Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting ...Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.展开更多
Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(...Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.展开更多
The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlin...The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.展开更多
Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals.However,few researches have considered the bilinear nonlinearity as well as its consequen...Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals.However,few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials.Hence,we introduce bilinear nonlinearity into acoustic metamaterials,and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method,revealing the influence of the system parameters.Furthermore,we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation,and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions.Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.展开更多
The presence of anticrossings induced by coupling between two states causes curvature in energy levels, yielding a nonlinearity in the quantum system. When the system is driven back and forth along the bending energy ...The presence of anticrossings induced by coupling between two states causes curvature in energy levels, yielding a nonlinearity in the quantum system. When the system is driven back and forth along the bending energy levels, subharmonic transitions and energy shifts can be observed, which would cause a significant influence as the system is applied to quantum computing. In this paper, we study a longitudinally driven singlet-triplet(ST) system in a double quantum dot(DQD)system, and illustrate the consequences of nonlinearity by driving the system close to the anticrossings. We provide a straightforward theory to quantitatively describe the energy shift and subharmonics caused by nonlinearity, and find good agreement between our theoretical result and the numerical simulation. Our results reveal the existence of nonlinearity in the vicinity of anticrossings and provide a direct way of analytically assessing its impact, which can be applied to other quantum systems without excessive labor.展开更多
A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high birefringence and nonlinearity at a wavelength of 1.55μm.The full vector finite element method was adop...A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high birefringence and nonlinearity at a wavelength of 1.55μm.The full vector finite element method was adopted to investigate its characteristics,including birefringence,nonlinearity,and dispersion.The PCF exhibited a very high birefringence of 2.89×10^(-2) and very high nonlinear coefficient of 102.69 W^(-1)·km^(-1).In particular,there were two zero-dispersion wavelengths(ZDWs)in the visible(X:640-720 nm and Y:730-760 nm)and near-infrared regions(X:1050-1606 nm and Y:850-1500 nm).The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum,with potential applications in nonlinear optics.展开更多
The acoustic nonlinearity of surface waves is studied to evaluate plastic deformation in aluminum alloys.A narrow-band surface wave is successfully generated by a pulsed Nd-YAG laser system consisting of a beam expand...The acoustic nonlinearity of surface waves is studied to evaluate plastic deformation in aluminum alloys.A narrow-band surface wave is successfully generated by a pulsed Nd-YAG laser system consisting of a beam expander and a slit mask.Various degrees of tensile deformation are induced by interrupting the tensile tests so as to obtain aluminum specimens with different degrees of plastic damage.The normalized acoustic nonlinearity increases as a function of tensile strain.The experimental results show that the acoustic nonlinearity of a laser-generated surface wave has a good correlation with the level of tensile deformation and has a potential to evaluate microdamage induced by dislocation microplasticity.展开更多
A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-...A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-sulfoxande,dioxane,ethanol,and methanol,etc.The nonlinear refractive index for the solvents at femtosecond time scale was measured.展开更多
Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H20 and catalyst. All poled polymer network films possess high second-...Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H20 and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d33) of 10-?～10-8 esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120°C) indicated that these films exhibit high d33 stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.展开更多
Optical dispersive nonlinearities in Er-doped optical fiber are discussed and measured at the third window wavelength 1.55μm for optical communications firstly. The experimental method, which is devel-oped by us,is b...Optical dispersive nonlinearities in Er-doped optical fiber are discussed and measured at the third window wavelength 1.55μm for optical communications firstly. The experimental method, which is devel-oped by us,is based on dynamic scanning for fixed-point-interference (DSFPI) of two fiber beams. The real part and complex value of tbe third-order susceptlbility at that wavelength are also obtained from the mea-sured Kerr coefficient and nonlinear-ahsorption coefficient reported elsewhere.展开更多
The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by...The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data.Firstly,the auxiliary model identification principle is used to estimate the unmeasurable variables,and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model.Then,the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem.It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation.Finally,the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.展开更多
The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally.In the theoretical work,a new theoretical algori...The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally.In the theoretical work,a new theoretical algorithm is presented for the coherent combining efficiency,which can be used to quantify the spectral coherence decay induced by optical nonlinearity imbalance between the sub-beams.The spectral information of the sub-beam is obtained by numerically solving the nonlinear Schrödinger equation(NLSE)in this algorithm to ensure an accurate prediction.In the experimental work,the coherent combining of two all-fiber picosecond lasers is achieved,and the influence of imbalanced optical nonlinearity on the combining efficiency is studied,which agrees with the theoretical prediction.This paper reveals the physical mechanism for the influence of optical nonlinearity on the combining efficiency,which is valuable for the coherent combining of ultrashort pulse fiber laser beams.展开更多
In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea co...In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction.Two sets of experiments are conducted in which zonal nonlinear factors,meridional nonlinear factors,or both are incorporated into the governing equations for the atmosphere or ocean.The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean.Thus,incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation.展开更多
A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components,i.e. turbine,PID type governor with saturation p...A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components,i.e. turbine,PID type governor with saturation part and generator included in the model. Existence,stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time waveforms. The analysis show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Moreover,the dynamic behavior of system with different parameters such as Tw,Tab,Tyand K are studied extensively. An example with numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.展开更多
Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrat...Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrated information-processing chip,high optical nonlinearity is indispensable for various fundamental functionalities,such as all-optical modulation,high order harmonic generation,optical switching and so on.Here we study the third-order optical nonlinearity of free-standing h-BN thin films,which is an ideal platform for on-chip integration and device formation without the need of transfer.The films were synthesized by a solution-based method with abundant functional groups enabling high third-order optical nonlinearity.Unlike the highly inert pristine h-BN films synthesized by conventional methods,the free-standing h-BN films could be locally oxidized upon tailored femtosecond laser irradiation,which further enhances the third-order nonlinearity,especially the nonlinear refraction index,by more than 20 times.The combination of the free-standing h-BN films with laser activation and patterning capability establishes a new promising platform for high performance on-chip photonic devices with modifiable optical performance.展开更多
In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" ...In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.展开更多
The stability and safety are very important issues for the dam structure which are built in seismic regions. The dam body consists of soil materials that behave nonlinearly modelled with finite elements. The numerical...The stability and safety are very important issues for the dam structure which are built in seismic regions. The dam body consists of soil materials that behave nonlinearly modelled with finite elements. The numerical investigation employs a fully nonlinear finite element analysis considering linear and elastic-plastic constitutive model to describe the material properties of the soil. In this paper, seismic analysis of an earthen dam is carried out using Geo-Studio software based on finite element method. Initially, the in-situ stress state analysis has been done before the earthquake established, and then its results are used in the seismic analysis as a parent analysis. A complete parametric study is carried out to identify the effects of input motion characteristics, soil behaviour and strength of the shell and core materials on the dynamic response of earthen dams. The real earthquake record is used as input motions. The analysis gives the overall pattern of the dam behaviour in terms of contours of displacements and stresses.展开更多
In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in...In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in the positive mass case in the sense of seeking a nontrivial solution of the above eigenvalue problem.展开更多
Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM...Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.展开更多
Theoretical studies so far on random wave groups have all been in linear ways.Methods to sim-ulate random wave groups,an important subject in ocean engineering,also employ relationship resulting froma Gaussian process...Theoretical studies so far on random wave groups have all been in linear ways.Methods to sim-ulate random wave groups,an important subject in ocean engineering,also employ relationship resulting froma Gaussian process.Many filed measurements have shown that the real sea surfase displacement deviatessomewhat from Gaussian distribution.Tayfun et al.have further depicted in theory that the envelope spectralpeak frequency is constantly zero for a Gaussian process which means that the groupiness factors will be con-stants,too.In this paper,the effect of nonlinearity on groupiness of a random wave field is examined via thetheoretical results derived by Tayfun et al.from an expression of amplitude-modulated Stokes waves.Whenthe surface displacement is treated as a non-Gaussian process,it is found that the group height factors GF<sub>1</sub>and GF<sub>2</sub> proposed by Zhao et al.and Yu et al.,respectively,depend on a nonlinearity factor as well as aspectrum-bandwidth factor,deferring from the case of a Gaussion process.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.62071411)the Research Foundation of Education Department of Hunan Province,China(Grant No.20B567).
文摘Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62273115,62173105)the Fundamental Research Funds for the Central Universities (Grant No.3072022FSC0401)。
文摘Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.
基金financially supported by the National Key Research and Development Program of China(Grant Nos.2021YFB2600700 and 2022YFC3102302)the Central Public-Interest Scientific Institution Basal Research Fund(Grant No.Y221007)+2 种基金the National Natural Science Foundation of China(Grant No.52271274)the Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202205)the Key Project of NSFC-Shandong Joint Research Funding POW3C(Grant No.U1906230).
文摘The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.
基金Project supported by the National Key Research and Development program of China(Grant No.2020YFA0211400)the State Key Program of the National Natural Science of China(Grant No.11834008)+2 种基金the National Natural Science Foundation of China(Grant No.12174192)the Fund fromthe State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.SKLA202008)the Fund from the Key Laboratory of Underwater Acoustic Environment,Chinese Academy of Sciences(Grant No.SSHJ-KFKT-1701)。
文摘Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals.However,few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials.Hence,we introduce bilinear nonlinearity into acoustic metamaterials,and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method,revealing the influence of the system parameters.Furthermore,we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation,and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions.Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074368, 92165207, 12034018 and 92265113)the Anhui Province Natural Science Foundation (Grant No. 2108085J03)。
文摘The presence of anticrossings induced by coupling between two states causes curvature in energy levels, yielding a nonlinearity in the quantum system. When the system is driven back and forth along the bending energy levels, subharmonic transitions and energy shifts can be observed, which would cause a significant influence as the system is applied to quantum computing. In this paper, we study a longitudinally driven singlet-triplet(ST) system in a double quantum dot(DQD)system, and illustrate the consequences of nonlinearity by driving the system close to the anticrossings. We provide a straightforward theory to quantitatively describe the energy shift and subharmonics caused by nonlinearity, and find good agreement between our theoretical result and the numerical simulation. Our results reveal the existence of nonlinearity in the vicinity of anticrossings and provide a direct way of analytically assessing its impact, which can be applied to other quantum systems without excessive labor.
基金Project supported by the National Natural Science Foundation of China(Grant No.61475029)
文摘A new type of V-shaped photonic crystal fiber with elliptical air-holes is proposed to realize simultaneous high birefringence and nonlinearity at a wavelength of 1.55μm.The full vector finite element method was adopted to investigate its characteristics,including birefringence,nonlinearity,and dispersion.The PCF exhibited a very high birefringence of 2.89×10^(-2) and very high nonlinear coefficient of 102.69 W^(-1)·km^(-1).In particular,there were two zero-dispersion wavelengths(ZDWs)in the visible(X:640-720 nm and Y:730-760 nm)and near-infrared regions(X:1050-1606 nm and Y:850-1500 nm).The combination of high birefringence and nonlinearity allowed the PCF to maintain the polarization state and generate a broadband super continuum,with potential applications in nonlinear optics.
文摘The acoustic nonlinearity of surface waves is studied to evaluate plastic deformation in aluminum alloys.A narrow-band surface wave is successfully generated by a pulsed Nd-YAG laser system consisting of a beam expander and a slit mask.Various degrees of tensile deformation are induced by interrupting the tensile tests so as to obtain aluminum specimens with different degrees of plastic damage.The normalized acoustic nonlinearity increases as a function of tensile strain.The experimental results show that the acoustic nonlinearity of a laser-generated surface wave has a good correlation with the level of tensile deformation and has a potential to evaluate microdamage induced by dislocation microplasticity.
基金Supported by the National Natural Science Foundation of China under Grant No.19525412National Science and Technology Commission of China。
文摘A femtosecond optical Kerr effect experiment has been used to study the dynamic process of third-order optical nonlinearity for organic solvents acetone,acetonitrile,alcohol,benzene,chloroform,dichlomathane,dimenthyl-sulfoxande,dioxane,ethanol,and methanol,etc.The nonlinear refractive index for the solvents at femtosecond time scale was measured.
文摘Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H20 and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d33) of 10-?～10-8 esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120°C) indicated that these films exhibit high d33 stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.
文摘Optical dispersive nonlinearities in Er-doped optical fiber are discussed and measured at the third window wavelength 1.55μm for optical communications firstly. The experimental method, which is devel-oped by us,is based on dynamic scanning for fixed-point-interference (DSFPI) of two fiber beams. The real part and complex value of tbe third-order susceptlbility at that wavelength are also obtained from the mea-sured Kerr coefficient and nonlinear-ahsorption coefficient reported elsewhere.
基金supported by the National Natural Science Foundation of China(61863034)
文摘The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data.Firstly,the auxiliary model identification principle is used to estimate the unmeasurable variables,and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model.Then,the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem.It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation.Finally,the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.
基金upported by the Key Program of Beijing Municipal Natural Science Foundation,China(Grant No.KZ201910005006)the National Natural Science Foundation of China(Grant No.62005004)+1 种基金Natural Science Foundation of Beijing Municipality,China(Grant No.4204091)National Science Foundation for Post-doctor Scientists of China(Grant No.212423)。
文摘The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally.In the theoretical work,a new theoretical algorithm is presented for the coherent combining efficiency,which can be used to quantify the spectral coherence decay induced by optical nonlinearity imbalance between the sub-beams.The spectral information of the sub-beam is obtained by numerically solving the nonlinear Schrödinger equation(NLSE)in this algorithm to ensure an accurate prediction.In the experimental work,the coherent combining of two all-fiber picosecond lasers is achieved,and the influence of imbalanced optical nonlinearity on the combining efficiency is studied,which agrees with the theoretical prediction.This paper reveals the physical mechanism for the influence of optical nonlinearity on the combining efficiency,which is valuable for the coherent combining of ultrashort pulse fiber laser beams.
基金supported by the National Natural Science Foundation of China (Grant No.40676016)
文摘In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction.Two sets of experiments are conducted in which zonal nonlinear factors,meridional nonlinear factors,or both are incorporated into the governing equations for the atmosphere or ocean.The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean.Thus,incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation.
文摘A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components,i.e. turbine,PID type governor with saturation part and generator included in the model. Existence,stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time waveforms. The analysis show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Moreover,the dynamic behavior of system with different parameters such as Tw,Tab,Tyand K are studied extensively. An example with numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.
基金We are grateful for financial supports from the Australian Research Council through the Discovery Project scheme(Grant No.DP190103186 and FT210100806)the Australian Research Council through Industrial Transformation Training Centres scheme(IC180100005).
文摘Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrated information-processing chip,high optical nonlinearity is indispensable for various fundamental functionalities,such as all-optical modulation,high order harmonic generation,optical switching and so on.Here we study the third-order optical nonlinearity of free-standing h-BN thin films,which is an ideal platform for on-chip integration and device formation without the need of transfer.The films were synthesized by a solution-based method with abundant functional groups enabling high third-order optical nonlinearity.Unlike the highly inert pristine h-BN films synthesized by conventional methods,the free-standing h-BN films could be locally oxidized upon tailored femtosecond laser irradiation,which further enhances the third-order nonlinearity,especially the nonlinear refraction index,by more than 20 times.The combination of the free-standing h-BN films with laser activation and patterning capability establishes a new promising platform for high performance on-chip photonic devices with modifiable optical performance.
文摘In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.
文摘The stability and safety are very important issues for the dam structure which are built in seismic regions. The dam body consists of soil materials that behave nonlinearly modelled with finite elements. The numerical investigation employs a fully nonlinear finite element analysis considering linear and elastic-plastic constitutive model to describe the material properties of the soil. In this paper, seismic analysis of an earthen dam is carried out using Geo-Studio software based on finite element method. Initially, the in-situ stress state analysis has been done before the earthquake established, and then its results are used in the seismic analysis as a parent analysis. A complete parametric study is carried out to identify the effects of input motion characteristics, soil behaviour and strength of the shell and core materials on the dynamic response of earthen dams. The real earthquake record is used as input motions. The analysis gives the overall pattern of the dam behaviour in terms of contours of displacements and stresses.
文摘In this paper, we study the following eigenvalue problem involving limiting nonlinearity by a new way of using the concentration-compactness principle. Even in the nonlimiting situation, we improve the known result in the positive mass case in the sense of seeking a nontrivial solution of the above eigenvalue problem.
基金Project supported by the National Natural Science Foundation of China(No.11802319)the National Key Research and Development Program of China(No.2017YFB1102801)。
文摘Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.
基金National Natural Science Foundation of China(Grant No.49706067)Natural Science Foundation of Shandong Province(Y98E05076)
文摘Theoretical studies so far on random wave groups have all been in linear ways.Methods to sim-ulate random wave groups,an important subject in ocean engineering,also employ relationship resulting froma Gaussian process.Many filed measurements have shown that the real sea surfase displacement deviatessomewhat from Gaussian distribution.Tayfun et al.have further depicted in theory that the envelope spectralpeak frequency is constantly zero for a Gaussian process which means that the groupiness factors will be con-stants,too.In this paper,the effect of nonlinearity on groupiness of a random wave field is examined via thetheoretical results derived by Tayfun et al.from an expression of amplitude-modulated Stokes waves.Whenthe surface displacement is treated as a non-Gaussian process,it is found that the group height factors GF<sub>1</sub>and GF<sub>2</sub> proposed by Zhao et al.and Yu et al.,respectively,depend on a nonlinearity factor as well as aspectrum-bandwidth factor,deferring from the case of a Gaussion process.
