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
In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomial...In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.展开更多
Lifting-line model is developed for a propeller of large aspect ratio inblade-attached noninertial system. In the analysis of the method of matched asymptoticexpansions, a fictitious velocity potential is introduced. ...Lifting-line model is developed for a propeller of large aspect ratio inblade-attached noninertial system. In the analysis of the method of matched asymptoticexpansions, a fictitious velocity potential is introduced. Control equation, boundarycondition and Bernoulli equation are derived in blade- attached system. The analysis ofthe matched asymptotic expansions shows that if the advance ratio of propeller is notvery small, lifting-line theory is still valid in blade-attached noninertial system for propeller.展开更多
By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series meth...By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.展开更多
The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag mod...The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag model and homogenization technique to compute the bending wavenumbers via a 6th-order equation.The General Laminate Model(GLM)employs Mindlin’s displacement field to establish displacement-constraint relationships and resolves a quadratic Eigenvalue Problem(EVP)of the dispersion relation.The Wave Finite Element(WFE)scheme formulates the Nonlinear Eigenvalue Problem(NEP)for waves in varying directions and tracks complex wavenumbers using Weighted Wave Assurance Criteria(WWAC).Two approaches are introduced to estimate the Damping Loss Factor(DLF)of HDS,with the average DLF calculated by the modal density at various angles where non-homogeneity is present.Evaluation of robustness and accuracy is made by comparing the wavenumbers and DLF obtained from AHM and GLM with WFE.WFE is finally extended to a sandwich metastructure with a non-homogeneous core,and the Power Input Method(PIM)with Finite Element Method(FEM)data is employed to assess the average DLF,demonstrating an enhanced DLF compared to layered configurations with the same material portion,indicating increased energy dissipation due to the bending-shear coupling effects.展开更多
The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is consider...The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.展开更多
Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solutio...Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.展开更多
This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method...This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.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
A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-la...A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.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
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
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
Based on a constitutive law which includes the shear components oftransformation plasticity. the asymptotic solutions to near-tip fields of plane-strainmode I steadity propagating cracks in rransformed ceramics are o...Based on a constitutive law which includes the shear components oftransformation plasticity. the asymptotic solutions to near-tip fields of plane-strainmode I steadity propagating cracks in rransformed ceramics are obtained for the caseof linear isotropic hardening. The Stress singularity. the distributions of stresses andvelocities at the crack tip are determmed for various material parameters. The factorsinfluencing the near-tip fields are discussed in detail.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
The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar a...The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S（x） = V（x）（β - 1）. In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.展开更多
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
In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term μ k successively. According this metnod the leading term μ 0 will be identified by an elliptic bou...In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term μ k successively. According this metnod the leading term μ 0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution u KT (x,ζ):=U(x)+Π 1Uζ+Π 2Uζ2, then we give the estimation.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 in part by the National Natural Science Foundation of China (10471154 and 10871212)
文摘In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.
文摘Lifting-line model is developed for a propeller of large aspect ratio inblade-attached noninertial system. In the analysis of the method of matched asymptoticexpansions, a fictitious velocity potential is introduced. Control equation, boundarycondition and Bernoulli equation are derived in blade- attached system. The analysis ofthe matched asymptotic expansions shows that if the advance ratio of propeller is notvery small, lifting-line theory is still valid in blade-attached noninertial system for propeller.
文摘By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.
基金supported by the Natural Sciences and Engineering Research Council of Canada-Discovery Grant(individual)Program(No.NSEC-DG#355433-2009)funded by the LabEx CeLyA(Centre Lyonnais d’Acoustique,No.ANR-10-LABX-0060)of Universite?de Lyon。
文摘The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag model and homogenization technique to compute the bending wavenumbers via a 6th-order equation.The General Laminate Model(GLM)employs Mindlin’s displacement field to establish displacement-constraint relationships and resolves a quadratic Eigenvalue Problem(EVP)of the dispersion relation.The Wave Finite Element(WFE)scheme formulates the Nonlinear Eigenvalue Problem(NEP)for waves in varying directions and tracks complex wavenumbers using Weighted Wave Assurance Criteria(WWAC).Two approaches are introduced to estimate the Damping Loss Factor(DLF)of HDS,with the average DLF calculated by the modal density at various angles where non-homogeneity is present.Evaluation of robustness and accuracy is made by comparing the wavenumbers and DLF obtained from AHM and GLM with WFE.WFE is finally extended to a sandwich metastructure with a non-homogeneous core,and the Power Input Method(PIM)with Finite Element Method(FEM)data is employed to assess the average DLF,demonstrating an enhanced DLF compared to layered configurations with the same material portion,indicating increased energy dissipation due to the bending-shear coupling effects.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 40676016 and 10471039）, the National Key Basics Research Special Foundation of China （Grant No 2004CB418304）, the Key Basic Research Foundation of Chinese Academy of Sciences （Grant No KZCX3-SW-221） and in part by E-Institutes of Shanghai Municipal Education Commission （Grant No NE03004）.
文摘The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.
基金supported by the National Natural Science Foundation of China (Grants 11332004, 11572071)the Program for Changjiang Scholars and Innovative Research Team in Dalian University of Technology (PCSIRT)+2 种基金111 Project (Grant B14013)the CATIC Industrial Production Projects (Grant CXY2013DLLG32)the Fundamental Research Funds for the Central Universities (Grant DUT15ZD101)
文摘Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.
基金financially supported by the funding of an independent research project from the Chinese State Key Laboratory of Ocean Engineering(Grant No.GKZD010038)
文摘This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11202106 and 61302188)the Specialized Research Fund for the Doctoral Program of Higher Education,China(Grant No.20123228120005)+2 种基金the Fund from the Jiangsu Sensor Network and Modern Meteorological Equipment Preponderant Discipline Platform,Chinathe Natural Science Fundation from the Universities of Jiangsu Province,China(Grant No.13KJB170016)the Advance Research Foundation in NUIST of China(Grant Nos.20110371 and 20110385)
文摘A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.
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.
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.
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Based on a constitutive law which includes the shear components oftransformation plasticity. the asymptotic solutions to near-tip fields of plane-strainmode I steadity propagating cracks in rransformed ceramics are obtained for the caseof linear isotropic hardening. The Stress singularity. the distributions of stresses andvelocities at the crack tip are determmed for various material parameters. The factorsinfluencing the near-tip fields are discussed in detail.
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.
基金supported by the Research Fund of Gaziantep University and the Scientific and Technological Research Council of Turkey (TUBITAK).
文摘The bound-state solution of the position dependent mass Klein-Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S（x） = V（x）（β - 1）. In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.
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.
文摘In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term μ k successively. According this metnod the leading term μ 0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution u KT (x,ζ):=U(x)+Π 1Uζ+Π 2Uζ2, then we give the estimation.
