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
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
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 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
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
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
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 the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by fo...In the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables.For linear systems,PFs are uniquely determined by the mode’s composition and shape,which are defined by the system’s left and right eigenvectors,respectively.However,the uniqueness of other types of PFs has not been thoroughly addressed in literatures.This paper establishes sufficient conditions for the uniqueness of nonlinear PFs and five other PF variants,taking into account uncertain scaling factors in a mode’s shape and composition.These scaling factors arise from variations in the choice of physical units,which depend on the value ranges of real-world state variables.Understanding these sufficient conditions is essential for the correct application of PFs in practical stability analysis and control design.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
Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imida...Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.展开更多
In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantita...In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantitative results of traditional methods,such as partial least squares regression(PLS),which can be used to construct linear models.The problem was addressed in this study by using deep learning(DL).We employed three different DL models:a one-dimensional convolutional neural network(1D CNN),a deep neural network(DNN),and a stacked autoencoder with feedforward neural networks(SAE-FNNs).By carefully selecting and tuning the architectures and parameters of these models,we were able to find the most suitable model for dealing with such nonlinear relationships.Our experimental findings reveal that both the DNN and the SAE-FNN models excel in addressing the nonlinear issues of pectin concentration in tobacco,surpassing the performance of the classic linear model(PLS).Specifically,the DNN model stands out for its low average root mean squared error of prediction(RMSEP)value and small standard deviation(SD)of RMSEPs,leading to a tighter and more centered distribution of residuals in the prediction set.These DL models not only proficiently identify complex patterns within NIR data but also boast high prediction accuracy and fast implementation,demonstrating their effectiveness in analytical applications.展开更多
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.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
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including at...Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.展开更多
The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex...The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex beams for various applications.In this work,the second harmonic(SH)optical vortex beams generated from nonlinear fork gratings under Gaussian beam illumination are numerically investigated.The far-field intensity and phase distributions,as well as the orbital angular momentum(OAM)spectra of the SH beams,are analyzed for different structural topological charges and diffraction orders.Results reveal that higher-order diffraction and larger structural topological charges lead to angular interference patterns and non-uniform intensity distributions,deviating from the standard vortex profile.To optimize the SH vortex quality,the effects of the fundamental wave beam waist,crystal thickness,and grating duty cycle are explored.It is shown that increasing the beam waist can effectively suppress diffraction order interference and improve the beam’s quality.This study provides theoretical guidance for enhancing the performance of nonlinear optical devices based on NPCs.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
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.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.
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.
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(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.
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 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.
文摘In the modal analysis and control of nonlinear dynamical systems,participation factors(PFs)of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables.For linear systems,PFs are uniquely determined by the mode’s composition and shape,which are defined by the system’s left and right eigenvectors,respectively.However,the uniqueness of other types of PFs has not been thoroughly addressed in literatures.This paper establishes sufficient conditions for the uniqueness of nonlinear PFs and five other PF variants,taking into account uncertain scaling factors in a mode’s shape and composition.These scaling factors arise from variations in the choice of physical units,which depend on the value ranges of real-world state variables.Understanding these sufficient conditions is essential for the correct application of PFs in practical stability analysis and control design.
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.
文摘Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.
基金supported by a joint project with SINOPEC(Dalian)Research Institute of Petroleum and Petrochemicals Co.,Ltd.(Contract No.323061).
文摘In the near-infrared(NIR)spectroscopic data of complex sample systems,such as tobacco leaves,nonlinearity is fairly significant between the absorbance and concentration.This nonlinearity severely degrades the quantitative results of traditional methods,such as partial least squares regression(PLS),which can be used to construct linear models.The problem was addressed in this study by using deep learning(DL).We employed three different DL models:a one-dimensional convolutional neural network(1D CNN),a deep neural network(DNN),and a stacked autoencoder with feedforward neural networks(SAE-FNNs).By carefully selecting and tuning the architectures and parameters of these models,we were able to find the most suitable model for dealing with such nonlinear relationships.Our experimental findings reveal that both the DNN and the SAE-FNN models excel in addressing the nonlinear issues of pectin concentration in tobacco,surpassing the performance of the classic linear model(PLS).Specifically,the DNN model stands out for its low average root mean squared error of prediction(RMSEP)value and small standard deviation(SD)of RMSEPs,leading to a tighter and more centered distribution of residuals in the prediction set.These DL models not only proficiently identify complex patterns within NIR data but also boast high prediction accuracy and fast implementation,demonstrating their effectiveness in analytical applications.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
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.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
基金supported by the Basic Science Center Project of the National Natural Science Foundation of China(42388102)the National Natural Science Foundation of China(42174030)+2 种基金the Special Fund of Hubei Luojia Laboratory(220100020)the Major Science and Technology Program for Hubei Province(2022AAA002)the Fundamental Research Funds for the Central Universities of China(2042022dx0001 and 2042023kfyq01)。
文摘Nonlinear variations in the coordinate time series of global navigation satellite system(GNSS) reference stations are strongly correlated with surface displacements caused by environmental loading effects,including atmospheric, hydrological, and nontidal ocean loading. Continuous improvements in the accuracy of surface mass loading products, performance of Earth models, and precise data-processing technologies have significantly advanced research on the effects of environmental loading on nonlinear variations in GNSS coordinate time series. However, owing to theoretical limitations, the lack of high spatiotemporal resolution surface mass observations, and the coupling of GNSS technology-related systematic errors, environmental loading and nonlinear GNSS reference station displacements remain inconsistent. The applicability and capability of these loading products across different regions also require further evaluation. This paper outlines methods for modeling environmental loading, surface mass loading products, and service organizations. In addition, it summarizes recent advances in applying environmental loading to address nonlinear variations in global and regional GNSS coordinate time series. Moreover, the scientific questions of existing studies are summarized, and insights into future research directions are provided. The complex nonlinear motion of reference stations is a major factor limiting the accuracy of the current terrestrial reference frame. Further refining the environmental load modeling method, establishing a surface mass distribution model with high spatiotemporal resolution and reliability, exploring other environmental load factors such as ice sheet and artificial mass-change effects, and developing an optimal data-processing model and strategy for reprocessing global reference station data consistently could contribute to the development of a millimeter-level nonlinear motion model for GNSS reference stations with actual physical significance and provide theoretical support for establishing a terrestrial reference frame with 1 mm accuracy by 2050.
基金supported by the National Nat-ural Science Foundation of China(Nos.12192251,12174185,92163216,and 62288101).
文摘The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex beams for various applications.In this work,the second harmonic(SH)optical vortex beams generated from nonlinear fork gratings under Gaussian beam illumination are numerically investigated.The far-field intensity and phase distributions,as well as the orbital angular momentum(OAM)spectra of the SH beams,are analyzed for different structural topological charges and diffraction orders.Results reveal that higher-order diffraction and larger structural topological charges lead to angular interference patterns and non-uniform intensity distributions,deviating from the standard vortex profile.To optimize the SH vortex quality,the effects of the fundamental wave beam waist,crystal thickness,and grating duty cycle are explored.It is shown that increasing the beam waist can effectively suppress diffraction order interference and improve the beam’s quality.This study provides theoretical guidance for enhancing the performance of nonlinear optical devices based on NPCs.
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.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
