A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether me...A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.展开更多
Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principl...Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400km and choose the measurement accuracies of 10-13/s2 –10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.展开更多
By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three hig...By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.展开更多
The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with de...The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.展开更多
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.展开更多
Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is propos...Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is proposed. The theoretical formula for an axial magnetic field generated by a single shielded coil is obtained and used to construct specific coils. The structural parameters of these coils are determined by fitting the theoretical formula with their specific requirements. The feasibility of this method is proved by realizing four concrete kinds of coils: uniform magnetic field generating coils, gradient magnetic field generating coils, asymmetrical uniform magnetic field generating coils, and parabolic magnetic field generating coils. The correctness of these theoretical results is demonstrated by both the finite element simulations and the relevant experimental results. Furthermore, the application of this method is of great significance for developing the quantum physics and quantum devices in future.展开更多
A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c...A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.展开更多
In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our resul...In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.展开更多
An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation o...An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.展开更多
The index system, code system, and weights of indexes are established to assess the effects of green construction. The index system consists of index level, factor level and sub-factor level. The analytic hierarchy pr...The index system, code system, and weights of indexes are established to assess the effects of green construction. The index system consists of index level, factor level and sub-factor level. The analytic hierarchy process is used to determine the weights of indexes, and the consistency test indicate that the weight assignment is reasonable. Using fuzzy synthetic judgment method, the assessment model is built, which includes factor set, weight set and conclusion set. An example is given to demonstrate the assessment procedures.展开更多
A anified plasma sheath model and its potential equation are proposed. Any higher-ordor-approximation analytical solutions for the unified plasma sheath potential equa tiop are derived by double decomposition method.
Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact as...Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.展开更多
The potential energy curves（PECs） of the first electronic excited state of S2（a^1△g） are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a ...The potential energy curves（PECs） of the first electronic excited state of S2（a^1△g） are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning： aug-cc-p VX Z（X = T, Q, 5, 6）. In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V（Q, 5）Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function（APEF） using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV（Q, 5）Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.展开更多
This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV）...This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.展开更多
A full-dimensional analytical potential energy surface （APES） for the F ＋ CH4 →HF ＋ CH3 reaction is developed based on 7127 ab initio energy points at the unrestricted coupled-cluster with single, double, and per...A full-dimensional analytical potential energy surface （APES） for the F ＋ CH4 →HF ＋ CH3 reaction is developed based on 7127 ab initio energy points at the unrestricted coupled-cluster with single, double, and perturbative triple excitations. The correlation-consistent polarized triple-split valence basis set is used. The APES is represented with a many-body expansion containing 239 parameters determined by the least square fitting method. The two-body terms of the APES are fitted by potential energy curves with multi-reference configuration interaction, which can describe the diatomic molecules （CH, H2, HF, and CF） accurately. It is found that the APES can reproduce the geometry and vibrational frequencies of the saddle point better than those available in the literature. The rate constants based on the present APES support the experimental results of Moore et al. [Int. J. Chem. Kin. 26, 813 （1994）]. The analytical first-order derivation of energy is also provided, making the present APES convenient and efficient for investigating the title reaction with quasiclassical trajectory calculations.展开更多
Plasma density and temperature can be diagnosed by x-ray line emission measurement with crystal,and bent crystals such as von Hamos and Hall structures are proposed to improve the diffraction brightness.In this study,...Plasma density and temperature can be diagnosed by x-ray line emission measurement with crystal,and bent crystals such as von Hamos and Hall structures are proposed to improve the diffraction brightness.In this study,a straightforward solution for the focusing schemes of flat and bent crystals is provided.Simulations with XOP code are performed to validate the analytical model,and good agreements are achieved.The von Hamos or multi-cone crystal can lead to several hundred times intensity enhancements for a 200μm plasma source.This model benefits the applications of the focusing bent crystals.展开更多
A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,accelerati...A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.展开更多
Sulfur contents olefins, aromatics, octane number and cetane number are very important indicators of clean fuel. The analytical methods of these indicators proposed by Research Institute of Petroleum Processing (RIPP)...Sulfur contents olefins, aromatics, octane number and cetane number are very important indicators of clean fuel. The analytical methods of these indicators proposed by Research Institute of Petroleum Processing (RIPP) were introduced in this article. These methods possess the advantages of fast, convenient and precise, and have been used in R&D work and production process control as well.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10272021） and the Doctorate Foundation of the State Education Ministry of China （Grant No 20040007022）.
文摘A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.
基金Project supported by the Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences for Distinguished Young Scholar (Grant No. KZCX2-EW-QN114)the National Natural Science Foundation of China for Young Scholar (Grant Nos. 41004006, 41131067, 11173049, and 41202094)+5 种基金the Merit-based Scientific Research Foundation of the State Ministry of Human Resources and Social Security of China for Returned Overseas Chinese Scholars(Grant No. 2011)the Open Research Fund Program of the Key Laboratory of Computational Geodynamics of Chinese Academy of Sciences (Grant No. 2011-04)the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, China (Grant No. 11-01-02)the Open Research Fund Program of the Key Laboratory of Geo-Informatics of National Administration of Surveying, Mapping and Geoinformation of China(Grant No. 201322)the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Grant No. PLN1113)the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing (Grant No. PRP/open-1206)
文摘Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400km and choose the measurement accuracies of 10-13/s2 –10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61078057 and 11204227)the Scientific Research Program of Education Department of Shaanxi Province, China (Grant No. 12JK0958)
文摘By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.
文摘The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.
基金Supported by the National Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61701515 and 61671458)the Postdoctoral Science Foundation,China(Grant No.2017M613367)+1 种基金the Natural Science Foundation of Hunan Province,China(Grant No.2018JJ3608)the Research Project of National University of Defense Technology,China(Grant No.ZK170204)
文摘Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is proposed. The theoretical formula for an axial magnetic field generated by a single shielded coil is obtained and used to construct specific coils. The structural parameters of these coils are determined by fitting the theoretical formula with their specific requirements. The feasibility of this method is proved by realizing four concrete kinds of coils: uniform magnetic field generating coils, gradient magnetic field generating coils, asymmetrical uniform magnetic field generating coils, and parabolic magnetic field generating coils. The correctness of these theoretical results is demonstrated by both the finite element simulations and the relevant experimental results. Furthermore, the application of this method is of great significance for developing the quantum physics and quantum devices in future.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Shanghai Rising-Star Program,China (Grant No. 08QA14030)+1 种基金the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX092021)the Foundation of the Science and Technology Commission of Shanghai Municipality,China (Grant No. 08JC14097)
文摘A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.
基金Project supported by Science Foundation of Nantong University (Grant Nos. 03080122 and 09ZY001)
文摘In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11604009,and 11704025)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe financial support of the Future and Emerging Technologies(FET)programme within the Seventh Framework Programme for Research of the European Commission,under FET-Open Grant No.618083(CNTQC)
文摘An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.
基金The Doctoral Program of Higher Educa-tion Institution of China (No.20050487017)
文摘The index system, code system, and weights of indexes are established to assess the effects of green construction. The index system consists of index level, factor level and sub-factor level. The analytic hierarchy process is used to determine the weights of indexes, and the consistency test indicate that the weight assignment is reasonable. Using fuzzy synthetic judgment method, the assessment model is built, which includes factor set, weight set and conclusion set. An example is given to demonstrate the assessment procedures.
文摘A anified plasma sheath model and its potential equation are proposed. Any higher-ordor-approximation analytical solutions for the unified plasma sheath potential equa tiop are derived by double decomposition method.
文摘Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304185 and 11074151)
文摘The potential energy curves（PECs） of the first electronic excited state of S2（a^1△g） are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning： aug-cc-p VX Z（X = T, Q, 5, 6）. In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V（Q, 5）Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function（APEF） using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV（Q, 5）Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries （KdV） equation and a coupled modified Korteweg-de Vries （mKdV） equation. This method provides a sequence Of functions which converges to the exact solution of the problem and is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11174117 and 10974078)
文摘A full-dimensional analytical potential energy surface （APES） for the F ＋ CH4 →HF ＋ CH3 reaction is developed based on 7127 ab initio energy points at the unrestricted coupled-cluster with single, double, and perturbative triple excitations. The correlation-consistent polarized triple-split valence basis set is used. The APES is represented with a many-body expansion containing 239 parameters determined by the least square fitting method. The two-body terms of the APES are fitted by potential energy curves with multi-reference configuration interaction, which can describe the diatomic molecules （CH, H2, HF, and CF） accurately. It is found that the APES can reproduce the geometry and vibrational frequencies of the saddle point better than those available in the literature. The rate constants based on the present APES support the experimental results of Moore et al. [Int. J. Chem. Kin. 26, 813 （1994）]. The analytical first-order derivation of energy is also provided, making the present APES convenient and efficient for investigating the title reaction with quasiclassical trajectory calculations.
基金Project supported by the National Natural Science Fundation of China(Grant Nos.11775203 and 12075219)the China Academy of Engineering Physics(CAEP)Foundation(Grant No.CX20210019).
文摘Plasma density and temperature can be diagnosed by x-ray line emission measurement with crystal,and bent crystals such as von Hamos and Hall structures are proposed to improve the diffraction brightness.In this study,a straightforward solution for the focusing schemes of flat and bent crystals is provided.Simulations with XOP code are performed to validate the analytical model,and good agreements are achieved.The von Hamos or multi-cone crystal can lead to several hundred times intensity enhancements for a 200μm plasma source.This model benefits the applications of the focusing bent crystals.
基金The authors are thankful to Shri J.Ramachandran,Chancellor,Col.Dr.G.Thiruvasagam,Vice-Chancellor,Academy of Maritime Education and Training(AMET),Deemed to be University,Chennai,for their support.
文摘A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.
文摘Sulfur contents olefins, aromatics, octane number and cetane number are very important indicators of clean fuel. The analytical methods of these indicators proposed by Research Institute of Petroleum Processing (RIPP) were introduced in this article. These methods possess the advantages of fast, convenient and precise, and have been used in R&D work and production process control as well.
