.Moreover,the tensile experiments were carried out by stretching U-type and V-type honeycomb structures to a global strain of 60%and 40%,respectively,to perform large deformation analysis and verify the theoretical model.Finally,experimental verification and finite element validation show that the curves of the theoretical model results,experimental results,and simulation results are in good agreement,illustrating the generalizability and accuracy of the proposed theoretical model.The theoretical model and experimental investigations in this paper are considered to provide an effective foundation for analyzing and predicting the mechanical behavior of SMA honeycomb flexible skins with large extensional deformations.
基金support of the RSF Grant No.24-11-00139(analytics,numerical results,manuscript writing)Daxing Xiong acknowledges the support of the NNSF Grant No.12275116,the NSF Grant No.2021J02051,and the startup fund Grant No.MJY21035For Aleksey A.Kudreyko,this work was supported by the Bashkir StateMedicalUniversity StrategicAcademic Leadership Program(PRIORITY-2030)(analytics).
文摘Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.
基金supported by the Ultrashort Quantum Beam Facility operation program(Grant No.140011)through APRI,GISTalso by the Institute of Basic Science(Grant No.IBSR038-D1).
文摘We present a 3+1 formulation of the light modes in nonlinear electrodynamics described by Plebanski-type Lagrangians,which include post-Maxwellian,Born-Infeld,ModMax,and Heisenberg-Euler-Schwinger QED Lagrangians.In nonlinear electrodynamics,strong electromagnetic fields modify the vacuum such that it acquires optical properties.Such a field-modified vacuum can possess electric permittivity,magnetic permeability,and a magneto-electric response,inducing novel phenomena such as vacuum birefringence.By exploiting the mathematical structures of Plebanski-type Lagrangians,we establish a streamlined procedure and explicit formulas to determine light modes,i.e.,refractive indices and polarization vectors for a given propagation direction.We also work out the light modes of the various Lagrangians for an arbitrarily strong magnetic field.The 3+1 formulation advanced in this paper has direct applications to the current vacuum birefringence research:terrestrial experiments using permanent magnets/ultra-intense lasers for the subcritical regime and astrophysical observation of X-rays from highly magnetized neutron stars for the near-critical and supercritical regimes.
基金the National Natural Science Foundation of China(22171076)Jing Li at the Technical Institute of Physics and Chemistry,Chinese Academy of Sciences(CAS),for his measurement of dynamic processes.
文摘In this paper,the third-order nonlinear optical(NLO)properties of covalent organic framework(COF)materials with conjugated amphoteric ion structure are studied for the first time.A highly ordered crystalline ultrathin films of the ionic COF material PySQ-iCOF was successfully fabricated using a solid-liquid interface method,meanwhile the building units extracted to be independent small molecule,1-PySA,were synthesized for comparative studies.Compared to 1-PySA,PySQ-iCOF possesses not only a larger conjugated system but also exhibits enhanced polarization and charge transfer capabilities.The NLO properties of PySQ-iCOF and the small molecule 1-PySA were investigated using Z-scan technique at a wavelength of 532 nm,revealing the PySQ-iCOF thin film exhibits outstanding NLO performance.Specifically,it demonstrates saturable absorption under nanosecond(ns)pulse laser irradiation(β=9.59×10^(-6) m/W),while exhibiting reverse saturable absorption under femtosecond(fs)pulse conditions(β=6.91×10^(-8) m/W).Furthermore,the PySQ-iCOF film exhibits strong negative refractive nonlinearity,−6×10^(-12) m^(2)/W for ns and -3.8×10^(-13) m^(2)/W for fs,respectively.Transient absorption spectroscopy studies indicate that the pulse-width-dependent nonlinear absorption char-acteristics of the PySQ-iCOF film originate from the generation of triplet excited states.Both nonlinear absorption coefficient and nonlinear refractive index of the PySQ-iCOF film surpass those of most reported organic materials measured under comparable conditions,which provides huge potential in all-optical manipulating and switching at the nanoscale as outstanding NLO materials.
文摘This paper,the first-part of a two part series of surveys on Incremental Nonlinear Dynamic Inversion(INDI),provides an overview of the evolution and developments in INDI.Written in a tutorial style,it presents different basic INDI variants and their specifics,such as modelbased INDI,sensor-based INDI,and hybrid INDI.Furthermore,it sets these different approaches in context with each other.Later developments of INDI explicitly consider actuator dynamics.Those concepts are summarized and discussed in detail.Subsequently,studies that relate INDI to other control methods are summarized.Finally,an overview of various applications of INDI is given,covering different types of control loops and various types of vehicles and plants.This paper seeks to set these developments into context with each other.The purpose of this paper is twofold.INDI is already well-known in the domain of flight control but less so in other fields.Therefore,the paper is written in a comprehensive tutorial style to provide easy access to readers unfamiliar with the topic.On the other hand,the paper can serve as a reference for readers familiar with the topic.
基金supported by the National Natural Science Foundation of China(Grant Nos.12575003 and 12235007)the K.C.Wong Magna Fund in Ningbo University。
文摘This paper develops a residual-based adaptive refinement physics-informed neural networks(RAR-PINNs)method for solving the Gross–Pitaevskii(GP)equation and Hirota equation,two paradigmatic nonlinear partial differential equations(PDEs)governing quantum condensates and optical rogue waves,respectively.The key innovation lies in the adaptive sampling strategy that dynamically allocates computational resources to regions with large PDE residuals,addressing critical limitations of conventional PINNs in handling:(1)Strong nonlinearities(|u|^(2)u terms)in the GP equation;(2)High-order derivatives(u_(xxx))in the Hirota equation;(3)Multi-scale solution structures.Through rigorous numerical experiments,we demonstrate that RAR-PINNs achieve superior accuracy[relative L^(2)errors of O(10^(−3))]and computational efficiency(faster than standard PINNs)for both equations.The method successfully captures:(1)Bright solitons in the GP equation;(2)First-and second-order rogue waves in the Hirota equation.The RAR adaptive sampling method demonstrates particularly remarkable effectiveness in solving steep gradient problems.Compared with uniform sampling methods,the errors of simulation results are reduced by two orders of magnitude.This study establishes a general framework for data-driven solutions of high-order nonlinear PDEs with complex solution structures.
基金Project supported by Science and Technology Project of Guangdong(Grant No.2020B010190001)the National Natural Science Foundation of China(Grant No.12434016)National Funded Postdoctoral Researcher Program(Grant No.GZB20240785)。
文摘When a laser beam is incident on a nonlinear grating with a laterally modulated second-order nonlinear coefficient,nonlinear diffraction of the noncollinear second-harmonic generation(SHG)signal occurs,with Raman–Nath nonlinear diffraction(NRND)being a prominent example.As these SHG NRND processes involve coupling between the fundamental-wave pump laser vectorial field and the SHG laser vectorial field through the second-order nonlinearity secondrank tensor of the nonlinear crystal,the nonlinear interaction between light and the nonlinear grating can be manipulated by adjusting the polarization state of the pump laser.In this paper,we derive the relationship between the polarization state of the incident light and the generated nonlinear diffraction signal based on the nonlinear coupled wave equation and experimentally validate the predicted diffraction characteristics.The results show that the optical properties of each order of NRND are highly sensitive to the polarization angle of the incident pump laser beam.
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supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
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.
文摘Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.
