Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CI...Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CIs)for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework.Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures.The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix,achieving near-nominal coverage probabilities even in small samples or highly dependent settings.Through simulation studies,we show that,although traditional methods may suffice with moderate dependence and large samples,the proposed CIs offer notable benefits when dependence is strong or data are sparse.We further illustrate our construction with a synthetic example illustrating how penalized estimation can mitigate the issue of a degenerate Hessian matrix under high dependence and limited observations,so enabling uncertainty quantification despite deviations from nominal assumptions.Overall,our results fill a gap in reliability modeling for systems prone to correlated failures,and contribute to more robust inference in engineering,industrial,and biomedical applications.展开更多
Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instr...Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.展开更多
In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for c...In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
The ti me dependent flow of upper-convected Maxwell fluid in a horizontal circular pip e is studied by spectral method. The time dependent problem is mathematically re duced to a partial differential equation of seco...The ti me dependent flow of upper-convected Maxwell fluid in a horizontal circular pip e is studied by spectral method. The time dependent problem is mathematically re duced to a partial differential equation of second order. By using spectral meth od the partial differential equation can be reduced to a system of ordinary diff erential equations for different terms of Chebyshev polynomials approximations. The ordinary differential equations are solved by Laplace transform and the eige nvalue method that leads to an analytical form of the solutions.展开更多
In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-differenc...In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-difference and finite element methods to approximate spatial derivatives, this new technique does not require a mesh in the problem domain, and a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions. Accuracy of the method is assessed in terms of the error norms L2, L∞ and the three invariants C1, C2, C3. Numerical experiments are performed to demonstrate the accuracy and easy implementation of this method for the three classes of time-dependent nonlinear coupled partial differential equations.展开更多
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio...A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.展开更多
Dear Editor,This letter deals with the controller synthesis problem of networked Takagi-Sugeno(T-S)fuzzy systems.Due to the introduction of network communications,the same premise is no longer shared by fuzzy plants a...Dear Editor,This letter deals with the controller synthesis problem of networked Takagi-Sugeno(T-S)fuzzy systems.Due to the introduction of network communications,the same premise is no longer shared by fuzzy plants and fuzzy controllers.This makes the classic parallel distribution compensation(PDC)control infeasible.To overcome this situation,a novel method for reconstructing the membership functions'grades is proposed,which synchronizes the time scales.Then,the membership function dependent method is adopted to introduce asynchronous errors and detailed membership function information.For the event-triggered control strategy,a series of robust H∞stable conditions in LMI form are derived.Finally,a simulation of a practical system is used to demonstrate the method proposed in this letter can reduce conservatism.展开更多
In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates ...In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates axe taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solu- tions of the numerical simulation axe in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.展开更多
The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength ...The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength and intensity of laser pulse, the population of each state changing with time is obtained. The photo-absorption spectra and kinetic- energy distribution of the dissociation fragments, which exhibit vibration-level structure and dispersion of the wave packet, respectively, are also obtained. The results show that by increasing the laser intensity, one can find not only the band center shift of the photo-absorption spectrum, but also the change of the fragment energy. The appearance of the diffusive band in the photo-absorption spectrum and the multiple peaks in the kinetic-energy spectrum can be attributed to the effects of the predissoeiation limit and the external field.展开更多
The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we success...The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.展开更多
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH). However, in general, most of the practical c...Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific timedependent periodic harmonic oscillator, the Berry phase is obtained exactly.展开更多
A numerical scheme is developed to extend the scope of the spectral method without solving the covariant and contravariant forms of the Navier-Stokes equations in the curvilinear coordinates. The primitive variables a...A numerical scheme is developed to extend the scope of the spectral method without solving the covariant and contravariant forms of the Navier-Stokes equations in the curvilinear coordinates. The primitive variables are represented by the Fourier series and the Chebyshev polynomials in the computational space. The time advancement is accomplished by a high-order time-splitting method, and a corresponding high-order pressure condition at the wall is introduced to reduce the splitting error. Compared with the previous pseudo-spectral scheme, in which the Navier-Stokes equations are solved in the covariant and contravariant forms, the present scheme reduces the computational cost and, at the same time, keeps the spectral accuracy. The scheme is tested in the simulations of the turbulent flow in a channel with a static streamwise wavy wall and the turbulent flow over a flexible wall undergoing the streamwise traveling wave motion. The turbulent flow over an oscillating dimple is studied with the present numerical scheme, and the periodic generation of the vortical structures is analyzed.展开更多
On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion tha...On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.展开更多
This paper reports that the （2＋1） resonance enhanced multi-photon ionization spectra of SH radical in external fields are simulated using the split-operator scheme of time-dependent wave-packet method. Two ionic st...This paper reports that the （2＋1） resonance enhanced multi-photon ionization spectra of SH radical in external fields are simulated using the split-operator scheme of time-dependent wave-packet method. Two ionic states, i.e. a1△ and b1∑＋, are involved in the simulation. It gives the simulated photoelectron spectra, the population in each electronic state, as well as the projection of the wave-packet in each electronic state on different vibrational states. These results show that the so-called four-state model can represent the experimental results well.展开更多
Shear-box test with strain measurement was used to study time-dependent stress and strain of in-plane shear(Mode Ⅱ) fracture process of rock and to reveal the mechanism of Mode Ⅱ fracture.Numerical results show that...Shear-box test with strain measurement was used to study time-dependent stress and strain of in-plane shear(Mode Ⅱ) fracture process of rock and to reveal the mechanism of Mode Ⅱ fracture.Numerical results show that the maximum shear stress τmax at the crack tip is much larger than the maximum tensile stress σ1 and the ratio of τmax/σ1 is about 5,which favors Mode Ⅱ fracture of rock.Test results indicate that the strain-time curve comprises three stages:the linear deformation stage,the micro-cracking stage and the macroscopic crack propagation.The strain in the direction of the original notch plane is negative,due to restraining effect of compressive loading applied to the original notch plane.Both σ1 and τmax are increased as the load increases,but the slope of τmax is larger than that of σ1 and the value of τmax is always larger than that of σ1.Therefore,τmax reaches its limited value at peak load before σ1 and results in Mode Ⅱ fracture of rock.Shear-box(i.e.compression-shear) test becomes a potential standard method for achieving the true Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock.展开更多
On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method o...On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.展开更多
We use the local Fourier analysis to determine the properties of the multigrid method when used in modeling the skin penetration of a drug. The analyses of these properties can be very in designing an efficient struct...We use the local Fourier analysis to determine the properties of the multigrid method when used in modeling the skin penetration of a drug. The analyses of these properties can be very in designing an efficient structure of the multigrid method and in comparing the element and finite difference discretization techniques. After the theoretical results obtained, we also present some numerical results for a problem for which the solution is known.展开更多
（-）-（3R, 4S）-3-Acetoxy-4-phenylazetidin-2-one （（-）-1） was the key intermediate for preparing optical C-13 side-chain moiety in partial synthesis of docetaxel and paclitaxel. It can be successfully prepared via...（-）-（3R, 4S）-3-Acetoxy-4-phenylazetidin-2-one （（-）-1） was the key intermediate for preparing optical C-13 side-chain moiety in partial synthesis of docetaxel and paclitaxel. It can be successfully prepared via enantioselective hydrolysis of racemic esters （（-4-）-1） catalyzed by bacterial lipases, but the current reaction evaluation method is tedious and inconvenient. Electronic circular dichroism （ECD） has been widely applied in the stereochemical study of chiral compounds. In this paper, a rapid ECD spectroscopic method has been proposed and established to detect the transformation directly. The absolute configurations of lipase-catalyzed hydrolysis products have also been confirmed by quantum-chemical calculation using time-dependent density functional theory （TDDFT） methodology.展开更多
Due to the size effects of rockfill materials, the settlement difference between numerical simulation and in situ monitoring of rockfill dams is a topic of general concern.The constitutive model parameters obtained fr...Due to the size effects of rockfill materials, the settlement difference between numerical simulation and in situ monitoring of rockfill dams is a topic of general concern.The constitutive model parameters obtained from laboratory triaxial tests often underestimate the deformation of high rockfill dams.Therefore, constitutive model parameters obtained by back analysis were used to calculate and predict the long-term deformation of rockfill dams.Instead of using artificial neural networks (ANNs), the response surface method (RSM) was employed to replace the finite element simulation used in the optimization iteration.Only 27 training samples were required for RSM, improving computational efficiency compared with ANN, which required 300 training samples.RSM can be used to describe the relationship between the constitutive model parameters and dam settlements.The inversion results of the Shuibuya concrete face rockfill dam (CFRD) show that the calculated settlements agree with the measured data, indicating the accuracy and efficiency of RSM.展开更多
基金supported by the Colombian government through COLCIENCIA scholarships,National Doctoral Program,Call 727 of 2015C.Castro gratefully acknowledges partial financial support from the Centro de Matematica da Universidade do Minho(CMAT/UM),through UID/00013V.Leiva acknowledges funding from the Agencia Nacional de Investigacion y Desarrollo(ANID)of the Chilean Ministry of Science,Technology,Knowledge and Innovation,through FONDECYT project grant 1200525.
文摘Most reliability studies assume large samples or independence among components,but these assump-tions often fail in practice,leading to imprecise inference.We address this issue by constructing confidence intervals(CIs)for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework.Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures.The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix,achieving near-nominal coverage probabilities even in small samples or highly dependent settings.Through simulation studies,we show that,although traditional methods may suffice with moderate dependence and large samples,the proposed CIs offer notable benefits when dependence is strong or data are sparse.We further illustrate our construction with a synthetic example illustrating how penalized estimation can mitigate the issue of a degenerate Hessian matrix under high dependence and limited observations,so enabling uncertainty quantification despite deviations from nominal assumptions.Overall,our results fill a gap in reliability modeling for systems prone to correlated failures,and contribute to more robust inference in engineering,industrial,and biomedical applications.
基金supported by the Center for Advanced Systems Understanding(CASUS),financed by Germany’s Federal Ministry of Education and Research(BMBF)and the Saxon State Government out of the State Budget approved by the Saxon State Parliamentfunding from the European Research Council(ERC)under the European Union’s Horizon 2022 research and innovation programme(Grant Agreement No.101076233,“PREXTREME”)funding from the European Union’s Just Transition Fund(JTF)within the project Röntgenlaser-Optimierung der Laserfusion(ROLF),Contract No.5086999001,co-financed by the Saxon State Government out of the State Budget approved by the Saxon State Parliament.
文摘Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.
基金Project supported by National Natural Science Foundation of China and China State Key project for Basic Researchcs.
文摘In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金SupportedbytheNationalNaturalScienceFoundation( No .19672 0 63)andbythekeyprojectoftheStateNationalitiesAffairsCommissionofChina(No .990 5 ) .
文摘The ti me dependent flow of upper-convected Maxwell fluid in a horizontal circular pip e is studied by spectral method. The time dependent problem is mathematically re duced to a partial differential equation of second order. By using spectral meth od the partial differential equation can be reduced to a system of ordinary diff erential equations for different terms of Chebyshev polynomials approximations. The ordinary differential equations are solved by Laplace transform and the eige nvalue method that leads to an analytical form of the solutions.
文摘In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-difference and finite element methods to approximate spatial derivatives, this new technique does not require a mesh in the problem domain, and a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions. Accuracy of the method is assessed in terms of the error norms L2, L∞ and the three invariants C1, C2, C3. Numerical experiments are performed to demonstrate the accuracy and easy implementation of this method for the three classes of time-dependent nonlinear coupled partial differential equations.
基金supported by the National Natural Science Foundation of China(No.10771150)the National Basic Research Program of China(No.2005CB321701)+1 种基金the Program for New Century Excellent Talents in University(No.NCET-07-0584)the Natural Science Foundation of Sichuan Province(No.07ZB087)
文摘A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.
基金supported by the National Natural Science Foundation of China(62173218,61833011)International International Cooperation Project of Shanghai Science and Technology Commission(21190780300).
文摘Dear Editor,This letter deals with the controller synthesis problem of networked Takagi-Sugeno(T-S)fuzzy systems.Due to the introduction of network communications,the same premise is no longer shared by fuzzy plants and fuzzy controllers.This makes the classic parallel distribution compensation(PDC)control infeasible.To overcome this situation,a novel method for reconstructing the membership functions'grades is proposed,which synchronizes the time scales.Then,the membership function dependent method is adopted to introduce asynchronous errors and detailed membership function information.For the event-triggered control strategy,a series of robust H∞stable conditions in LMI form are derived.Finally,a simulation of a practical system is used to demonstrate the method proposed in this letter can reduce conservatism.
基金supported by the National Natural Science Foundation of China (No. 10972162)
文摘In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates axe taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solu- tions of the numerical simulation axe in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.
基金Project supported by the National Natural Science Foundation of China(Grant No.11074151)the Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.20123704110002)
文摘The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength and intensity of laser pulse, the population of each state changing with time is obtained. The photo-absorption spectra and kinetic- energy distribution of the dissociation fragments, which exhibit vibration-level structure and dispersion of the wave packet, respectively, are also obtained. The results show that by increasing the laser intensity, one can find not only the band center shift of the photo-absorption spectrum, but also the change of the fragment energy. The appearance of the diffusive band in the photo-absorption spectrum and the multiple peaks in the kinetic-energy spectrum can be attributed to the effects of the predissoeiation limit and the external field.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 1057508 and 10302018）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y605056）.
文摘The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.
基金supported by the National Natural Science Foundation of China(Grant No.11347171)the Natural Science Foundation of Hebei Province of China(Grant No.A2012108003)the Key Project of Educational Commission of Hebei Province of China(Grant No.ZD2014052)
文摘Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific timedependent periodic harmonic oscillator, the Berry phase is obtained exactly.
基金supported by the National Natural Science Foundation of China (No. 10772098)
文摘A numerical scheme is developed to extend the scope of the spectral method without solving the covariant and contravariant forms of the Navier-Stokes equations in the curvilinear coordinates. The primitive variables are represented by the Fourier series and the Chebyshev polynomials in the computational space. The time advancement is accomplished by a high-order time-splitting method, and a corresponding high-order pressure condition at the wall is introduced to reduce the splitting error. Compared with the previous pseudo-spectral scheme, in which the Navier-Stokes equations are solved in the covariant and contravariant forms, the present scheme reduces the computational cost and, at the same time, keeps the spectral accuracy. The scheme is tested in the simulations of the turbulent flow in a channel with a static streamwise wavy wall and the turbulent flow over a flexible wall undergoing the streamwise traveling wave motion. The turbulent flow over an oscillating dimple is studied with the present numerical scheme, and the periodic generation of the vortical structures is analyzed.
基金supported by the Meteorological Special Project of China(GYHY200806005)the National Natural Sciences Foundation of China(40805028,40675039,40575036)the Key Technologies R&D Program of China(2009BAC51B04)
文摘On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574083)the Natural Science Foundation of Shandong Province of China (Grant No Y2006A23)Partial financial support from the National Basic Research Program of China (Grant No 2006CB806000)
文摘This paper reports that the （2＋1） resonance enhanced multi-photon ionization spectra of SH radical in external fields are simulated using the split-operator scheme of time-dependent wave-packet method. Two ionic states, i.e. a1△ and b1∑＋, are involved in the simulation. It gives the simulated photoelectron spectra, the population in each electronic state, as well as the projection of the wave-packet in each electronic state on different vibrational states. These results show that the so-called four-state model can represent the experimental results well.
基金Project(50374073) supported by the National Natural Science Foundation of ChinaProject(1343-77239) supported by the GraduaEducation Innovation Project of Central South University,China
文摘Shear-box test with strain measurement was used to study time-dependent stress and strain of in-plane shear(Mode Ⅱ) fracture process of rock and to reveal the mechanism of Mode Ⅱ fracture.Numerical results show that the maximum shear stress τmax at the crack tip is much larger than the maximum tensile stress σ1 and the ratio of τmax/σ1 is about 5,which favors Mode Ⅱ fracture of rock.Test results indicate that the strain-time curve comprises three stages:the linear deformation stage,the micro-cracking stage and the macroscopic crack propagation.The strain in the direction of the original notch plane is negative,due to restraining effect of compressive loading applied to the original notch plane.Both σ1 and τmax are increased as the load increases,but the slope of τmax is larger than that of σ1 and the value of τmax is always larger than that of σ1.Therefore,τmax reaches its limited value at peak load before σ1 and results in Mode Ⅱ fracture of rock.Shear-box(i.e.compression-shear) test becomes a potential standard method for achieving the true Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock.
文摘On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.
文摘We use the local Fourier analysis to determine the properties of the multigrid method when used in modeling the skin penetration of a drug. The analyses of these properties can be very in designing an efficient structure of the multigrid method and in comparing the element and finite difference discretization techniques. After the theoretical results obtained, we also present some numerical results for a problem for which the solution is known.
文摘（-）-（3R, 4S）-3-Acetoxy-4-phenylazetidin-2-one （（-）-1） was the key intermediate for preparing optical C-13 side-chain moiety in partial synthesis of docetaxel and paclitaxel. It can be successfully prepared via enantioselective hydrolysis of racemic esters （（-4-）-1） catalyzed by bacterial lipases, but the current reaction evaluation method is tedious and inconvenient. Electronic circular dichroism （ECD） has been widely applied in the stereochemical study of chiral compounds. In this paper, a rapid ECD spectroscopic method has been proposed and established to detect the transformation directly. The absolute configurations of lipase-catalyzed hydrolysis products have also been confirmed by quantum-chemical calculation using time-dependent density functional theory （TDDFT） methodology.
基金supported by the National Natural Science Foundation of China(Grant No.51579193)the Science and Technology Planning Project of Guizhou Province(Grant No.[2016]1154)
文摘Due to the size effects of rockfill materials, the settlement difference between numerical simulation and in situ monitoring of rockfill dams is a topic of general concern.The constitutive model parameters obtained from laboratory triaxial tests often underestimate the deformation of high rockfill dams.Therefore, constitutive model parameters obtained by back analysis were used to calculate and predict the long-term deformation of rockfill dams.Instead of using artificial neural networks (ANNs), the response surface method (RSM) was employed to replace the finite element simulation used in the optimization iteration.Only 27 training samples were required for RSM, improving computational efficiency compared with ANN, which required 300 training samples.RSM can be used to describe the relationship between the constitutive model parameters and dam settlements.The inversion results of the Shuibuya concrete face rockfill dam (CFRD) show that the calculated settlements agree with the measured data, indicating the accuracy and efficiency of RSM.
