A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of...A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of simulated moving bed chromatography (SMBC). The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of concentration vector. The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of l,1'-bi-2-naphthol enantiomers using SMBC. This model is useful for design, operation, optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects, especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.展开更多
Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as w...Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian in- ter-tidal concentration(LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is nu- merically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as ‘flat-bottom', ‘stairs' and ‘cape' case, re- spectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the ‘flat-bottom' case still meets the convectively weakly nonlinear condi- tion. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the de- pendence of the LIS(Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coast- lines, and that in the latter region is due to the presence of the estuarine salinity front.展开更多
In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint me...In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.展开更多
A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electro-magnetic field is obtained. F12 is the non-vanishing component of electromagnetic field tensor. To get a deterministic solu...A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electro-magnetic field is obtained. F12 is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, we assume the free gravitational field is Petrov type-Ⅱ non-degenerate. Some physical and geometric properties of the model are also discussed.展开更多
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a gen...We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature, 2000, 405: 546). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.展开更多
In this paper, a lattice Boltzmann equation (LBE) model with multiple-relaxation-time (MRT) colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of t...In this paper, a lattice Boltzmann equation (LBE) model with multiple-relaxation-time (MRT) colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time (SRT) LBE model (Guo and Zhao in Phys Rev E 68:035302, 2003). The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen (SC) model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.展开更多
In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of...In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of DEA, because of some limitations in resources and DMU's ability, these variations cannot be made arbitrarily. Moreover, in some situations, undesirable factors with different disposability, strong or weak disposability, are found. In this paper, a DEA-based model is proposed to determine the relative efficiency of DMUs in such a restricted environment and in presence of undesirable factors. Indeed, variation levels of inputs and outputs are pre-defined and are considered to evaluate the performance of DMUs. Numerical examples are utilized to demonstrate the approach.展开更多
基金Supported by the National Natural Science Foundation of China(No.20206027)and the Natural Science Foundation of Zhejiang Province(No.202046).
文摘A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of simulated moving bed chromatography (SMBC). The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of concentration vector. The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of l,1'-bi-2-naphthol enantiomers using SMBC. This model is useful for design, operation, optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects, especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.
基金supported by National Basic Research Program of China (No. 2010CB428904)National Science Foundation of China (Nos. 41106006, 40976003)
文摘Inter-tidal(subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al.(2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian in- ter-tidal concentration(LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is nu- merically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as ‘flat-bottom', ‘stairs' and ‘cape' case, re- spectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the ‘flat-bottom' case still meets the convectively weakly nonlinear condi- tion. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the de- pendence of the LIS(Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coast- lines, and that in the latter region is due to the presence of the estuarine salinity front.
基金Application investigation of conditional nonlinear optimal perturbation in typhoon adaptive observation (40830955)
文摘In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.
文摘A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electro-magnetic field is obtained. F12 is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, we assume the free gravitational field is Petrov type-Ⅱ non-degenerate. Some physical and geometric properties of the model are also discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.11074305,10935010,11074261 and 11121403)the National Basic Research Program of China(Grant Nos.2012CB922104 and 2014CB921402)
文摘We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature, 2000, 405: 546). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly enhanced by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
基金This work was financially supported by the National Natural Science Foundation of China (51125024) and the National Basic Research Programme of China (2011CB707305).
文摘In this paper, a lattice Boltzmann equation (LBE) model with multiple-relaxation-time (MRT) colli- sion operator is developed based on the Enskog theory for isothermal nonideal mixtures, which is an extension of the previous single relaxation time (SRT) LBE model (Guo and Zhao in Phys Rev E 68:035302, 2003). The present MRT-LBE model overcomes some inherent defects of the original SRT-LBE model such as the fixed Schmidt num- ber and limited viscosity ratio. It is also interestingly shown that the widely used Shan-Chen (SC) model, which is constructed heuristically based on the pseudo-potential concept, can also be regarded as a special case of the present model, and thus putting a solid foundation for this well-accepted multiphase LBE model. A series of nu- merical simulations, including the static droplet and lay- ered co-current flow, are conducted to test the applicability of the present model for immiscible fluids with different Schmidt numbers and large viscosity ratio, which may be difficult for the original SRT-LBE model and the SC model.
文摘In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of DEA, because of some limitations in resources and DMU's ability, these variations cannot be made arbitrarily. Moreover, in some situations, undesirable factors with different disposability, strong or weak disposability, are found. In this paper, a DEA-based model is proposed to determine the relative efficiency of DMUs in such a restricted environment and in presence of undesirable factors. Indeed, variation levels of inputs and outputs are pre-defined and are considered to evaluate the performance of DMUs. Numerical examples are utilized to demonstrate the approach.