A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In th...A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.展开更多
We present a study of the so called relaxed field equations of general relativity in terms of a decomposition of the metric;which is designed to deal with the notion of particles. Several known results are generalized...We present a study of the so called relaxed field equations of general relativity in terms of a decomposition of the metric;which is designed to deal with the notion of particles. Several known results are generalized to a coordinate free covariant discussion. We apply our techniques to the study of a particle up to second order.展开更多
Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocit...Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocities, into a macroparticle, and do a global motion. This is a distorted picture because what each macroparticle do is to break into, because of differences among velocities of contained realistic particles, pieces with different destinations at next time point, rather than a global moving to a destination at next time point. Therefore, the scientific validity of results obtained from such an approximation cannot be warranted. Here, we propose a solution to this problem. It can fundamentally warrant exact solutions of plasma self-consistent fields and hence those of microscopic distribution function.展开更多
In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- ma...In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm展开更多
We used discrete dipole approximation(DDA)to examine the scattering and absorption characteristics of spherical ice crystal particles.On this basis,we studied the scattering characteristics of spherical ice crystal pa...We used discrete dipole approximation(DDA)to examine the scattering and absorption characteristics of spherical ice crystal particles.On this basis,we studied the scattering characteristics of spherical ice crystal particles at different frequencies and non-spherical ice crystal particles with different shapes,aspect ratios,and spatial orientations.The results indicate that the DDA and Mie methods yield almost the same results for spherical ice crystal particles,illustrating the superior calculation accuracy of the DDA method.Compared with the millimeter wave band,the terahertz band particles have richer scattering characteristics and can detect ice crystal particles more easily.Different frequencies,shapes,aspect ratios,and spatial orientations have specific effects on the scattering and absorption characteristics o f ice crystal particles.The results provide an important theoretical basis for the design of terahertz cloud radars and related cirrus detection methods.展开更多
In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potentia...In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.展开更多
In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that thi...In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, called second-order nonlinear Kalman particle filter algorithms, by means of second-order Taylor expansion and linearization approximation, and correspondingly two recursive formulas are derived. A simulation example is given to illustrate the effectiveness of two algorithms. It is shown that the extended Kalman particle filter algorithm based on second-order Taylor expansion has a more satisfactory performance in reducing systematic deviations and running time in comparison with the extended Kalman filter algorithm and the other second-order nonlinear Kalman particle filter algorithm.展开更多
The effective medium approximation (EMA) theory is the basis of a capacitance sensor used for concen-tration measurementof a particulate solid flow, its measurementresultis independenton particle size. In existence of...The effective medium approximation (EMA) theory is the basis of a capacitance sensor used for concen-tration measurementof a particulate solid flow, its measurementresultis independenton particle size. In existence ofparticle agglomeration or aggradation, however, it is found that the effective permittivity of a gas/solid mixture is de-pendent on particle size. In this paper, a parallel plate, differential capacitance sensor is utilized to investigate theinfluence of particle size on the effective permittivity of the mixture in such a case. Static experiments using threematerials including glass, limestone and quartz particles were carried out in an off-line manner. The volume fractionof particles being tested ranged from20×10-6to 600×10-6, while the particle size was between 3 and 100μm.Experimental results showthat the effective permittivity of a particle-gas mixture with particle agglomeration is largerthan that predicted by EMA and the smaller the particle size, the larger the effective permittivity. The experimentprocess and analysis results are discussed in detail in the paper.展开更多
The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filt...The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.展开更多
The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(M...The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.展开更多
Dark matter is an essential component of the universe,accounting for approximately 85%of all matter.However,what the nature of dark matter actually is remains a huge mystery.So far,all evidence for the existence of da...Dark matter is an essential component of the universe,accounting for approximately 85%of all matter.However,what the nature of dark matter actually is remains a huge mystery.So far,all evidence for the existence of dark matter has come from gravitational interactions.Since gravitational interactions are universal,it is challenging to reveal the nature of dark matter through gravitational interactions.To unravel the mystery of dark matter,it is essential to directly detect dark matter.展开更多
The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order...The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.展开更多
基金supported by the National Natural Science Foundation of China (10872030)
文摘A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.
文摘We present a study of the so called relaxed field equations of general relativity in terms of a decomposition of the metric;which is designed to deal with the notion of particles. Several known results are generalized to a coordinate free covariant discussion. We apply our techniques to the study of a particle up to second order.
文摘Current mainstream method of simulating plasma is based on rigid-macroparticle approximation in which many realistic particles are merged, according to their initial space positions regardless of their initial velocities, into a macroparticle, and do a global motion. This is a distorted picture because what each macroparticle do is to break into, because of differences among velocities of contained realistic particles, pieces with different destinations at next time point, rather than a global moving to a destination at next time point. Therefore, the scientific validity of results obtained from such an approximation cannot be warranted. Here, we propose a solution to this problem. It can fundamentally warrant exact solutions of plasma self-consistent fields and hence those of microscopic distribution function.
基金the National Natural Science Foundation of China (No. 60404011)
文摘In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61527805 and 41776181).
文摘We used discrete dipole approximation(DDA)to examine the scattering and absorption characteristics of spherical ice crystal particles.On this basis,we studied the scattering characteristics of spherical ice crystal particles at different frequencies and non-spherical ice crystal particles with different shapes,aspect ratios,and spatial orientations.The results indicate that the DDA and Mie methods yield almost the same results for spherical ice crystal particles,illustrating the superior calculation accuracy of the DDA method.Compared with the millimeter wave band,the terahertz band particles have richer scattering characteristics and can detect ice crystal particles more easily.Different frequencies,shapes,aspect ratios,and spatial orientations have specific effects on the scattering and absorption characteristics o f ice crystal particles.The results provide an important theoretical basis for the design of terahertz cloud radars and related cirrus detection methods.
基金The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N.
文摘In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.
文摘In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, called second-order nonlinear Kalman particle filter algorithms, by means of second-order Taylor expansion and linearization approximation, and correspondingly two recursive formulas are derived. A simulation example is given to illustrate the effectiveness of two algorithms. It is shown that the extended Kalman particle filter algorithm based on second-order Taylor expansion has a more satisfactory performance in reducing systematic deviations and running time in comparison with the extended Kalman filter algorithm and the other second-order nonlinear Kalman particle filter algorithm.
文摘The effective medium approximation (EMA) theory is the basis of a capacitance sensor used for concen-tration measurementof a particulate solid flow, its measurementresultis independenton particle size. In existence ofparticle agglomeration or aggradation, however, it is found that the effective permittivity of a gas/solid mixture is de-pendent on particle size. In this paper, a parallel plate, differential capacitance sensor is utilized to investigate theinfluence of particle size on the effective permittivity of the mixture in such a case. Static experiments using threematerials including glass, limestone and quartz particles were carried out in an off-line manner. The volume fractionof particles being tested ranged from20×10-6to 600×10-6, while the particle size was between 3 and 100μm.Experimental results showthat the effective permittivity of a particle-gas mixture with particle agglomeration is largerthan that predicted by EMA and the smaller the particle size, the larger the effective permittivity. The experimentprocess and analysis results are discussed in detail in the paper.
基金supported in part by the National Key R&D Program of China (2022ZD0116401,2022ZD0116400)the National Natural Science Foundation of China (62203016,U2241214,T2121002,62373008,61933007)+2 种基金the China Postdoctoral Science Foundation (2021TQ0009)the Royal Society of the UKthe Alexander von Humboldt Foundation of Germany。
文摘The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.
基金supported by the Board of Research in Nuclear Sciences of the Department of Atomic Energy,India(2012/36/69-BRNS/2012)
文摘The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.
文摘Dark matter is an essential component of the universe,accounting for approximately 85%of all matter.However,what the nature of dark matter actually is remains a huge mystery.So far,all evidence for the existence of dark matter has come from gravitational interactions.Since gravitational interactions are universal,it is challenging to reveal the nature of dark matter through gravitational interactions.To unravel the mystery of dark matter,it is essential to directly detect dark matter.
基金the Key Project of Fund of Science and Technology Development of Shanghai (No. 07JC14023)the National Natural Science Foundation of China(No. 50778111)
文摘The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.
