A high-speed train travelling from the open air into a narrow tunnel will cause the“sonic boom”at tunnel exit.When the maglev train’s speed reaches 600 km/h,the train-tunnel aerodynamic effect is intensified,so a n...A high-speed train travelling from the open air into a narrow tunnel will cause the“sonic boom”at tunnel exit.When the maglev train’s speed reaches 600 km/h,the train-tunnel aerodynamic effect is intensified,so a new mitigation method is urgently expected to be explored.This study proposed a novel asymptotic linear method(ALM)for micro pressure wave(MPW)mitigation to achieve a constant gradient of initial c ompression waves(ICWs),via a study with various open ratios on hoods.The properties of ICWs and MPWs under various open ratios of hoods were analyzed.The results show that as the open ratio increases,the MPW amplitude at the tunnel exit initially decreases before rising.At the open ratio of 2.28%,the slope of the ICW curve is linearly coincident with a supposed straight line in the ALM,which further reduces the MPW amplitude by 26.9%at 20 m and 20.0%at 50 m from the exit,as compared to the unvented hood.Therefore,the proposed method effectively mitigates MPW and quickly determines the upper limit of alleviation for the MPW amplitude at a fixed train-tunnel operation condition.All achievements provide a ne w potential measure for the adaptive design of tunnel hoods.展开更多
Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. ...Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.展开更多
The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients....The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.展开更多
A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the clas...A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.展开更多
The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering ...The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to il-lustrate the computational accuracy and efficiency of the proposed method.展开更多
In this paper a new time explicit asymptotic method is presented through introducing an auxiliary parameter for the solution of an exact controllability problem of scattering waves. Based on an exact control function...In this paper a new time explicit asymptotic method is presented through introducing an auxiliary parameter for the solution of an exact controllability problem of scattering waves. Based on an exact control function, the asymptotic iteration is controlled by the auxiliary parameter and the optimal auxiliary parameter is updated during the iteration based on the existing or current iterated solutions of the wave equation. The numerical results show that the new method presented has a significant advantage over the purely asymptotic method in the history of convergence and has the ability to solve the scattering by the multi bodies.展开更多
The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenv...The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.展开更多
A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very t...A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very thin compared with the characteristic length of the structural component, and the nonhomogeneity exists only in the thin layer. Based on these features, by choosing a small parameter I which characterizes the stiffness of the layer relative to the component, and expanding the stresses and displacements on the two sides of the interface according to the parameter lambda, then asymptotically using the continuity conditions of the stresses and displacements on the interface, a decoupling computing process of the coupling control equations of the layer and the structural component is realized. Finally, two examples are given to illustrate the application of the method proposed.展开更多
In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems f...In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.展开更多
This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small ...This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.展开更多
The non-relativistic radial Schr¨odinger equation is analytically solved using asymptotic iteration method within the framework of a general interaction potential whose special cases are the Cornell and Cornell p...The non-relativistic radial Schr¨odinger equation is analytically solved using asymptotic iteration method within the framework of a general interaction potential whose special cases are the Cornell and Cornell plus harmonic potentials. The energy eigenvalues expression is derived in three dimensional space, which is further used to calculate the mass spectra of ˉcc,ˉbb,ˉbc, cˉs, bˉs and b ˉq mesons. The obtained results of this work are in good agreement with experimental and other relativistic results and also improved in comparison with other non-relativistic recent studies.展开更多
Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the f...Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.展开更多
Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain...Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain analytical solutions describing these systems,which hinders analysis and design.In this work,we propose a self-vibrating liquid crystal elastomer(LCE)fiber-spring system exposed to spatially-constant gradient light,and determine analytical solutions for its amplitude and period.First,using a dynamic model of LCE,we obtain the equations governing the self-vibration.Then,we analyze two different motion states and elucidate the mechanism of self-vibration.Subsequently,we derive analytical solutions for the amplitude and frequency using the multi-scale method,and compare the solutions with numerical results.The analytical outcomes are shown to be consistent with the numerical calculations,while taking far less computational time.Our findings reveal the utility of the multi-scale method in describing self-vibration,which may contribute to more efficient and accurate analyses of self-vibrating systems.展开更多
In this paper,we investigate the integrable fractional coupled Gerdjikov-Ivanov equation and derive its explicit form by employing the completeness relation of squared eigenfunctions.Based on the Riemann-Hilbert metho...In this paper,we investigate the integrable fractional coupled Gerdjikov-Ivanov equation and derive its explicit form by employing the completeness relation of squared eigenfunctions.Based on the Riemann-Hilbert method,we construct the fractional N-soliton solutions.We find that as the powerεof the Riesz fractional derivative increases,the amplitudes of the fractional soliton solutions remain invariant,while their widths decrease and the absolute values of the wave velocity,group velocity,and phase velocity increase.Additionally,we examine the long-time asymptotic behavior of the fractional N-soliton solution.The results show that as t→±∞,the solution can be approximated by the sum of N fractional one-soliton solutions,with each soliton's amplitude and velocity remaining constant,whereas both position and phase shifts are observed.展开更多
The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also app...The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.展开更多
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are...The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.展开更多
This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux.The global solution is shown to converge to a combination of a rarefaction wave an...This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux.The global solution is shown to converge to a combination of a rarefaction wave and a viscous contact wave as time tends to infinity by employing the L^(2) energy method and a refined wave interaction analysis.This is the first result on the asymptotics toward multiwave for the damped wave equation,and this asymptotic stability result does not rely on the small assumption of neither the initial perturbations nor the wave strength.展开更多
A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate sol...A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.展开更多
This paper is a continuation of part (Ⅰ), on the asymptotics behaviors of the series solutions investigated in (Ⅰ). The remainder terms of the series solutions are estimated by the maximum norm.
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
基金Project(24A0006)supported by the Key Project of Scientific Research Fund of Hunan Provincial Department of Education,ChinaProject(2024JJ5430)supported by the Natural Science Foundation of Hunan Province,ChinaProjects(2024JK2045,2023RC3061)supported by the Science and Technology Innovation Program of Hunan Province,China。
文摘A high-speed train travelling from the open air into a narrow tunnel will cause the“sonic boom”at tunnel exit.When the maglev train’s speed reaches 600 km/h,the train-tunnel aerodynamic effect is intensified,so a new mitigation method is urgently expected to be explored.This study proposed a novel asymptotic linear method(ALM)for micro pressure wave(MPW)mitigation to achieve a constant gradient of initial c ompression waves(ICWs),via a study with various open ratios on hoods.The properties of ICWs and MPWs under various open ratios of hoods were analyzed.The results show that as the open ratio increases,the MPW amplitude at the tunnel exit initially decreases before rising.At the open ratio of 2.28%,the slope of the ICW curve is linearly coincident with a supposed straight line in the ALM,which further reduces the MPW amplitude by 26.9%at 20 m and 20.0%at 50 m from the exit,as compared to the unvented hood.Therefore,the proposed method effectively mitigates MPW and quickly determines the upper limit of alleviation for the MPW amplitude at a fixed train-tunnel operation condition.All achievements provide a ne w potential measure for the adaptive design of tunnel hoods.
基金supported by the National Natural Science Foundation of China (Grant Nos.40334040 and 40974033)the Promoting Foundation for Advanced Persons of Talent of NCWU
文摘Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.
基金Project supported by the National Natural Science Foundation of China(No.11672008)
文摘The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.
基金the National Natural Science Foundation of China(Nos.11672191,11772206,and U1934201)the Hundred Excellent Innovative Talents Support Program in Hebei University(No.SLRC2017053)。
文摘A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.
基金Supported by the National Natural Science Foundation of China (No. 60771034 )the 211 Project of Anhui University
文摘The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to il-lustrate the computational accuracy and efficiency of the proposed method.
文摘In this paper a new time explicit asymptotic method is presented through introducing an auxiliary parameter for the solution of an exact controllability problem of scattering waves. Based on an exact control function, the asymptotic iteration is controlled by the auxiliary parameter and the optimal auxiliary parameter is updated during the iteration based on the existing or current iterated solutions of the wave equation. The numerical results show that the new method presented has a significant advantage over the purely asymptotic method in the history of convergence and has the ability to solve the scattering by the multi bodies.
文摘The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.
文摘A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very thin compared with the characteristic length of the structural component, and the nonhomogeneity exists only in the thin layer. Based on these features, by choosing a small parameter I which characterizes the stiffness of the layer relative to the component, and expanding the stresses and displacements on the two sides of the interface according to the parameter lambda, then asymptotically using the continuity conditions of the stresses and displacements on the interface, a decoupling computing process of the coupling control equations of the layer and the structural component is realized. Finally, two examples are given to illustrate the application of the method proposed.
基金the National Natural Science Foundation of China(No.11501449 and 11471262)the Center for high performance computing of Northwestern Polytechnical University.
文摘In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.
文摘This paper presents the recursive asymptotic hybrid matrix method for acoustic waves in multilayered piezoelectric media. The hybrid matrix method preserves the numerical stability and accuracy across large and small thicknesses. For discussion and comparison, the scattering matrix method is also presented in physics-based form and coherent form. The latter form resembles closely that of hybrid matrix method and helps to highlight their relationship and distinction. For both scattering and hybrid matrix methods, their formulations in terms of eigenwaves solution are provided concisely. Making use of the hybrid matrix, the recursive asymptotic method without eigenwaves solution is described and discussed. The method bypasses the intricacies of eigenvalue-eigenvector approach and requires only elementary matrix operations along with thin- layer asymptotic approximation. It can be used to determine Green’s function matrix readily and facilitates the trade-off between computation efficiency and accuracy.
基金financial support through the UGC-BSR fellowship
文摘The non-relativistic radial Schr¨odinger equation is analytically solved using asymptotic iteration method within the framework of a general interaction potential whose special cases are the Cornell and Cornell plus harmonic potentials. The energy eigenvalues expression is derived in three dimensional space, which is further used to calculate the mass spectra of ˉcc,ˉbb,ˉbc, cˉs, bˉs and b ˉq mesons. The obtained results of this work are in good agreement with experimental and other relativistic results and also improved in comparison with other non-relativistic recent studies.
文摘Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.
基金supported by the National Natural Science Foundation of China(No.12172001)the University Natural Science Research Project of Anhui Province(No.2022AH020029)+1 种基金the Anhui Provincial Natural Science Foundation(Nos.2208085Y01 and 2008085QA23)the Housing and Urban-Rural Development Science and Technology Project of Anhui Province(No.2023-YF129),China.
文摘Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain analytical solutions describing these systems,which hinders analysis and design.In this work,we propose a self-vibrating liquid crystal elastomer(LCE)fiber-spring system exposed to spatially-constant gradient light,and determine analytical solutions for its amplitude and period.First,using a dynamic model of LCE,we obtain the equations governing the self-vibration.Then,we analyze two different motion states and elucidate the mechanism of self-vibration.Subsequently,we derive analytical solutions for the amplitude and frequency using the multi-scale method,and compare the solutions with numerical results.The analytical outcomes are shown to be consistent with the numerical calculations,while taking far less computational time.Our findings reveal the utility of the multi-scale method in describing self-vibration,which may contribute to more efficient and accurate analyses of self-vibrating systems.
基金funded by the National Natural Science Foundation of China(Grant Nos.12305003,12101246,12471237)。
文摘In this paper,we investigate the integrable fractional coupled Gerdjikov-Ivanov equation and derive its explicit form by employing the completeness relation of squared eigenfunctions.Based on the Riemann-Hilbert method,we construct the fractional N-soliton solutions.We find that as the powerεof the Riesz fractional derivative increases,the amplitudes of the fractional soliton solutions remain invariant,while their widths decrease and the absolute values of the wave velocity,group velocity,and phase velocity increase.Additionally,we examine the long-time asymptotic behavior of the fractional N-soliton solution.The results show that as t→±∞,the solution can be approximated by the sum of N fractional one-soliton solutions,with each soliton's amplitude and velocity remaining constant,whereas both position and phase shifts are observed.
文摘The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.
文摘The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.
基金supported by the National Key R&D Program of China(2021YFA1000800)the National Natural Sciences Foundation of China(12288201)supported by the National Science Foundation of China(12371223)。
文摘This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux.The global solution is shown to converge to a combination of a rarefaction wave and a viscous contact wave as time tends to infinity by employing the L^(2) energy method and a refined wave interaction analysis.This is the first result on the asymptotics toward multiwave for the damped wave equation,and this asymptotic stability result does not rely on the small assumption of neither the initial perturbations nor the wave strength.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41175058,11071205,1202106,and 11101349)the Carbon Budget and Relevant Issues of the Chinese Academy of Sciences(Grant Nos.XDA01020304,KJ2012A001,and KJ2012Z245)+1 种基金the Natural Science Foundation of the Education Department of Anhui Province,China(Grant No.KJ2011A135)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011042)
文摘A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.
文摘This paper is a continuation of part (Ⅰ), on the asymptotics behaviors of the series solutions investigated in (Ⅰ). The remainder terms of the series solutions are estimated by the maximum norm.
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
