In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having thre...In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the tempo...In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the temporal parts of the translated Lax pairs and its adjoint Lax pairs of the Levi equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems. Finally,the involutive solutions of the Levi equations are presented.展开更多
Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2)....Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. Wit...In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.展开更多
This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator ...This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve, which leads to the formula of DubrovinNovikov＇s type. Further, by calculation of residues on the complex sphere and via gauge transformation, we get the trace formulae of eigenfunctions corresponding to the left endpoints and right end-points of the spectral bands, respectively. As an application, we obtain a completely integrable Hamiltonian system in Liouville sense through nonlinearization of the Dirac spectral problem.展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the sup...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,...Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.展开更多
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
By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of th...By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of the nonlinear Schrodinger equation. We show that this system is a completely integrable Hamiltonian system.展开更多
Second-harmonic generation(SHG)is a fundamental nonlinear optical process widely used in photonics;however,it is strictly forbidden in the bulk of centrosymmetric materials due to their inversion symmetry.Nevertheless...Second-harmonic generation(SHG)is a fundamental nonlinear optical process widely used in photonics;however,it is strictly forbidden in the bulk of centrosymmetric materials due to their inversion symmetry.Nevertheless,applying an external electric field breaks this inversion symmetry.It induces an effective second-order nonlinear response known as the electric-field-induced second-harmonic generation(EFISH)effect.This mechanism enables SHG in centrosymmetric media and provides a effective mechanism for electrically tunable nonlinear nanophotonics.Here,we present a comprehensive overview of the EFISH effect,covering the fundamentals,various material platforms(including bulk semiconductor crystals,ferroelectrics,van der Waals materials,and polymers),as well as diverse strategies for electric field engineering.We distinguish EFISH from related effects including currentinduced SHG and the quantum-confined Stark effect,and highlight emerging applications of EFISH in tunable photonic devices,carrier dynamics probing,and nonlinear optical modulation across optical,electronic,and THz regimes.Finally,we outline key challenges and prospects for the future development of electrically controlled nonlinear optical systems.展开更多
Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing struc...Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing structural alignment through linear groups and fluoride ions.We report on two new compounds:HgGa_(2)(SeO_(3))_(4) and Hg_(2)Ga(Se_(O)_(3))_(2)F.HgGa_(2)(SeO_(3))_(4) crystallizes in a non-centrosymmetric(NCS)space group,exhibiting a second harmonic generation(SHG)efficiency of approximately 60% that of commercial KH2PO4(KDP),with a birefringence of 0.032@546 nm.Hg_(2)Ga(Se_(O)_(3))_(2)F,on the other hand,crystallizes in a centrosymmetric space(CS)group and represents the first reported HgI-based selenite birefringent material.Due to the influence of the linear group Hg_(2)O_(2),its birefringence is significantly enhanced to 0.111@546 nm,which is 3.5 times that of HgGa_(2)(SeO_(3))_(4).Moreover,both compounds demonstrate high stability and a broad optical transparency window.These findings indicate that Hg_(2)Ga(Se_(O)_(3))_(2)F is a promising candidate for birefringent material in the mid-infrared(MIR)range.Our research provides an innovative strategy for improving the birefringence of compounds.展开更多
Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility ar...Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility are key to mitigating disaster risk.This study integrated multi-source historical landslide data with 15 predictive factors and used several machine learning models—Random Forest(RF),Gradient Boosting Regression Trees(GBRT),Extreme Gradient Boosting(XGBoost),and Categorical Boosting(CatBoost)—to generate susceptibility maps.The Shapley additive explanation(SHAP)method was applied to quantify factor importance and explore their nonlinear effects.The results showed that:(1)CatBoost was the best-performing model(CA=0.938,AUC=0.980)in assessing landslide susceptibility,with altitude emerging as the most significant factor,followed by distance to roads and earthquake sites,precipitation,and slope;(2)the SHAP method revealed critical nonlinear thresholds,demonstrating that historical landslides were concentrated at mid-altitudes(1400-4000 m)and decreased markedly above 4000 m,with a parallel reduction in probability beyond 700 m from roads;and(3)landslide-prone areas,comprising 13%of the QTP,were concentrated in the southeastern and northeastern parts of the plateau.By integrating machine learning and SHAP analysis,this study revealed landslide hazard-prone areas and their driving factors,providing insights to support disaster management strategies and sustainable regional planning.展开更多
This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural condit...This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).展开更多
Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper ...Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper equations are one of the main and most efficient methods for estimating stem volume to any merchantable limit of a species.There is currently no taper equation for Eucalyptus species in Nigeria.Therefore,this study developed taper equations for E.camaldulensis in northern Nigeria.Data for this study were obtained from a private plantation in Jalingo Local Government Area,Taraba State,Nigeria.68 trees were felled and sectioned into 1-m bolt across the stem to a merchantable limit of 5 cm,which were used as the fitting dataset.An additional 22 trees were felled and used to validate the taper equations for stem volume estimation.Seven taper equations were initially fitted to the dataset using nonlinear least squares.The best taper equation was then refitted using a nonlinear mixed-effects approach and calibrated using diameters of one to five sections from the butt end.The taper equations were numerically integrated to obtain the stem volume,which was compared with empirical volume equations.The result shows that the Kozak(Can J For Res 27(5):619-629.10.1139/x97-011,1997)equation,which included eight parameters,provided the best fit for predicting section diameters for under and over bark.The mixed-effects taper equation(NLME-TE)explained most stem diameter variations in the fitting dataset(pseudo-R2:0.986-0.987;RMSE:0.547-0.578 cm)without substantial residual trends.The validation showed that the prediction accuracy of the integrated NLME-TE improved as the number of sectional diameter measurements increased,with at least a 35%reduction in volume estimate error.For practical implementation,two calibration sectional diameter measurements taken from the butt end per tree are recommended.This approach would reduce measurement effort and cost while improving model performance.展开更多
In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemota...In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemotaxis systems in the stability of equilibrium points,the influence mechanism of chemotaxis on the dynamic behavior of the system is deeply studied.Theoretical analysis shows that chemotaxis significantly changes the stability characteristics of the system,and the reliability of theoretical results is further verified by numerical simulation.展开更多
This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
This study examines the dynamic response of two adjacent 9-and 20-story benchmark steel buildings subjected to six near-fault earthquake records.Two-dimensional numerical models were employed to account for the comple...This study examines the dynamic response of two adjacent 9-and 20-story benchmark steel buildings subjected to six near-fault earthquake records.Two-dimensional numerical models were employed to account for the complexities of structure-soil-structure interaction(SSSI).The research focuses on the separation gap between the buildings and the effects of pounding while considering Fixed Base(FB)and SSSI models,evaluated according to UBC 94 and ASCE 7-16 seismic codes.Key findings reveal that pounding occurs with the UBC 94 separation gap when earthquake frequency aligns with system frequency,leading to increased column stresses in the 9-story building.In contrast,the ASCE 7-16 standard effectively prevents pounding in both the FB and SSSI models.Additionally,drifts and displacements of lower floors in SSSI models exceed the allowable limits of ASCE 7-16,underscoring the impact of soil-structure interaction on seismic response.展开更多
The objective of the current study is to investigate an adaptive predictive observer-based autopilot for a skid-to-turn(STT)missile model with uncertainties and unknown dynamic equations.A predictive control for the S...The objective of the current study is to investigate an adaptive predictive observer-based autopilot for a skid-to-turn(STT)missile model with uncertainties and unknown dynamic equations.A predictive control for the STT missile is designed based on nonlinear model predictive control(NMPC)using Taylor series expansion,after which,via a neural network(NN),unknown functions are approximated.The present study also evaluates an adaptive optimal observer of a new strategy-based nonlinear system.Specifically,to estimate the missile states such as normal acceleration and its derivatives for the future,originally the Taylor series states expansion was gained to any specified order,based on their receding horizons.To address the problem of prediction error,an analytic solution was prepared that led to a closed form regarding the nonlinear optimal observer.Out of the gains resulting from the analytic solution,as developed for the problem of prediction error,the selection of the proposed observer gain was optimally conducted to meet the stability condition.Thus,combining the adaptive predictive autopilot and the adaptive optimal observer scheme was implemented to secure the performance,which needed only estimated normal acceleration and its derivatives.Meanwhile,no angular velocity measurement or wind angle estimation was required.Ultimately,the proposed technique was found effective,as confirmed by the qualitative simulation results.展开更多
文摘In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the temporal parts of the translated Lax pairs and its adjoint Lax pairs of the Levi equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems. Finally,the involutive solutions of the Levi equations are presented.
文摘Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.
基金Supported by the National Natural Science Foundation of China(Grant No.61473332)the Natural Science Foundation of Zhejiang Province(Grant No.LQ14A010009)the Natural Science Foundation of Huzhou City(Grant No.2013YZ06)
文摘This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve, which leads to the formula of DubrovinNovikov＇s type. Further, by calculation of residues on the complex sphere and via gauge transformation, we get the trace formulae of eigenfunctions corresponding to the left endpoints and right end-points of the spectral bands, respectively. As an application, we obtain a completely integrable Hamiltonian system in Liouville sense through nonlinearization of the Dirac spectral problem.
基金Project supported by the Hangdian Foundation (No. KYS075608072)the National Natural Science Foundation of China (Nos. 10671187, 10971109)the Program for New Century Excellent Talents in University of China (No. NCET-08-0515)
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.
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(No.11001069,61273077,11271210 and 10971109)Program for NCET under Grant No.NCET-08-0515Zhejiang Provincial Natural Science Foun-dation of China under Grant No.LQ12A01002 and LQ12A01003
文摘By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of the nonlinear Schrodinger equation. We show that this system is a completely integrable Hamiltonian system.
基金supported by Priority 2030 FederalAcademic Leadership ProgramBASIS Foundation
文摘Second-harmonic generation(SHG)is a fundamental nonlinear optical process widely used in photonics;however,it is strictly forbidden in the bulk of centrosymmetric materials due to their inversion symmetry.Nevertheless,applying an external electric field breaks this inversion symmetry.It induces an effective second-order nonlinear response known as the electric-field-induced second-harmonic generation(EFISH)effect.This mechanism enables SHG in centrosymmetric media and provides a effective mechanism for electrically tunable nonlinear nanophotonics.Here,we present a comprehensive overview of the EFISH effect,covering the fundamentals,various material platforms(including bulk semiconductor crystals,ferroelectrics,van der Waals materials,and polymers),as well as diverse strategies for electric field engineering.We distinguish EFISH from related effects including currentinduced SHG and the quantum-confined Stark effect,and highlight emerging applications of EFISH in tunable photonic devices,carrier dynamics probing,and nonlinear optical modulation across optical,electronic,and THz regimes.Finally,we outline key challenges and prospects for the future development of electrically controlled nonlinear optical systems.
基金supported by the National Natural Science Foundation of China(Nos.22475215,22031009 and 21921001)the NSF of Fujian Province(Nos.2023J01216,2024J010039)the Selfdeployment Project Research Program of Haixi Institutes,Chinese Academy of Sciences(No.CXZX-2022-GH06).
文摘Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing structural alignment through linear groups and fluoride ions.We report on two new compounds:HgGa_(2)(SeO_(3))_(4) and Hg_(2)Ga(Se_(O)_(3))_(2)F.HgGa_(2)(SeO_(3))_(4) crystallizes in a non-centrosymmetric(NCS)space group,exhibiting a second harmonic generation(SHG)efficiency of approximately 60% that of commercial KH2PO4(KDP),with a birefringence of 0.032@546 nm.Hg_(2)Ga(Se_(O)_(3))_(2)F,on the other hand,crystallizes in a centrosymmetric space(CS)group and represents the first reported HgI-based selenite birefringent material.Due to the influence of the linear group Hg_(2)O_(2),its birefringence is significantly enhanced to 0.111@546 nm,which is 3.5 times that of HgGa_(2)(SeO_(3))_(4).Moreover,both compounds demonstrate high stability and a broad optical transparency window.These findings indicate that Hg_(2)Ga(Se_(O)_(3))_(2)F is a promising candidate for birefringent material in the mid-infrared(MIR)range.Our research provides an innovative strategy for improving the birefringence of compounds.
基金The National Key Research and Development Program of China,No.2023YFC3206601。
文摘Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility are key to mitigating disaster risk.This study integrated multi-source historical landslide data with 15 predictive factors and used several machine learning models—Random Forest(RF),Gradient Boosting Regression Trees(GBRT),Extreme Gradient Boosting(XGBoost),and Categorical Boosting(CatBoost)—to generate susceptibility maps.The Shapley additive explanation(SHAP)method was applied to quantify factor importance and explore their nonlinear effects.The results showed that:(1)CatBoost was the best-performing model(CA=0.938,AUC=0.980)in assessing landslide susceptibility,with altitude emerging as the most significant factor,followed by distance to roads and earthquake sites,precipitation,and slope;(2)the SHAP method revealed critical nonlinear thresholds,demonstrating that historical landslides were concentrated at mid-altitudes(1400-4000 m)and decreased markedly above 4000 m,with a parallel reduction in probability beyond 700 m from roads;and(3)landslide-prone areas,comprising 13%of the QTP,were concentrated in the southeastern and northeastern parts of the plateau.By integrating machine learning and SHAP analysis,this study revealed landslide hazard-prone areas and their driving factors,providing insights to support disaster management strategies and sustainable regional planning.
基金Supported by the National Natural Science Foundation of China(Grant No.12371110).
文摘This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).
文摘Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper equations are one of the main and most efficient methods for estimating stem volume to any merchantable limit of a species.There is currently no taper equation for Eucalyptus species in Nigeria.Therefore,this study developed taper equations for E.camaldulensis in northern Nigeria.Data for this study were obtained from a private plantation in Jalingo Local Government Area,Taraba State,Nigeria.68 trees were felled and sectioned into 1-m bolt across the stem to a merchantable limit of 5 cm,which were used as the fitting dataset.An additional 22 trees were felled and used to validate the taper equations for stem volume estimation.Seven taper equations were initially fitted to the dataset using nonlinear least squares.The best taper equation was then refitted using a nonlinear mixed-effects approach and calibrated using diameters of one to five sections from the butt end.The taper equations were numerically integrated to obtain the stem volume,which was compared with empirical volume equations.The result shows that the Kozak(Can J For Res 27(5):619-629.10.1139/x97-011,1997)equation,which included eight parameters,provided the best fit for predicting section diameters for under and over bark.The mixed-effects taper equation(NLME-TE)explained most stem diameter variations in the fitting dataset(pseudo-R2:0.986-0.987;RMSE:0.547-0.578 cm)without substantial residual trends.The validation showed that the prediction accuracy of the integrated NLME-TE improved as the number of sectional diameter measurements increased,with at least a 35%reduction in volume estimate error.For practical implementation,two calibration sectional diameter measurements taken from the butt end per tree are recommended.This approach would reduce measurement effort and cost while improving model performance.
基金Supported by the National Natural Science Foundation of China(Grant No.12161080).
文摘In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemotaxis systems in the stability of equilibrium points,the influence mechanism of chemotaxis on the dynamic behavior of the system is deeply studied.Theoretical analysis shows that chemotaxis significantly changes the stability characteristics of the system,and the reliability of theoretical results is further verified by numerical simulation.
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
文摘This study examines the dynamic response of two adjacent 9-and 20-story benchmark steel buildings subjected to six near-fault earthquake records.Two-dimensional numerical models were employed to account for the complexities of structure-soil-structure interaction(SSSI).The research focuses on the separation gap between the buildings and the effects of pounding while considering Fixed Base(FB)and SSSI models,evaluated according to UBC 94 and ASCE 7-16 seismic codes.Key findings reveal that pounding occurs with the UBC 94 separation gap when earthquake frequency aligns with system frequency,leading to increased column stresses in the 9-story building.In contrast,the ASCE 7-16 standard effectively prevents pounding in both the FB and SSSI models.Additionally,drifts and displacements of lower floors in SSSI models exceed the allowable limits of ASCE 7-16,underscoring the impact of soil-structure interaction on seismic response.
文摘The objective of the current study is to investigate an adaptive predictive observer-based autopilot for a skid-to-turn(STT)missile model with uncertainties and unknown dynamic equations.A predictive control for the STT missile is designed based on nonlinear model predictive control(NMPC)using Taylor series expansion,after which,via a neural network(NN),unknown functions are approximated.The present study also evaluates an adaptive optimal observer of a new strategy-based nonlinear system.Specifically,to estimate the missile states such as normal acceleration and its derivatives for the future,originally the Taylor series states expansion was gained to any specified order,based on their receding horizons.To address the problem of prediction error,an analytic solution was prepared that led to a closed form regarding the nonlinear optimal observer.Out of the gains resulting from the analytic solution,as developed for the problem of prediction error,the selection of the proposed observer gain was optimally conducted to meet the stability condition.Thus,combining the adaptive predictive autopilot and the adaptive optimal observer scheme was implemented to secure the performance,which needed only estimated normal acceleration and its derivatives.Meanwhile,no angular velocity measurement or wind angle estimation was required.Ultimately,the proposed technique was found effective,as confirmed by the qualitative simulation results.
