A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical...A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.展开更多
Reliable process monitoring is important for ensuring process safety and product quality.A production process is generally characterized bymultiple operation modes,and monitoring thesemultimodal processes is challengi...Reliable process monitoring is important for ensuring process safety and product quality.A production process is generally characterized bymultiple operation modes,and monitoring thesemultimodal processes is challenging.Most multimodal monitoring methods rely on the assumption that the modes are independent of each other,which may not be appropriate for practical application.This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring.This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data.This process enables the identified modes to reflect the stability of actual working conditions,improve mode identification accuracy,and enhance monitoring reliability in cases of mode overlap.Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach inmultimodal process monitoring with mode overlap.展开更多
The Unit Vector Method (UVM) is an orbit determination method extensively applied. In this paper, the UVM and classical Differential Orbit Improvement (DOI) are compared, and a fusion method is given for the orbit det...The Unit Vector Method (UVM) is an orbit determination method extensively applied. In this paper, the UVM and classical Differential Orbit Improvement (DOI) are compared, and a fusion method is given for the orbit determination with different kind data. Based on non-orthogonal decomposition of position and velocity vectors, an approximation scheme is constructed to calculate the state transition matrix. This method simplifies the calculation of the approximate state transition matrix, analyzes the convergence mechanism of the UVM, and makes clear the defect of weight strategy in UVM. Results of orbit the determination with simulating and real data show that this method has good numerical stability and rational weight distribution.展开更多
State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an...State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an approach to determine zero-input responses is developed, and the design of simulation experiments with the aid of Matlab is used to illustrate the physical meaning of it. Furthermore, during the engineering application, for the discrimination of state transition matrix, a discrimination method of state transition matrix is proposed based on related theorems and an effective method is derived by calculating characteristics during tedious verification of theorem. The simulation results have proved the correctness of system analysis by using such discrimination method under different parameter models.展开更多
For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively descr...For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.展开更多
We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system h...We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.展开更多
According to our scheme to construct quantum phase transitions （QPTs） in spin chain systems with matrix product ground states, we first successfully combine matrix product state （MPS） QPTs with spontaneous symmetr...According to our scheme to construct quantum phase transitions （QPTs） in spin chain systems with matrix product ground states, we first successfully combine matrix product state （MPS） QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.展开更多
文摘A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.
基金supported in part by National Natural Science Foundation of China under Grants 61973119 and 61603138in part by Shanghai Rising-Star Program under Grant 20QA1402600+1 种基金in part by the Open Funding from Shandong Key Laboratory of Big-data Driven Safety Control Technology for Complex Systems under Grant SKDN202001in part by the Programme of Introducing Talents of Discipline to Universities(the 111 Project)under Grant B17017.
文摘Reliable process monitoring is important for ensuring process safety and product quality.A production process is generally characterized bymultiple operation modes,and monitoring thesemultimodal processes is challenging.Most multimodal monitoring methods rely on the assumption that the modes are independent of each other,which may not be appropriate for practical application.This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring.This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data.This process enables the identified modes to reflect the stability of actual working conditions,improve mode identification accuracy,and enhance monitoring reliability in cases of mode overlap.Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach inmultimodal process monitoring with mode overlap.
文摘状态迁移矩阵(State Transition Matrix,STM)是一种基于表结构的程序建模语言。事件变量类型单一,事件和状态数量的增加很容易造成状态空间爆炸问题,无法表达具有时间语义的软件系统等原因,极大限制了该建模方法的推广应用。文中针对这些问题,首先提出层次化时间状态迁移矩阵(Hierarchical Time State Transition Matrix,HTSTM)模型,用于设计、建模和验证具有时间条件约束的软件系统,并给出形式化表示方法。基于该表示方法提出一种符号化编码方法,采用有界模型检测思想将需要验证的LTL性质输入SMT(Satisfiability Modulo Theories)求解器进行验证,从而在一定程度上证明了软件设计的正确性。
文摘The Unit Vector Method (UVM) is an orbit determination method extensively applied. In this paper, the UVM and classical Differential Orbit Improvement (DOI) are compared, and a fusion method is given for the orbit determination with different kind data. Based on non-orthogonal decomposition of position and velocity vectors, an approximation scheme is constructed to calculate the state transition matrix. This method simplifies the calculation of the approximate state transition matrix, analyzes the convergence mechanism of the UVM, and makes clear the defect of weight strategy in UVM. Results of orbit the determination with simulating and real data show that this method has good numerical stability and rational weight distribution.
基金Supported by the National Natural Science Foundation of China(11605147)the Education and Teaching Reform Project of Xianyang Normal University(2015Z006).
文摘State transition matrix is an important concept in modern control system. It studies the motion law of linear control system from initial state to any state at time t. In this paper, joining an engineering example, an approach to determine zero-input responses is developed, and the design of simulation experiments with the aid of Matlab is used to illustrate the physical meaning of it. Furthermore, during the engineering application, for the discrimination of state transition matrix, a discrimination method of state transition matrix is proposed based on related theorems and an effective method is derived by calculating characteristics during tedious verification of theorem. The simulation results have proved the correctness of system analysis by using such discrimination method under different parameter models.
基金Supported by National Natural Science Foundation of China(10974137)by Educational Commission of Sichuan Province of China(14ZA0167)
文摘For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.
基金Supported by National Natural Science Foundation of China(10974137)Major Natural Science Foundation of Educational Department of Sichuan Province(14ZA0167)
文摘We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.
基金Supported by Scientific Research Foundation of CUIT (KYTZ201024)
文摘According to our scheme to construct quantum phase transitions （QPTs） in spin chain systems with matrix product ground states, we first successfully combine matrix product state （MPS） QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.
