We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures （...Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbu- lent cavitation under the framework of Navier-Stokes flow computations. For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream re- gion after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the ad- verse pressure gradient is strong enough. It represents a bar- rier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FFLE field has the potential to identify the structures of mul- tiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region.展开更多
In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions ...In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.展开更多
Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the...Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.展开更多
It is essential to precisely predict the crack growth,especially the near-threshold regime crack growth under different stress ratios,for most engineering structures consume their fatigue lives in this regime under ra...It is essential to precisely predict the crack growth,especially the near-threshold regime crack growth under different stress ratios,for most engineering structures consume their fatigue lives in this regime under random loading.In this paper,an improved unique curve model is proposed based on the unique curve model,and the determination of the shape exponents of this model is provided.The crack growth rate curves of some materials taken from the literature are evaluated using the improved model,and the results indicate that the improved model can accurately predict the crack growth rate in the nearthreshold and Paris regimes.The improved unique curve model can solve the problems about the shape exponents determination and weak ability around the near-threshold regime meet in the unique curve model.In addition,the shape exponents in the improved model at negative stress ratios are discussed,which can directly adopt that in the unique curve model.展开更多
In this paper, we deal with the following problem：By variational method, we prove the existenceof a nontrivial weak solution whenand the existence of a cylindricalweak solution when
The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of ...The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.展开更多
Pixel-based or texture-based classification technique individually does not yield an appropriate result in classifying the high spatial resolution remote sensing imagery since it comprises textured and non-textured re...Pixel-based or texture-based classification technique individually does not yield an appropriate result in classifying the high spatial resolution remote sensing imagery since it comprises textured and non-textured regions.In this study,Hölder exponents(HE)and variance(VAR)are used together to transform the image for measuring texture.A threshold is derived to segment the transformed image into textured and non-textured regions.Subsequently,the original image is extracted into textured and non-textured regions using this segmented image mask.Afterward,extracted textured region is classified using ISODATA classification algorithm considering HE,VAR,and intensity values of individual pixel of textured region.And extracted non-textured region of the image is classified using ISODATA classification algorithm.In case of non-textured region,HE and VAR value of individual pixel is not considered for classification for significant textural variation is not found among different classes.Consequently,the classified outputs of non-textured and textured regions that are generated independently are merged together to get the final classified image.IKONOS 1 m PAN images are classified using the proposed algorithm,and the classification accuracy is more than 88%.展开更多
In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape ...In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.展开更多
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical syste...A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.展开更多
In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decay...In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.展开更多
The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, i...The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations （QFs）, quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3（STO） with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x（Ca0.6389Ba0.3611）xTiO3（SCBT） with the averaged Sr-site ionic radius identical to the Sr2＋ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO （e.g., Sr1-xCaxTiO3） at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.展开更多
Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves ...Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem △^u-μ u/{x}^4=｜μ｜^2＊-2u＋f（x） with Dirichlet boundary condition on 偏dΩ under some assumptions on f（x） and μ.展开更多
A double system of exponents with piecewise continuous complex-valued coefficients are considered. Under definite conditions on the coefficients the frame property of this system in Lebesgue spaces of functions is inv...A double system of exponents with piecewise continuous complex-valued coefficients are considered. Under definite conditions on the coefficients the frame property of this system in Lebesgue spaces of functions is investigated. Such systems arise in the spectral problems for discontinuous differential operators.展开更多
The dynamics characteristics of the robotic arm system are usually highly nonlinear and strongly coupling,which will make it difficult to analyze the stability by the methods of solving kinetic equations or constructi...The dynamics characteristics of the robotic arm system are usually highly nonlinear and strongly coupling,which will make it difficult to analyze the stability by the methods of solving kinetic equations or constructing Lyapunov function,especially,these methods cannot calculate the quantitative relationship between mechanical structures or control input and dynamics parameters and stability.The theoretical analysis process from symbol dynamics modeling of the robotic arm system to the movement stability is studied by using the concept of Lyapunov exponents method. To verify the algorithm effectiveness,the inner relation between its joint input torque and stability or chaotic and stable motion of the 2-DOF robotic arm system is analyzed quantitatively. As compared with its counterpart of Lyapunov's direct method,the main advantage of the concept of Lyapunov exponents is that the methods for calculating the exponents are constructive to provide an effective analysis tool for analyzing robotic arm system movement stability of nonlinear systems.展开更多
We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unu...We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies ?to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at kF, 3kF, 5kF, 7kF and 9kF. Our analytical results will provide insights into criticality in condensed matter physics.展开更多
I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the...I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.展开更多
For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is t...For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.展开更多
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
文摘Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbu- lent cavitation under the framework of Navier-Stokes flow computations. For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream re- gion after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the ad- verse pressure gradient is strong enough. It represents a bar- rier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FFLE field has the potential to identify the structures of mul- tiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region.
文摘In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.
基金supported by the National Natural Science Foundation of China (Grant No 40675044)the State Key development program for Basic Research (Grant No 2006CB400503)
文摘Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.
文摘It is essential to precisely predict the crack growth,especially the near-threshold regime crack growth under different stress ratios,for most engineering structures consume their fatigue lives in this regime under random loading.In this paper,an improved unique curve model is proposed based on the unique curve model,and the determination of the shape exponents of this model is provided.The crack growth rate curves of some materials taken from the literature are evaluated using the improved model,and the results indicate that the improved model can accurately predict the crack growth rate in the nearthreshold and Paris regimes.The improved unique curve model can solve the problems about the shape exponents determination and weak ability around the near-threshold regime meet in the unique curve model.In addition,the shape exponents in the improved model at negative stress ratios are discussed,which can directly adopt that in the unique curve model.
基金Supported by the National Science Foundation of China(11071245 and 11101418)
文摘In this paper, we deal with the following problem：By variational method, we prove the existenceof a nontrivial weak solution whenand the existence of a cylindricalweak solution when
基金Project(2012CB725402)supported by the National Key Basic Research Program of ChinaProjects(51338003,50908051)supported by the National Natural Science Foundation of China
文摘The techniques to forecast available parking space(APS) are indispensable components for parking guidance systems(PGS). According to the data collected in Newcastle upon Tyne, England, the changing characteristics of APS were studied. Thereafter, aiming to build up a multi-step APS forecasting model that provides richer information than a conventional one-step model, the largest Lyapunov exponents(largest LEs) method was introduced into PGS. By experimental tests conducted using the same dataset, its prediction performance was compared with traditional wavelet neural network(WNN) method in both one-step and multi-step processes. Based on the results, a new multi-step forecasting model called WNN-LE method was proposed, where WNN, which enjoys a more accurate performance along with a better learning ability in short-term forecasting, was applied in the early forecast steps while the Lyapunov exponent prediction method in the latter steps precisely reflect the chaotic feature in latter forecast period. The MSE of APS forecasting for one hour time period can be reduced from 83.1 to 27.1(in a parking building with 492 berths) by using largest LEs method instead of WNN and further reduced to 19.0 by conducted the new method.
文摘Pixel-based or texture-based classification technique individually does not yield an appropriate result in classifying the high spatial resolution remote sensing imagery since it comprises textured and non-textured regions.In this study,Hölder exponents(HE)and variance(VAR)are used together to transform the image for measuring texture.A threshold is derived to segment the transformed image into textured and non-textured regions.Subsequently,the original image is extracted into textured and non-textured regions using this segmented image mask.Afterward,extracted textured region is classified using ISODATA classification algorithm considering HE,VAR,and intensity values of individual pixel of textured region.And extracted non-textured region of the image is classified using ISODATA classification algorithm.In case of non-textured region,HE and VAR value of individual pixel is not considered for classification for significant textural variation is not found among different classes.Consequently,the classified outputs of non-textured and textured regions that are generated independently are merged together to get the final classified image.IKONOS 1 m PAN images are classified using the proposed algorithm,and the classification accuracy is more than 88%.
基金Sponsored by the NSFC (10531070)Research Foundation for Outstanding Young Teachers of China University of Geoscience (Wuhan) (0816)
文摘In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.
文摘A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
基金Project supported by the Major Program of the National Natural Science Foundation (Grant No 10335010)the National Natural Science Foundation-the Science Foundation of China Academy of Engineering Physics NSAF(Grant No 10576005)
文摘In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.
基金the National Basic Research Program of China(Grant Nos.2011CB922101 and 2009CB623303)the National Natural Science Foundation of China(Grant Nos.11234005 and 11074113)the Priority Academic Development Program of Jiangsu Higher Education Institutions,China
文摘The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations （QFs）, quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3（STO） with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x（Ca0.6389Ba0.3611）xTiO3（SCBT） with the averaged Sr-site ionic radius identical to the Sr2＋ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO （e.g., Sr1-xCaxTiO3） at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.
文摘Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem △^u-μ u/{x}^4=｜μ｜^2＊-2u＋f（x） with Dirichlet boundary condition on 偏dΩ under some assumptions on f（x） and μ.
文摘A double system of exponents with piecewise continuous complex-valued coefficients are considered. Under definite conditions on the coefficients the frame property of this system in Lebesgue spaces of functions is investigated. Such systems arise in the spectral problems for discontinuous differential operators.
基金Supported by the National Natural Science Foundation of China(No.51405243,51575283)
文摘The dynamics characteristics of the robotic arm system are usually highly nonlinear and strongly coupling,which will make it difficult to analyze the stability by the methods of solving kinetic equations or constructing Lyapunov function,especially,these methods cannot calculate the quantitative relationship between mechanical structures or control input and dynamics parameters and stability.The theoretical analysis process from symbol dynamics modeling of the robotic arm system to the movement stability is studied by using the concept of Lyapunov exponents method. To verify the algorithm effectiveness,the inner relation between its joint input torque and stability or chaotic and stable motion of the 2-DOF robotic arm system is analyzed quantitatively. As compared with its counterpart of Lyapunov's direct method,the main advantage of the concept of Lyapunov exponents is that the methods for calculating the exponents are constructive to provide an effective analysis tool for analyzing robotic arm system movement stability of nonlinear systems.
文摘We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies ?to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at kF, 3kF, 5kF, 7kF and 9kF. Our analytical results will provide insights into criticality in condensed matter physics.
文摘I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.
基金supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502)the National Program on Global Change and Air–Sea Interaction (Grant No. GASI-IPOVAI06)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07)
文摘For an n-dimensional chaotic system, we extend the definition of the nonlinear local Lyapunov exponent （NLLE） from one- to n-dimensional spectra, and present a method for computing the NLLE spectrum. The method is tested on three chaotic systems with different complexity. The results indicate that the NLLE spectrum realistically characterizes the growth rates of initial error vectors along different directions from the linear to nonlinear phases of error growth. This represents an improvement over the traditional Lyapunov exponent spectrum, which only characterizes the error growth rates during the linear phase of error growth. In addition, because the NLLE spectrum can effectively separate the slowly and rapidly growing perturbations, it is shown to be more suitable for estimating the predictability of chaotic systems, as compared to the traditional Lyapunov exponent spectrum.
