Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate ...Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate of composites was established. Then the upper limit of strain rate, restricted by stress equilibrium and constant loading rate, was rationally estimated and confirmed by tests. Within the achievable range of 0.001/s-895/s, it was found that the strength increased first and subsequently decreased as the strain rate increased. This feature was also reflected by the turning point(579/s) of the bilinear model for strength prediction. The transition in failure mechanism, from local opening damage to completely splitting destruction, was mainly responsible for such strain rate effects. And three major failure modes were summarized under microscopic observations: fiber fracture, inter-fiber fracture, and interface delamination. Finally, by introducing a nonlinear damage variable, a simplified ZWT model was developed to characterize the dynamic mechanical response. Excellent agreement was shown between the experimental and simulated results.展开更多
A novel method for designing chalcogenide long-period fiber grating(LPFG) sensors based on the dual-peak resonance effect of the LPFG near the phase matching turning point(PMTP) is presented. Refractive index sensing ...A novel method for designing chalcogenide long-period fiber grating(LPFG) sensors based on the dual-peak resonance effect of the LPFG near the phase matching turning point(PMTP) is presented. Refractive index sensing in a high-refractive-index chalcogenide fiber is achieved with a coated thinly clad film. The dual-peak resonant characteristics near the PMTP and the refractive index sensing properties of the LPFG are analyzed first by the phase-matching condition of the LPFG. The effects of film parameters and cladding radius on the sensitivity of refractive index sensing are further discussed. The sensor is optimized by selecting the appropriate film parameters and cladding radius. Simulation results show that the ambient refractive index sensitivity of a dual-peak coated thinly clad chalcogenide LPFG at the PMTP can be 2400 nm/RIU, which is significantly higher than that of non-optimized gratings. It has great application potential in the field of chemical sensing and biosensors.展开更多
Long period fiber gratings are emerging as a potential candidate in the list of surrounding refractive index optical fiber sensors. Their sensitivity can be enhanced greatly if the grating period, fiber dimensions and...Long period fiber gratings are emerging as a potential candidate in the list of surrounding refractive index optical fiber sensors. Their sensitivity can be enhanced greatly if the grating period, fiber dimensions and surrounding refractive index are optimized in a way to operate at a point called turn around point on phase matching curves of these gratings. Turn around point LPFGs are well known for their ultrahigh sensitivity to external parameters. Potential of operating LPFG at or near turn around point has been investigated by many researchers in various applications including physical parameter sensing, adulteration detection, radiation dose, etc. Since TAP LPFGs are in investigation phase therefore a lot of rigorous & efficient work in finding techniques for optimizing their potential as sensor in chemical, biochemical, structural health monitoring is still to be carried out. A brief review of work carried out in this domain till now is presented here and key findings from literature review are highlighted.展开更多
In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theore...In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.展开更多
The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to...The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.展开更多
A two-phase trend model is presented to investigate the turning-point signals of evolution trend in long-term series of a climatic element. Based on nonlinear fitting, the revised model brings out more evident improve...A two-phase trend model is presented to investigate the turning-point signals of evolution trend in long-term series of a climatic element. Based on nonlinear fitting, the revised model brings out more evident improvement of the linear model proposed by Solow et al. (1987). Both theoretical deduction and case calculation show that our version can search the turning point and period accurately and objectively. In particular it is fit for computer exploring the turning points in long-range records from stations covering a large area, thus avoiding subjective judgement by a usual drawing method.展开更多
Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature tre...Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature trend and future climate. Detection of turning points in time series of meteorological parameters puts challenges to the researches. In this work, the temperature time series from 1941 to 2010 for Asansol observatory, West Bengal, India, has been considered to understand the nature, trends and change points in the data set using sequential version of Mann-Kendall test statistic. Literatures suggest that use of this test statistic is the most appropriate for detecting climatic abrupt changes as compared to other statistical tests in use. This method has been employed upon monthly average temperatures recorded over the said 70 years for detection of abrupt changes in the average temperature of each of the months. The approximate potential trend turning points have been calculated separately for each month (January to December). Sequential version of Mann-Kendall test statistic values for the months of July and August is significant at 95% confidence level (p 0.05). The average temperature for most of the other months has shown an increasing trend but more significant rise in July and August temperature has been recognized since 1960s.展开更多
This paper uses age-related productivity gaps to analyze the Lewis turning point in China. The age-related productivity gap implies that under same wage rate, older and less productive rural laborers working in cities...This paper uses age-related productivity gaps to analyze the Lewis turning point in China. The age-related productivity gap implies that under same wage rate, older and less productive rural laborers working in cities will earn less than the reservation wage. Thus, they may elect instead to return to the countryside. Therefore, this paper argues that while the supply of younger, high-productivity migrant workers fails demand and Lewis turning point emerges, there still exists a high volume of lower-productivity rural surplus labor.展开更多
Studies on surface wettability have received tremendous interest due to their potential applications in research and industrial processes. One of the strategies to tune surface wettability is modifying surface topogra...Studies on surface wettability have received tremendous interest due to their potential applications in research and industrial processes. One of the strategies to tune surface wettability is modifying surface topography at micro-and nanoscales. In this research, periodic micro-and nanostructures were patterned on several polymer surfaces by ultra-precision single point diamond turning to investigate the relationships between surface topographies at the micro-and nanoscales and their surface wettability. This research revealed that single-point diamond turning could be used to enhance the wettability of a variety of polymers, including polyvinyl chloride(PVC), polyethylene 1000(PE1000), polypropylene copolymer(PP) and polytetrafluoroethylene(PFTE), which cannot be processed by conventional semiconductor-based manufacturing processes. Materials exhibiting common wettability properties(θ≈ 90°) changed to exhibit "superhydrophobic" behavior(θ > 150°). Compared with the size of the structures, the aspect ratio of the void space between micro-and nanostructures has a strong impact on surface wettability.展开更多
Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning poin...Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning points and triple S bieaking turning points,one ts quadratic turning pornt path and one is quadratic pitch fork bifurcation point path.Some simple regular extended systems to corn pute double and triple S-breaking turning points are proposed.Numerical examples are also展开更多
We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,...We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,λ,μ)= 0. The method proposed could produce an extended system which does not introduce the null vectors as variables, and could therefore reduce the computational effort and storage. One numerical example is presented to demonstrate that the method is efficient.展开更多
In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introduc...In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.展开更多
The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active spac...The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.展开更多
The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutio...The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions： either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature： the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.展开更多
In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x...In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x - mu(1))(x - mu(2))(x - mu(3))f(x), f(x) not equal 0, mu(1) < mu(2) < mu(3) and lambda is a large parameter, but q(2)(x, lambda) = Sigma(i = 0)(epsilon a) g(i)(x)lambda(-i) (here g(0)(x) not equivalent to 0). By using JL function, the complete expression of the formal uniformly, valid asymptotic solutions of the equation near turning point is obtained.展开更多
This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal...This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method. By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.展开更多
Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) ...Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.展开更多
The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for th...The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.展开更多
A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for t...A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.展开更多
In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t...In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.展开更多
基金the National Science and Technology Major Project(Grant No.2017-VII-0011-0106)Natural Science Foundation of Heilongjiang Province(Grant No.ZD2019A001).
文摘Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate of composites was established. Then the upper limit of strain rate, restricted by stress equilibrium and constant loading rate, was rationally estimated and confirmed by tests. Within the achievable range of 0.001/s-895/s, it was found that the strength increased first and subsequently decreased as the strain rate increased. This feature was also reflected by the turning point(579/s) of the bilinear model for strength prediction. The transition in failure mechanism, from local opening damage to completely splitting destruction, was mainly responsible for such strain rate effects. And three major failure modes were summarized under microscopic observations: fiber fracture, inter-fiber fracture, and interface delamination. Finally, by introducing a nonlinear damage variable, a simplified ZWT model was developed to characterize the dynamic mechanical response. Excellent agreement was shown between the experimental and simulated results.
基金Project supported by the Natural Science Foundation of China (Grant Nos.62075107,61935006,62090064,and62090065)K.C.Wong Magna Fund in Ningbo University。
文摘A novel method for designing chalcogenide long-period fiber grating(LPFG) sensors based on the dual-peak resonance effect of the LPFG near the phase matching turning point(PMTP) is presented. Refractive index sensing in a high-refractive-index chalcogenide fiber is achieved with a coated thinly clad film. The dual-peak resonant characteristics near the PMTP and the refractive index sensing properties of the LPFG are analyzed first by the phase-matching condition of the LPFG. The effects of film parameters and cladding radius on the sensitivity of refractive index sensing are further discussed. The sensor is optimized by selecting the appropriate film parameters and cladding radius. Simulation results show that the ambient refractive index sensitivity of a dual-peak coated thinly clad chalcogenide LPFG at the PMTP can be 2400 nm/RIU, which is significantly higher than that of non-optimized gratings. It has great application potential in the field of chemical sensing and biosensors.
文摘Long period fiber gratings are emerging as a potential candidate in the list of surrounding refractive index optical fiber sensors. Their sensitivity can be enhanced greatly if the grating period, fiber dimensions and surrounding refractive index are optimized in a way to operate at a point called turn around point on phase matching curves of these gratings. Turn around point LPFGs are well known for their ultrahigh sensitivity to external parameters. Potential of operating LPFG at or near turn around point has been investigated by many researchers in various applications including physical parameter sensing, adulteration detection, radiation dose, etc. Since TAP LPFGs are in investigation phase therefore a lot of rigorous & efficient work in finding techniques for optimizing their potential as sensor in chemical, biochemical, structural health monitoring is still to be carried out. A brief review of work carried out in this domain till now is presented here and key findings from literature review are highlighted.
文摘In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574039）, the Henan Innovation for University Prominent Research Talents （Grant No 2006KYCX002） and the Natural Science Foundation of Henan Province （Grant Nos 2006140008 and 2007140015）.
文摘The density functional theory （B3LYP, B3P86） and the quadratic configuration-interaction method including single and double substitutions （QCISD（T）, QCISD） presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance Re, the dissociation energy De and the harmonic frequency We for the XIEg＋ state of sodium dimer in a number of basis sets. The conclusion is gained that the best Re, De and We results can be attained at the QCISD/6-311G（3df,3pd） level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0 nm and is fitted to the analytic Murrell-Sorbie function. The spectroscopic parameters De, DO, Re, ωe, ωe Xe, αe and Be are calculated to be 0.7219 eV, 0.7135 eV, 0.31813 nm, 151.63 cm^-1, 0.7288 cm^-1, 0.000729 cm^-1 and 0.1449 cm^-1, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G（3df,3pd） level of theory, a total of 63 vibrational states is found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants （Dr Hv, Lv, Mv, Nv and Ov） are reported for the first time for the first 31 vibrational states when J = 0.
基金This wirk is supported jointly National Natural Science Foundation of China and China Meteoroloical Administration 8th-Five-year Major Project Foundation.
文摘A two-phase trend model is presented to investigate the turning-point signals of evolution trend in long-term series of a climatic element. Based on nonlinear fitting, the revised model brings out more evident improvement of the linear model proposed by Solow et al. (1987). Both theoretical deduction and case calculation show that our version can search the turning point and period accurately and objectively. In particular it is fit for computer exploring the turning points in long-range records from stations covering a large area, thus avoiding subjective judgement by a usual drawing method.
文摘Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature trend and future climate. Detection of turning points in time series of meteorological parameters puts challenges to the researches. In this work, the temperature time series from 1941 to 2010 for Asansol observatory, West Bengal, India, has been considered to understand the nature, trends and change points in the data set using sequential version of Mann-Kendall test statistic. Literatures suggest that use of this test statistic is the most appropriate for detecting climatic abrupt changes as compared to other statistical tests in use. This method has been employed upon monthly average temperatures recorded over the said 70 years for detection of abrupt changes in the average temperature of each of the months. The approximate potential trend turning points have been calculated separately for each month (January to December). Sequential version of Mann-Kendall test statistic values for the months of July and August is significant at 95% confidence level (p 0.05). The average temperature for most of the other months has shown an increasing trend but more significant rise in July and August temperature has been recognized since 1960s.
文摘This paper uses age-related productivity gaps to analyze the Lewis turning point in China. The age-related productivity gap implies that under same wage rate, older and less productive rural laborers working in cities will earn less than the reservation wage. Thus, they may elect instead to return to the countryside. Therefore, this paper argues that while the supply of younger, high-productivity migrant workers fails demand and Lewis turning point emerges, there still exists a high volume of lower-productivity rural surplus labor.
基金financial support from Heriot-Watt University (Edinburgh)the Engineering and Physical Sciences Research Council (EP/K018345/1) for this study
文摘Studies on surface wettability have received tremendous interest due to their potential applications in research and industrial processes. One of the strategies to tune surface wettability is modifying surface topography at micro-and nanoscales. In this research, periodic micro-and nanostructures were patterned on several polymer surfaces by ultra-precision single point diamond turning to investigate the relationships between surface topographies at the micro-and nanoscales and their surface wettability. This research revealed that single-point diamond turning could be used to enhance the wettability of a variety of polymers, including polyvinyl chloride(PVC), polyethylene 1000(PE1000), polypropylene copolymer(PP) and polytetrafluoroethylene(PFTE), which cannot be processed by conventional semiconductor-based manufacturing processes. Materials exhibiting common wettability properties(θ≈ 90°) changed to exhibit "superhydrophobic" behavior(θ > 150°). Compared with the size of the structures, the aspect ratio of the void space between micro-and nanostructures has a strong impact on surface wettability.
基金This work is supported by NSFC amd Slate Major Key Project for Baslc Research
文摘Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning points and triple S bieaking turning points,one ts quadratic turning pornt path and one is quadratic pitch fork bifurcation point path.Some simple regular extended systems to corn pute double and triple S-breaking turning points are proposed.Numerical examples are also
基金This work was supported by Natural Science Foundation of Guangdong
文摘We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,λ,μ)= 0. The method proposed could produce an extended system which does not introduce the null vectors as variables, and could therefore reduce the computational effort and storage. One numerical example is presented to demonstrate that the method is efficient.
文摘In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574039） and Henan Innovation for University Prominent Research Talents of China （Grant No 2006KYCX002）.Acknowledgment We heartily thank Professor Zhu Z H, of Sichuan University, for helpful discussion about the reasonable dissociation limit of ^7Li2（2^1Пu） during the planning stages of these calculations.
文摘The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.
基金Project supported by the Shanghai Leading Academic Discipline Project(No.Y0103)the Natural Science Foundation of Zhejiang Province of China(No.100039)
文摘The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions： either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature： the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.
文摘In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x - mu(1))(x - mu(2))(x - mu(3))f(x), f(x) not equal 0, mu(1) < mu(2) < mu(3) and lambda is a large parameter, but q(2)(x, lambda) = Sigma(i = 0)(epsilon a) g(i)(x)lambda(-i) (here g(0)(x) not equivalent to 0). By using JL function, the complete expression of the formal uniformly, valid asymptotic solutions of the equation near turning point is obtained.
文摘This paper studies a second order linear ordinary differential equation with n-turning points d2y/dx2+[λ2q1(x)+q2(x)]y=0 Where q1(x) = (X-μ1) (x-μ2) ... (x-μn) f(x), F(x)≠0, and λ is a large parameter The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method. By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.
文摘Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.
文摘The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.
基金Project supported by the National Natural Science Foundation of China (No. 40876010)the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+3 种基金the Research and Development Special Fund for Public Welfare Industry (meteorol-ogy) (No. GYHY200806010)the LASG State Key Laboratory Special Fundthe Foundation of E-Institutes of Shanghai Municipal Education Commission (No. E03004)the Natural Science Foundation of Zhejiang Province (No. Y6090164)
文摘A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.
文摘In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.
