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
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SH...Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.展开更多
Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic devel...Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.展开更多
Dear Editor,This letter investigates the fuzzy prescribed-time control(PTC)problem for a class of uncertain pure feedback nonlinear systems.Firstly,a novel prescribed-time stability lemma is introduced,which plays a c...Dear Editor,This letter investigates the fuzzy prescribed-time control(PTC)problem for a class of uncertain pure feedback nonlinear systems.Firstly,a novel prescribed-time stability lemma is introduced,which plays a critical role in stability analysis.Unlike existing PTC algorithms,where the nonlinear functions are typically known or satisfy a linear growth condition,our approach does not require such assumptions.To address these unknown factors,fuzzy logic systems(FLSs)are employed.Based on the new prescribed-time stability lemma,it is proven that the controller and all system states converge to the origin within the prescribed time and remain there.Finally,the effectiveness of the proposed algorithm is validated through a simulation example.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
This paper introduces a sampled-data and intermittent-hold controller for nonlinear feedforward systems.The intermittent hold allows the control signal to be held in a portion of each sampled period,which does not req...This paper introduces a sampled-data and intermittent-hold controller for nonlinear feedforward systems.The intermittent hold allows the control signal to be held in a portion of each sampled period,which does not require the control to be persistently implemented,and thus has less control time.But,less control time degrades the performance of a continuous-time control system or even destabilizes it,especially when the holding portion is sufficiently small.To tackle this obstacle,we first introduce the notion of activating rate to describe the intermittent hold,and give the sampled-data and intermittent-hold controller based on some tuning parameters.Then it is proved that for any activating rate,these parameters can be designed to achieve the stability of the considered systems under appropriately choosing the sampling size.Finally,simulation examples are given to illustrate the effectiveness of the proposed method.展开更多
Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relation...Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relationship between PID parameters is established to reduce the number of adjustable parameters to one.Then,based on the incremental triangular data model,a data-driven APID tracking control(DD-APIDTC)method is proposed to adjust only one controller parameter and one model parameter online,both of which have clear physical meaning.Subsequently,sufficient conditions are derived for the boundedness of the system tracking error.Finally,simulation results are given to illustrate the effectiveness of the proposed method.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
The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model struc...The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.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
The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posed...The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posedness,as well as the existence of blowing-up solutions for large and irregular initial data.The main results presented in this paper can be summarized as follows:(1)Discrete Nonlinear Schrodinger Equation:Global well-posedness in l^(p) spaces for all1≤p≤∞,regardless of whether it is in the defocusing or focusing cases.(2)Discrete Klein-Gordon Equation:Local well-posedness in l^(p) spaces for all 1≤p≤∞.Furthermore,in the defocusing case,we establish global well-posedness in l^(p) spaces for any2≤p≤2σ+2(σ>0).In contrast,in the focusing case,we show that solutions with negative energy blow up within a finite time.These conclusions reveal the distinct dynamic behaviors exhibited by the solutions of the equations in discrete settings compared to their continuous setting.Additionally,they illuminate the significant role that discretization plays in preventing ill-posedness,and collapse for the nonlinear Schrodinger equation.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
Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,comm...Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,commencing with its rigorous definition and its integration with Lyapunov theory,along which a consequential corollary emerges.Particularly,the positive definiteness of the expectation of settling time is established,and a less conservative upper bound is derived.The effectiveness of the proposed fixed-time theorem is verified by an example.展开更多
Dear Editor,It is well known that event-triggered control(ETC)is an effective approach in addressing networked control problems for Industry 5.0.Its feasibility,however,is still restricted to canonical nonlinear syste...Dear Editor,It is well known that event-triggered control(ETC)is an effective approach in addressing networked control problems for Industry 5.0.Its feasibility,however,is still restricted to canonical nonlinear systems so far.Considering this,a gradient-based adaptive ETC scheme for noncanonical nonlinear systems is newly developed in this letter,where the hysteresis input constraints are considered also.By proper decomposition,the technical issue of handling ETC-induced measurement errors and hysteresis inputs can be transformed into the robustness problem to bounded disturbance-like terms,which is then addressed by integrating a switching modification strategy in adaptive design and developing a novel augmented error-based analysis framework.Experimental results based on a practical piezoactuator confirm the effectiveness of the proposed scheme.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 Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金supported by the National Natural Science Foundation of China (No.22275052)Department of Science and Technology of Hubei Province (Nos.2025AFA111 and 2024CSA076)。
文摘Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.
基金Under the auspices of National Natural Science Foundation of China(No.42571300)。
文摘Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.
基金supported by the National Natural Science Foundation of China(U20A20187,U22A2050)the Science Fund of Hebei Province(F2024203134,F2023203100)+3 种基金the Science and Technology Development Grant of Hebei Province(20311803D)Hebei Innovation Capability Improvement Plan project(22567619H)Basic Research Project of Shijiazhuang(241791007A)the China Scholarship Council(CSC 202308130190).
文摘Dear Editor,This letter investigates the fuzzy prescribed-time control(PTC)problem for a class of uncertain pure feedback nonlinear systems.Firstly,a novel prescribed-time stability lemma is introduced,which plays a critical role in stability analysis.Unlike existing PTC algorithms,where the nonlinear functions are typically known or satisfy a linear growth condition,our approach does not require such assumptions.To address these unknown factors,fuzzy logic systems(FLSs)are employed.Based on the new prescribed-time stability lemma,it is proven that the controller and all system states converge to the origin within the prescribed time and remain there.Finally,the effectiveness of the proposed algorithm is validated through a simulation example.
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supported in part by research grants from the National Natural Science Foundation of China(12201365)the Natural Science Foundation of Shandong Province(ZR2021QF106).
文摘This paper introduces a sampled-data and intermittent-hold controller for nonlinear feedforward systems.The intermittent hold allows the control signal to be held in a portion of each sampled period,which does not require the control to be persistently implemented,and thus has less control time.But,less control time degrades the performance of a continuous-time control system or even destabilizes it,especially when the holding portion is sufficiently small.To tackle this obstacle,we first introduce the notion of activating rate to describe the intermittent hold,and give the sampled-data and intermittent-hold controller based on some tuning parameters.Then it is proved that for any activating rate,these parameters can be designed to achieve the stability of the considered systems under appropriately choosing the sampling size.Finally,simulation examples are given to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(62173002,62403010,52301408)the Beijing Natural Science Foundation(L241015,4222045)+1 种基金the Yuxiu Innovation Project of NCUT(2024NCUTYXCX111)the China Postdoctoral Science Foundation(2024M750192).
文摘Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relationship between PID parameters is established to reduce the number of adjustable parameters to one.Then,based on the incremental triangular data model,a data-driven APID tracking control(DD-APIDTC)method is proposed to adjust only one controller parameter and one model parameter online,both of which have clear physical meaning.Subsequently,sufficient conditions are derived for the boundedness of the system tracking error.Finally,simulation results are given to illustrate the effectiveness of the proposed method.
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funded by the project new smart and adaptive robotics solutions for personalized minimally invasive surgery in cancer treatment−ATHENA,European Union-NextGenerationEU and Romanian Government,under National Recovery and Resilience Plan for Romania(CF116/15.11.2022)through the Romanian Ministry of Research,Innovation and Digitalization(within Component 9,investment I8)。
文摘The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.
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in part supported by the NSFC(12171356,12494544)supported by the National Key R&D Program of China(2020 YFA0713300)+1 种基金the NSFC(12531006)the Nankai Zhide Foundation。
文摘The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrodinger and Klein-Gordon equations.These theories encompass both local and global well-posedness,as well as the existence of blowing-up solutions for large and irregular initial data.The main results presented in this paper can be summarized as follows:(1)Discrete Nonlinear Schrodinger Equation:Global well-posedness in l^(p) spaces for all1≤p≤∞,regardless of whether it is in the defocusing or focusing cases.(2)Discrete Klein-Gordon Equation:Local well-posedness in l^(p) spaces for all 1≤p≤∞.Furthermore,in the defocusing case,we establish global well-posedness in l^(p) spaces for any2≤p≤2σ+2(σ>0).In contrast,in the focusing case,we show that solutions with negative energy blow up within a finite time.These conclusions reveal the distinct dynamic behaviors exhibited by the solutions of the equations in discrete settings compared to their continuous setting.Additionally,they illuminate the significant role that discretization plays in preventing ill-posedness,and collapse for the nonlinear Schrodinger equation.
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.
基金supported by the National Natural Science Foundation of China(62103203).
文摘Dear Editor,This letter embarks on an examination of fixed-time stability(FxTS)for random nonlinear systems(RNSs)governed by random differential equations.This endeavor encompasses a multifaceted analysis of FxTS,commencing with its rigorous definition and its integration with Lyapunov theory,along which a consequential corollary emerges.Particularly,the positive definiteness of the expectation of settling time is established,and a less conservative upper bound is derived.The effectiveness of the proposed fixed-time theorem is verified by an example.
文摘Dear Editor,It is well known that event-triggered control(ETC)is an effective approach in addressing networked control problems for Industry 5.0.Its feasibility,however,is still restricted to canonical nonlinear systems so far.Considering this,a gradient-based adaptive ETC scheme for noncanonical nonlinear systems is newly developed in this letter,where the hysteresis input constraints are considered also.By proper decomposition,the technical issue of handling ETC-induced measurement errors and hysteresis inputs can be transformed into the robustness problem to bounded disturbance-like terms,which is then addressed by integrating a switching modification strategy in adaptive design and developing a novel augmented error-based analysis framework.Experimental results based on a practical piezoactuator confirm the effectiveness of the proposed scheme.
