A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. Th...A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.展开更多
To analyze the parachute dynamics and stability characteristics of precision airdrop system, the fluid-structure interaction （FSI） dynamics coupling with the flight trajectory of a para- chute payload system is comp...To analyze the parachute dynamics and stability characteristics of precision airdrop system, the fluid-structure interaction （FSI） dynamics coupling with the flight trajectory of a para- chute payload system is comprehensively predicted by numerical methods. The inflation behavior of a disk-gap-band parachute is specifically investigated using the arbitrary Lagrangian Euler （ALE） penalty coupling method. With the available aerodynamic data obtained from the FSI sim- ulation, a nine-degree-of-freedom （9DOF） dynamic model of a parachute-payload system is built and solved to simulate the descent trajectory of the multi-body dynamic system. Finally, a linear five-degree-of-freedom （5DOF） dynamic model is developed, the perturbation characteristics and the motion laws of the parachute and payload under a wind gust are analyzed by the linearization method and verified by a comparison with flight test data. The results of airdrop test demonstrate that our method can be further applied to the guidance and control of precision airdrop systems.展开更多
The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a ...The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.展开更多
This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sher...This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sherman-Morrison-Woodbury(SMW)formula to the t-product tensor scenarios.The SMW formula can be used to perform the sensitivity analy-sis for a multilinear system of equations.展开更多
In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the ...In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.展开更多
In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported r...In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.展开更多
We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the i...We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.展开更多
We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral grap...We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.展开更多
Scheduling of finite capacity discrete manufacturing processes is attracting increasing attention. The major difficulty in this area is concerned with the combinatorial explosion which occurs once one begins to consi...Scheduling of finite capacity discrete manufacturing processes is attracting increasing attention. The major difficulty in this area is concerned with the combinatorial explosion which occurs once one begins to consider the scheduling of workpieces through more than a few machines. What kind of laws must be satisfied in modelling、simulation and perturbation analysis? In this paper, we show how to deal with the structure of complex assembly production systems hierarchically to achieve simplicity for these purposes. We will also describe two ′conservation laws of workpieces′ applicable to manufacturing scheduling problems and then develop a complete state space representation. Some experiments and results will also be included. This approach can be used for both stochastic and deterministic dynamical systems in this area and can also be extended to other areas which require decision support.展开更多
We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to ob...We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.展开更多
Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear ...Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.展开更多
In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries...In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.展开更多
We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated...We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
Compact accelerator-based neutron source facilities are garnering attention and play an important and expanding role in material and engineering sciences,as well as in neutron science education and training.Neutrons a...Compact accelerator-based neutron source facilities are garnering attention and play an important and expanding role in material and engineering sciences,as well as in neutron science education and training.Neutrons are produced by bombarding a low-energy proton beam onto a beryllium or lithium target.In such an acceleratorbased neutron source,a radio frequency quadrupole(RFQ)is usually utilized to accelerate a high-intensity proton beam to a few MeV.This study mainly covers the highfrequency structure design optimizations of a 4-vane RFQ with pi-mode stabilizer loops(PISLs)and its RF stability analysis.A 176 MHz RFQ accelerator is designed to operate at a 10%duty factor and could accelerate an80 mA proton beam from 65 keV to 2.5 MeV within a length of 5.3 m.The adoption of PISLs ensures high RF stability,eases the operation of the accelerator,and implies less stringent alignment and machining tolerances.展开更多
For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the ...For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.展开更多
The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the flui...The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.展开更多
The generalized adjoint property and adjoint matching condition for systems that contain discontinuous on/off switches are derived by a perturbation analysis of the Lagranging-form costfunction.
The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated an...The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.展开更多
文摘A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.
基金co-supported by Research Project of Chinese National University of Defense Technology(No.:JC13-0104)the National Natural Science Foundation of China(Nos.:51375486 and 11272345)the found support from China Scholarship Council(CSC)
文摘To analyze the parachute dynamics and stability characteristics of precision airdrop system, the fluid-structure interaction （FSI） dynamics coupling with the flight trajectory of a para- chute payload system is comprehensively predicted by numerical methods. The inflation behavior of a disk-gap-band parachute is specifically investigated using the arbitrary Lagrangian Euler （ALE） penalty coupling method. With the available aerodynamic data obtained from the FSI sim- ulation, a nine-degree-of-freedom （9DOF） dynamic model of a parachute-payload system is built and solved to simulate the descent trajectory of the multi-body dynamic system. Finally, a linear five-degree-of-freedom （5DOF） dynamic model is developed, the perturbation characteristics and the motion laws of the parachute and payload under a wind gust are analyzed by the linearization method and verified by a comparison with flight test data. The results of airdrop test demonstrate that our method can be further applied to the guidance and control of precision airdrop systems.
基金Project supported by the National Key Basic Pre-Research Fund of the Ministry of Science and Technology of Chinathe Fund for Outstanding Young Researchers of the National Natural Sciences Foundation of China (No.10025208)+2 种基金 the KeyFund of the National Natural Science Foundation of China the Youth Fund of the National Natural Science Foundationof China (No.10302009) and the Youth Fund of Lanzhou University (Lzu200305).
文摘The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.
基金supported by the National Natural Science Foundation of China under grant number 11801534.
文摘This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sherman-Morrison-Woodbury(SMW)formula to the t-product tensor scenarios.The SMW formula can be used to perform the sensitivity analy-sis for a multilinear system of equations.
文摘In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.
文摘In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.
基金supported by National Natural Science Foundation of China(Grant No.11211120144)the Fundamental Research Funds for the Central Universities(Grant No.2010QYZD001)
文摘We investigate perturbation for continuous-time Markov chains(CTMCs) on a countable state space. Explicit bounds on ?D and D are derived in terms of a drift condition, where ? and D represent the perturbation of the intensity matrices and the deviation matrix, respectively. Moreover, we obtain perturbation bounds on the stationary distributions, which extends the results by Liu(2012) for uniformly bounded CTMCs to general(possibly unbounded) CTMCs. Our arguments are mainly based on the technique of augmented truncations.
基金supported by the National Natural Science Foundation of China (No.60375003)the Aeronautics and Astronautics Basal Science Foundation of China (No.03I53059)the Science and Technology Innovation Foundation of Northwestern Polytechnical University (No.2007KJ01033)
文摘We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.
文摘Scheduling of finite capacity discrete manufacturing processes is attracting increasing attention. The major difficulty in this area is concerned with the combinatorial explosion which occurs once one begins to consider the scheduling of workpieces through more than a few machines. What kind of laws must be satisfied in modelling、simulation and perturbation analysis? In this paper, we show how to deal with the structure of complex assembly production systems hierarchically to achieve simplicity for these purposes. We will also describe two ′conservation laws of workpieces′ applicable to manufacturing scheduling problems and then develop a complete state space representation. Some experiments and results will also be included. This approach can be used for both stochastic and deterministic dynamical systems in this area and can also be extended to other areas which require decision support.
基金This work was supported in part by the National Science Foundation under Grant EFRI-0735794by AFOSR under Grants FA9550-07-1-0361 and FA9550-09-1-0095+1 种基金by DOE under Grant DE-FG52-06NA27490by ONR under Grant N00014-09-1-1051.
文摘We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.
基金Supported by the National Natural Science Foundation of China(12001142).
文摘Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.
基金supported by Natural Science Foundation of Hebei Province,China(Grant No.A2018207030)Youth Key Program of Hebei University of Economics and Business(2018QZ07)+2 种基金Key Program of Hebei University of Economics and Business(2020ZD11)Youth Team Support Program of Hebei University of Economics and BusinessNational Natural Science Foundation of China(Grant No.11801133)。
文摘In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.
基金Projects supported by the Natural Science Foundation of Hunan Province(2016JJ6020)the Scientific Research Fund of Hunan Provincial Education Department(18A436)the Scientific Research Fund of Hunan First normal University(XYS13N16)。
文摘We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘Compact accelerator-based neutron source facilities are garnering attention and play an important and expanding role in material and engineering sciences,as well as in neutron science education and training.Neutrons are produced by bombarding a low-energy proton beam onto a beryllium or lithium target.In such an acceleratorbased neutron source,a radio frequency quadrupole(RFQ)is usually utilized to accelerate a high-intensity proton beam to a few MeV.This study mainly covers the highfrequency structure design optimizations of a 4-vane RFQ with pi-mode stabilizer loops(PISLs)and its RF stability analysis.A 176 MHz RFQ accelerator is designed to operate at a 10%duty factor and could accelerate an80 mA proton beam from 65 keV to 2.5 MeV within a length of 5.3 m.The adoption of PISLs ensures high RF stability,eases the operation of the accelerator,and implies less stringent alignment and machining tolerances.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. U1706230 and51379071)the Key Project of NSFC-Shandong Joint Research Funding POW3C (Grant No. U1906230)the National Science Fund for Distinguished Young Scholars (Grant No. 51425901)
文摘For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.
基金Project supported by the National Natural Science Foundation of China (No. 10871225)the Pujiang Talent Program of China (No. 06PJ14416)
文摘The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.
文摘The generalized adjoint property and adjoint matching condition for systems that contain discontinuous on/off switches are derived by a perturbation analysis of the Lagranging-form costfunction.
基金financially supported by the Council of Scientific and Industrial Research(CSIR),Govt.of India
文摘The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.
