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
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 m KdV 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
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
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
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
In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the...In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the recommended density function by introducing a fifth-degree cubature Kalman filter algorithm to guide particle sampling,which effectively alleviates the problem of particle degradation and significantly improves the estimation accuracy of the filter.However,the 5CPF algorithm exhibits high computational complexity,particularly in scenarios with a large number of particles.Therefore,we propose the extended Kalman filter(EKF)-5CPF algorithm,which employs an EKF to replace the time update step for each particle in the 5CPF.This enhances the algorithm’s real-time capability while maintaining the high precision advantage of the 5CPF algorithm.In addition,we construct bearing-only dual-station and single-motion station target tracking systems,and the filtering performances of 5CPF and EKF-5CPF algorithms under different conditions are analyzed.The results show that both the 5CPF algorithm and EKF-5CPF have strong robustness and can adapt to different noise environments.Furthermore,both algorithms significantly outperform traditional nonlinear filtering algorithms in terms of convergence speed,tracking accuracy,and overall stability.展开更多
Conducting predictability studies is essential for tracing the source of forecast errors,which not only leads to the improvement of observation and forecasting systems,but also enhances the understanding of weather an...Conducting predictability studies is essential for tracing the source of forecast errors,which not only leads to the improvement of observation and forecasting systems,but also enhances the understanding of weather and climate phenomena.In the past few decades,dynamical numerical models have been the primary tools for predictability studies,achieving significant progress.Nowadays,with the advances in artificial intelligence(AI)techniques and accumulations of vast meteorological data,modeling weather and climate events using modern data-driven approaches is becoming trendy,where FourCastNet,Pangu-Weather,and GraphCast are successful pioneers.In this perspective article,we suggest AI models should not be limited to forecasting but be expanded to predictability studies,leveraging AI's advantages of high efficiency and self-contained optimization modules.To this end,we first remark that AI models should possess high simulation capability with fine spatiotemporal resolution for two kinds of predictability studies.AI models with high simulation capabilities comparable to numerical models can be considered to provide solutions to partial differential equations in a data-driven way.Then,we highlight several specific predictability issues with well-determined nonlinear optimization formulizations,which can be well-studied using AI models,holding significant scientific value.In addition,we advocate for the incorporation of AI models into the synergistic cycle of the cognition–observation–model paradigm.Comprehensive predictability studies have the potential to transform“big data”to“big and better data”and shift the focus from“AI for forecasts”to“AI for science”,ultimately advancing the development of the atmospheric and oceanic sciences.展开更多
Ten physical and environmental variables collected from an on-the-go soil sensor at two field sites (MF3E and MF11S) in Mississippi, USA, were analyzed to assess soil variability and the interrelationships among the m...Ten physical and environmental variables collected from an on-the-go soil sensor at two field sites (MF3E and MF11S) in Mississippi, USA, were analyzed to assess soil variability and the interrelationships among the measurements. At MF3E, moderate variability was observed in apparent electrical conductivity shallow (ECas), slope, and ECa ratio measurements, with coefficients of variation ranging from 20% to 27%. In contrast, MF11S exhibited higher variability, particularly in ECas and ECad (deep) measurements, which exceeded 30% in their coefficient of variation values, indicating significant differences in soil composition and moisture content. Correlation analysis revealed strong positive relationships between the near-infrared-to-red ratio and red reflectance (r = 0.897***) soil values at MF3E. MF11S demonstrated a strong negative correlation between ECas and ECad readings with the x-coordinate (r ***). Scatter plots and fitted models illustrated the complexity of relationships, with many showing nonlinear trends. These findings emphasize the need for continuous monitoring and advanced modeling to understand the dynamic nature of soil properties and their implications for agricultural practices. Future research should explore the underlying mechanisms driving variability in the soil characteristics to enhance soil management strategies at the study sites.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
The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The n...The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.展开更多
We investigate theoretically the enhancement of mechanical squeezing in a multimode optomechanical system by introducing a coherent phonon–photon interaction via the backward stimulated Brillouin scattering(BSBS)proc...We investigate theoretically the enhancement of mechanical squeezing in a multimode optomechanical system by introducing a coherent phonon–photon interaction via the backward stimulated Brillouin scattering(BSBS)process.The coherent photon–phonon interaction where two optical modes couple to a Brillouin acoustic mode with a large decay rate provides an extra channel for the cooling of a Duffing mechanical oscillator.The squeezing degree and the robustness to the thermal noises of the Duffing mechanical mode can be enhanced greatly.When the Duffing nonlinearity is weak,the squeezing degree of the mechanical mode in the presence of BSBS can be improved by more than one order of magnitude compared with that in the absence of BSBS.Our scheme may be extended to other quantum systems to study novel quantum effects.展开更多
Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evi...Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evidence of biphonation and other nonlinear phenomena.Here,we analyze the acoustic structure of captive wapiti vocalizations to compare the male bugle with 3 categories of distress vocalizations:neonate distress(capture)calls,calf isolation calls,and adult female isolation calls.These 4 high-arousal call categories serve a common general function in recruiting conspecifics but occur in different behavioral contexts(capture,isolation,reproduction).Our goal was to distinguish characteristics that vary in graded steps that may correspond to an animal’s age or size from characteristics that are unique to the bugle.Characteristics of the high and loud fundamental(G0)varied in an age/size-graded manner with a decrease in minimum G0,an increase in the maximum and range of G0,with no evidence of sex differences.The nonlinear phenomena of deterministic chaos,biphonation,and frequency jumps were present in all 4 call categories and became more common from the distress vocalizations of neonates to calves to adult females to the male bugle.Two temporal characteristics sharply distinguished the bugle from the 3 categories of distress vocalizations:these included a prolonged call duration and a maximum G0 that occurred much later in the call for the bugle than for distress vocalizations.Our results suggest that distress vocalizations of different age groups and the reproductive bugle of wapiti share a high G0,with age/size-graded changes in G0 and nonlinear phenomena,but differ sharply in temporal characteristics.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
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.
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 m KdV 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 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.
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 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 Guangxi Special Program for Technological Innovation Guidance(No.GuiKeAC25069006).
文摘In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the recommended density function by introducing a fifth-degree cubature Kalman filter algorithm to guide particle sampling,which effectively alleviates the problem of particle degradation and significantly improves the estimation accuracy of the filter.However,the 5CPF algorithm exhibits high computational complexity,particularly in scenarios with a large number of particles.Therefore,we propose the extended Kalman filter(EKF)-5CPF algorithm,which employs an EKF to replace the time update step for each particle in the 5CPF.This enhances the algorithm’s real-time capability while maintaining the high precision advantage of the 5CPF algorithm.In addition,we construct bearing-only dual-station and single-motion station target tracking systems,and the filtering performances of 5CPF and EKF-5CPF algorithms under different conditions are analyzed.The results show that both the 5CPF algorithm and EKF-5CPF have strong robustness and can adapt to different noise environments.Furthermore,both algorithms significantly outperform traditional nonlinear filtering algorithms in terms of convergence speed,tracking accuracy,and overall stability.
基金in part supported by the National Natural Science Foundation of China(Grant Nos.42288101,42405147 and 42475054)in part by the China National Postdoctoral Program for Innovative Talents(Grant No.BX20230071)。
文摘Conducting predictability studies is essential for tracing the source of forecast errors,which not only leads to the improvement of observation and forecasting systems,but also enhances the understanding of weather and climate phenomena.In the past few decades,dynamical numerical models have been the primary tools for predictability studies,achieving significant progress.Nowadays,with the advances in artificial intelligence(AI)techniques and accumulations of vast meteorological data,modeling weather and climate events using modern data-driven approaches is becoming trendy,where FourCastNet,Pangu-Weather,and GraphCast are successful pioneers.In this perspective article,we suggest AI models should not be limited to forecasting but be expanded to predictability studies,leveraging AI's advantages of high efficiency and self-contained optimization modules.To this end,we first remark that AI models should possess high simulation capability with fine spatiotemporal resolution for two kinds of predictability studies.AI models with high simulation capabilities comparable to numerical models can be considered to provide solutions to partial differential equations in a data-driven way.Then,we highlight several specific predictability issues with well-determined nonlinear optimization formulizations,which can be well-studied using AI models,holding significant scientific value.In addition,we advocate for the incorporation of AI models into the synergistic cycle of the cognition–observation–model paradigm.Comprehensive predictability studies have the potential to transform“big data”to“big and better data”and shift the focus from“AI for forecasts”to“AI for science”,ultimately advancing the development of the atmospheric and oceanic sciences.
文摘Ten physical and environmental variables collected from an on-the-go soil sensor at two field sites (MF3E and MF11S) in Mississippi, USA, were analyzed to assess soil variability and the interrelationships among the measurements. At MF3E, moderate variability was observed in apparent electrical conductivity shallow (ECas), slope, and ECa ratio measurements, with coefficients of variation ranging from 20% to 27%. In contrast, MF11S exhibited higher variability, particularly in ECas and ECad (deep) measurements, which exceeded 30% in their coefficient of variation values, indicating significant differences in soil composition and moisture content. Correlation analysis revealed strong positive relationships between the near-infrared-to-red ratio and red reflectance (r = 0.897***) soil values at MF3E. MF11S demonstrated a strong negative correlation between ECas and ECad readings with the x-coordinate (r ***). Scatter plots and fitted models illustrated the complexity of relationships, with many showing nonlinear trends. These findings emphasize the need for continuous monitoring and advanced modeling to understand the dynamic nature of soil properties and their implications for agricultural practices. Future research should explore the underlying mechanisms driving variability in the soil characteristics to enhance soil management strategies at the study sites.
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Projects(52205069,52075083,52304049)supported by the National Natural Science Foundation of ChinaProject(2021-BS-164)supported by the Liaoning Province Doctoral Research Startup Fund,China+2 种基金Project(LJKZ0264)supported by the Science and Technology Research Projects of Education Department of Liaoning Province,ChinaProject(G2022003010L)supported by the High-end Foreign Experts Recruitment Plan of ChinaProject(E2021203095)supported by the Natural Science Foundation for Young Scholars of Hebei Province,China。
文摘The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.
基金Project supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202400624)the Natural Science Foundation of Chongqing CSTC(Grant No.CSTB2022NSCQBHX0020)+3 种基金the China Electronics Technology Group Corporation 44th Research Institute(Grant No.6310001-2)the Project Grant“Noninvasive Sensing Measurement based on Terahertz Technology”from Province and MOE Collaborative Innovation Centre for New Generation Information Networking and Terminalsthe Key Research Program of CQUPT on Interdisciplinary and Emerging Field(A2018-01)the Venture&Innovation Support program for Chongqing Overseas Returnees Year 2022。
文摘We investigate theoretically the enhancement of mechanical squeezing in a multimode optomechanical system by introducing a coherent phonon–photon interaction via the backward stimulated Brillouin scattering(BSBS)process.The coherent photon–phonon interaction where two optical modes couple to a Brillouin acoustic mode with a large decay rate provides an extra channel for the cooling of a Duffing mechanical oscillator.The squeezing degree and the robustness to the thermal noises of the Duffing mechanical mode can be enhanced greatly.When the Duffing nonlinearity is weak,the squeezing degree of the mechanical mode in the presence of BSBS can be improved by more than one order of magnitude compared with that in the absence of BSBS.Our scheme may be extended to other quantum systems to study novel quantum effects.
基金The University of Winnipeg and The University of Winnipeg Foundation contributed funding to this research.
文摘Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evidence of biphonation and other nonlinear phenomena.Here,we analyze the acoustic structure of captive wapiti vocalizations to compare the male bugle with 3 categories of distress vocalizations:neonate distress(capture)calls,calf isolation calls,and adult female isolation calls.These 4 high-arousal call categories serve a common general function in recruiting conspecifics but occur in different behavioral contexts(capture,isolation,reproduction).Our goal was to distinguish characteristics that vary in graded steps that may correspond to an animal’s age or size from characteristics that are unique to the bugle.Characteristics of the high and loud fundamental(G0)varied in an age/size-graded manner with a decrease in minimum G0,an increase in the maximum and range of G0,with no evidence of sex differences.The nonlinear phenomena of deterministic chaos,biphonation,and frequency jumps were present in all 4 call categories and became more common from the distress vocalizations of neonates to calves to adult females to the male bugle.Two temporal characteristics sharply distinguished the bugle from the 3 categories of distress vocalizations:these included a prolonged call duration and a maximum G0 that occurred much later in the call for the bugle than for distress vocalizations.Our results suggest that distress vocalizations of different age groups and the reproductive bugle of wapiti share a high G0,with age/size-graded changes in G0 and nonlinear phenomena,but differ sharply in temporal characteristics.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
