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Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces
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作者 刘通 夏旭 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第1期68-76,共9页
Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it canno... Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena. 展开更多
关键词 STATE exponent CRITICAL
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Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability
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作者 Ming ZHANG Ruiqiang DING +2 位作者 Quanjia ZHONG Jianping LI Deyu LU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第9期1769-1786,共18页
In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The eff... In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere. 展开更多
关键词 conditional nonlinear local Lyapunov exponent second-kind predictability coupled Lorenz model ENSO
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Potential sliding zone recognition method for the slow-moving landslide based on the Hurst exponent
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作者 Haiqing Yang Lili Qu +3 位作者 Lichuan Chen Kanglei Song Yong Yang Zhenxing Liang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第10期4105-4124,共20页
The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the... The abrupt occurrence of the Zhongbao landslide is totally unexpected,resulting in the destruction of local infrastructure and river blockage.To review the deformation history of the Zhongbao landslide and prevent the threat of secondary disasters,the small baseline subsets(SBAS)technology is applied to process 59 synthetic aperture radar(SAR)images captured from Sentinel-1A satellite.Firstly,the time series deformation of the Zhongbao landslide along the radar line of sight(LOS)direction is calculated by SBAS technology.Then,the projection transformation is conducted to determine the slope displacement.Furthermore,the Hurst exponent of the surface deformation along the two directions is calculated to quantify the hidden deformation development trend and identify the unstable deformation areas.Given the suddenness of the Zhongbao landslide failure,the multi-temporal interferometric synthetic aperture radar(InSAR)technology is the ideal tool to obtain the surface deformation history without any monitoring equipment.The obtained deformation process indicates that the Zhongbao landslide is generally stable with slow creep deformation before failure.Moreover,the Hurst exponent distribution on the landslide surface in different time stages reveals more deformation evolution information of the Zhongbao landslide,with partially unstable areas detected before the failure.Two potential unstable areas after the Zhongbao landslide disaster are revealed by the Hurst exponent distribution and verified by the GNSS monitoring results and deformation mechanism discussion.The method combining SBASInSAR and Hurst exponent proposed in this study could help prevent and control secondary landslide disasters. 展开更多
关键词 Zhongbao landslide Interferometric synthetic aperture radar (InSAR)technology Hurst exponent Deformation process Unstable area identification
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The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)
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作者 Sambourou Massinanke Sékou Coulibaly Mamadou Traore 《Journal of Applied Mathematics and Physics》 2024年第2期383-431,共49页
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ... Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual. 展开更多
关键词 Amalgam Spaces Variable exponent Lebesgue Spaces Dual of a Vector Space
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TWO DISJOINT AND INFINITE SETS OF SOLUTIONS FOR AN ELLIPTIC EQUATION INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS
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作者 Khalid BOUABID Rachid ECHARGHAOUI Mohssine EL MANSOUR 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2061-2074,共14页
In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with ... In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively. 展开更多
关键词 Laplacien critical Sobolev-Hardy exponent critical Sobolev exponent infinitely many solutions Pohozaev identity
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Solutions for Schrodinger-Poisson system involving nonlocal term and critical exponent
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作者 MO Xiu-ming MAO An-min WANG Xiang-xiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期357-372,共16页
In this paper,we consider the following Kirchhoff-Schrodinger-Poisson system:{−(a+b∫_(R^(3))|∇u|^(2))△u+u+ϕu=μQ(x)|u|^(q-2)u+K(x)|u|^(4)u,in R^(3),−△ϕ=u^(2) the nonlinear growth of|u|^(4)u reaches the Sobolev crit... In this paper,we consider the following Kirchhoff-Schrodinger-Poisson system:{−(a+b∫_(R^(3))|∇u|^(2))△u+u+ϕu=μQ(x)|u|^(q-2)u+K(x)|u|^(4)u,in R^(3),−△ϕ=u^(2) the nonlinear growth of|u|^(4)u reaches the Sobolev critical exponent.By combining the variational method with the concentration-compactness principle of Lions,we establish the existence of a positive solution and a positive radial solution to this problem under some suitable conditions.The nonlinear term includes the nonlinearity f(u)~|u|^(q-2)u for the well-studied case q∈[4,6),and the less-studied case q∈(2,3),we adopt two different strategies to handle these cases.Our result improves and extends some related works in the literature. 展开更多
关键词 variational methods critical exponent concentration-compactness principle
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General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents
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作者 蒋盛莲 刘彦霞 郎利君 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期79-86,共8页
We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critica... We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models. 展开更多
关键词 non-Hermitian mosaic model mosaic-to-non-mosaic mapping mobility edge Lyapunov exponent
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New seismic attribute:Fractal scaling exponent based on gray detrended fluctuation analysis 被引量:1
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作者 黄亚平 耿建华 郭彤楼 《Applied Geophysics》 SCIE CSCD 2015年第3期343-352,467,共11页
Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition sy... Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition system, and noise interference, seismic attributes for seismic data interpretation have uncertainties. Especially, the antinoise ability of seismic attributes directly affects the reliability of seismic interpretations. Gray system theory is used in time series to minimize data randomness and increase data regularity. Detrended fluctuation analysis (DFA) can effectively reduce extrinsic data tendencies. In this study, by combining gray system theory and DFA, we propose a new method called gray detrended fluctuation analysis (GDFA) for calculating the fractal scaling exponent. We consider nonlinear time series generated by the Weierstrass function and add random noise to actual seismic data. Moreover, we discuss the antinoise ability of the fractal scaling exponent based on GDFA. The results suggest that the fractal scaling exponent calculated using the proposed method has good antinoise ability. We apply the proposed method to 3D poststack migration seismic data from southern China and compare fractal scaling exponents calculated using DFA and GDFA. The results suggest that the use of the GDFA-calculated fractal scaling exponent as a seismic attribute can match the known distribution of sedimentary facies. 展开更多
关键词 Seismic attribute gray system theory detrended fluctuation analysis fractal scaling exponent
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Exponent及Gauss型遥测数据建模初始化算法 被引量:2
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作者 王永生 杜彬彬 +1 位作者 孙瑾 杨海峰 《海军航空工程学院学报》 2015年第6期547-552,共6页
在对某大型航天电子设备的遥测数据建模时,经常遇到含有指数类变化规律的数据,对其进行建模可以为研究设备性能的变化规律、实际与设计的差异等提供手段。针对有指数变化趋势的遥测数据,采用Exponent模型、Gauss模型对遥测数据建模,给... 在对某大型航天电子设备的遥测数据建模时,经常遇到含有指数类变化规律的数据,对其进行建模可以为研究设备性能的变化规律、实际与设计的差异等提供手段。针对有指数变化趋势的遥测数据,采用Exponent模型、Gauss模型对遥测数据建模,给出了这种数据模型的表达式,研究了2种模型的参数初始化算法。通过数值实验说明模型参数初始化算法的有效性,为后续利用最优化理论求解模型精确参数提供了良好的初试点。 展开更多
关键词 遥测数据 指数模型 GAUSS模型 初始参数
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CALCULATION OF CRITICAL EXPONENT β(L) OF MAGNETIC THIN FILMS BY USING ISING MODEL
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作者 霍炳海 区镜添 《Transactions of Tianjin University》 EI CAS 1998年第2期51-54,共4页
The variational cumulant expansion developed in recent years has been extended to treat the Ising model in statistical physics.In this paper,a detailed calculation of the critical temperature T c (L) and criti... The variational cumulant expansion developed in recent years has been extended to treat the Ising model in statistical physics.In this paper,a detailed calculation of the critical temperature T c (L) and critical exponent β(L) for the magnetic film of L layers are presented by means of the variational cumulant expansion.For L >1,the results of our theoretical calculations are in approximate coincidence with the experimental ones made before,and for the special case of L =1 (2 D),the results of the calculation are identical to the data from other reports. 展开更多
关键词 variational cumulant expansion critical temperature critical exponent
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MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR ELLIPTIC SYSTEMS WITH CRITICAL SOBOLEV-HARDY AND CONCAVE EXPONENTS 被引量:9
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作者 Tsing-San Hsu Huei-Lin Li 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期791-804,共14页
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
关键词 elliptic system critical Sobolev-Hardy exponent concave exponents Nehari manifold
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Determining the Spectrum of the Nonlinear Local Lyapunov Exponents in a Multidimensional Chaotic System 被引量:6
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作者 Ruiqiang DING Jianping LI Baosheng LI 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2017年第9期1027-1034,共8页
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
关键词 Lyapunov exponent nonlinear local Lyapunov exponent PREDICTABILITY
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Multilinear singular integrals and commutators in variable exponent Lebesgue spaces 被引量:24
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作者 HUANG Ai-wu XU Jing-shi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第1期69-77,共9页
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
关键词 Multilinear singular integral COMMUTATOR variable exponent Lebesgue space BMO function maximal operator.
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Lagrangian-based investigation of multiphase flows by finite-timeLyapunov exponents 被引量:12
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作者 Jia-Ning Tang Chien-Chou Tseng Ning-FeiWang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期612-624,共13页
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
关键词 Finite-time Lyapunov exponents Lagrangiancoherent structures Multiphase flow Gaseous jets injectedinto water CAVITATION
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SOLUTIONS FOR A NONHOMOGENEOUS ELLIPTIC PROBLEM INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT IN R^N 被引量:10
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作者 王征平 周焕松 《Acta Mathematica Scientia》 SCIE CSCD 2006年第3期525-536,共12页
For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy expon... For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy exponent, h(x) ∈ (D^1,2(R^N))^*, the dual space of (D^1,2(R^N)), with h(x)≥(≠)0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if ||h||*〈CN,sAs^N-s/4-2s(1-μ/μ)^1/2, CN,s=4-2s/N-2(N-2/N+2-2s)^N+2-2s/4-2s and As = inf u∈D^1,2(R^N)/{0}∫R^N(|△↓u|^2-μu^2/|x|^2)dx/(∫R^N|u|^2^*(s)/|x|^sdx)^2/2^*(s). 展开更多
关键词 Critical Sobolev-Hardy exponent elliptic equation Mountain Pass theorem subsuper solutions NONHOMOGENEOUS
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SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS 被引量:6
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作者 康东升 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1529-1540,共12页
In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions... In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions to the problem. 展开更多
关键词 quasilinear problem critical exponent solution variational method
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NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR BIHARMONIC EQUATION INVOLVING CRITICAL EXPONENTS 被引量:9
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作者 姚仰新 王荣鑫 沈尧天 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期509-514,共6页
In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequal... In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality. 展开更多
关键词 Biharmonic equation critical exponent singular term nontrivial solution Sobolev-Hardy inequality
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Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchronization 被引量:6
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作者 Shihui Fu Qi Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第3期277-283,共7页
Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the... Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics. 展开更多
关键词 Multibody system Dry friction Lyapunov exponent Chaos synchronization
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MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT 被引量:6
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作者 李工宝 张国 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期903-918,共16页
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:{-△pu-△qu=│u│^p*-2u+μ│u│^r-2u in Ω u... In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:{-△pu-△qu=│u│^p*-2u+μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^*=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ (0, μ0), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem. 展开更多
关键词 p&q-Laplacian multiplicity of solutions critical exponent
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New prediction of chaotic time series based on local Lyapunov exponent 被引量:9
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作者 张勇 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期191-197,共7页
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in stat... A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. 展开更多
关键词 chaotic time series prediction of chaotic time series local Lyapunov exponent least squaresmethod
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