Using quantum discord(QD)and geometric quantum discord(GQD),quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir,under bo...Using quantum discord(QD)and geometric quantum discord(GQD),quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir,under both weak and strong qubit-reservoir coupling regimes.The multiqubit system is connected with either a common bosonic reservoir(CBR)or multiple independent bosonic reservoirs(IBRs).In the CBR case,our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system.Furthermore,we study the steady state QD and GQD in the strong coupling regime,and find that the stable value in the long-time limit is determined exclusively by the number of qubits.The evolution period of QD and GQD gets longer as the dipole–dipole interaction(DDI)strength increases,which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime.Further analysis reveals notable differences between the CBR and IBRs scenarios.In the IBRs case,the decay of QD and GQD becomes slower compared to the CBR case,with both measures tending to zero at a reduced rate.Moreover,GQD consistently exhibits lower values than QD in both scenarios.These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.展开更多
This paper considers the optimal replacement problem of a repairable system consisting of one component and a single repairman, assume that the system after repair is not 'as good as new', by using the geometr...This paper considers the optimal replacement problem of a repairable system consisting of one component and a single repairman, assume that the system after repair is not 'as good as new', by using the geometric process, we consider a placement policy T based on the age of the system. The problem is to determine the optimal replacement policy T * such that the long_run expected benefit per unit time is maximized. Also, the explicit expression of the long_run expected benefit per unit time can be found. In some conditions, the existence and uniqueness of the optimal policy T * can be proved, finally, we prove that the policy T * is better than the policy T * in .展开更多
A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficien...A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algor...This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algorithm （GA） for calculating the radar cross section （RCS） and optimizing the geometric parameters of a large and complex target respectively. A new wedge modeling （WM） scheme is presented for calculating the high-frequency RCS of wedge with only one visible facet based on the method of equivalent currents （MEC）. The applications of GODS to 2D cross-section and 3D surface are respectively implemented by choosing an average of monostatic RCS values corresponding to a series of incident angles over a frequency band as the optimum objective function. And the results demonstrate that the RCS can be effectively and conveniently reduced by the GODS presented in this article.展开更多
A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） ...A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.展开更多
A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedbac...A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.展开更多
Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterativ...Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.展开更多
A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repa...A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repair finished. When the system failure, the repairman repair it immediately. The time interval of the preventive repair and the failure correction is described with the extended geometric process. Different from the available replacement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T,N) is considered. The explicit expression of the long-run average cost rate function C(T,N) of the system is derived. Through alternatively minimize the cost rate function C(T,N), the optimal replacement policy (T?,N?) is obtained, and it proves that the optimal policy is unique. Numerical cases illustrate the conclusion, and the sensitivity analysis of the parameters is carried out.展开更多
It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are ...It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.展开更多
Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the g...Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.展开更多
We study theoretically the geometric phase of a double-quantum-dot(DQD) system measured by a quantum point contact(QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these ...We study theoretically the geometric phase of a double-quantum-dot(DQD) system measured by a quantum point contact(QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer.In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero,which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment,the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.展开更多
In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active me...In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system.By using numerical measures,complex dynamical behaviors of the memristive laser system are uncovered.It appears the alternating appearance of quasi-periodic and chaotic oscillations.The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy.Interestingly,initial-values-oriented extreme multi-stability patterns are found,where the coexisting attractors have the same Lyapunov exponents.In addition,the introduction of a memristor greatly improves the complexity of the laser system.Moreover,to control the amplitude and offset of the chaotic signal,two kinds of geometric control methods including amplitude control and rotation control are designed.The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics.Finally,a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.展开更多
We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as m...We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as memory instead of the vibrational mode. And the system is robust against the spontaneous radiation and the dephasing.展开更多
A coordinate system of the original image is established using a facial feature point localization technique. After the original image transformed into a new image with the standard coordinate system, a redundant wate...A coordinate system of the original image is established using a facial feature point localization technique. After the original image transformed into a new image with the standard coordinate system, a redundant watermark is adaptively embedded in the discrete wavelet transform（DWT） domain based on the statistical characteristics of the wavelet coefficient block. The coordinate system of watermarked image is reestablished as a calibration system. Regardless of the host image rotated, scaled, or translated（RST）, all the geometric attacks are eliminated while the watermarked image is transformed into the standard coordinate system. The proposed watermark detection is a blind detection. Experimental results demonstrate the proposed scheme is robust against common and geometric image processing attacks, particularly its robustness against joint geometric attacks.展开更多
We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of ...We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.展开更多
Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to ca...Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.展开更多
We analyze the dynamics of geometric measure of discord （GMOD） and measurement-induced non-locality （MIN） in the presence of initial system-reservoir correlations without Born and Markov approximation. Although th...We analyze the dynamics of geometric measure of discord （GMOD） and measurement-induced non-locality （MIN） in the presence of initial system-reservoir correlations without Born and Markov approximation. Although the initial system-environment states have the same reduced density matrices for both the system and environment, the effects of different initial system-environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.展开更多
We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state ...We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit＇s ground state and first-excited state along different circular trajectories in phase space. We identify the resonator＇s phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit It-phase gate with a process fidelity of 0.851± 0.001.展开更多
The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ fai...The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11564013 and 11964010)the Natural Science Foundation of Hunan Province(Grant No.2020JJ4495)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant Nos.22A0377 and 21A0333).
文摘Using quantum discord(QD)and geometric quantum discord(GQD),quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir,under both weak and strong qubit-reservoir coupling regimes.The multiqubit system is connected with either a common bosonic reservoir(CBR)or multiple independent bosonic reservoirs(IBRs).In the CBR case,our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system.Furthermore,we study the steady state QD and GQD in the strong coupling regime,and find that the stable value in the long-time limit is determined exclusively by the number of qubits.The evolution period of QD and GQD gets longer as the dipole–dipole interaction(DDI)strength increases,which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime.Further analysis reveals notable differences between the CBR and IBRs scenarios.In the IBRs case,the decay of QD and GQD becomes slower compared to the CBR case,with both measures tending to zero at a reduced rate.Moreover,GQD consistently exhibits lower values than QD in both scenarios.These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.
文摘This paper considers the optimal replacement problem of a repairable system consisting of one component and a single repairman, assume that the system after repair is not 'as good as new', by using the geometric process, we consider a placement policy T based on the age of the system. The problem is to determine the optimal replacement policy T * such that the long_run expected benefit per unit time is maximized. Also, the explicit expression of the long_run expected benefit per unit time can be found. In some conditions, the existence and uniqueness of the optimal policy T * can be proved, finally, we prove that the policy T * is better than the policy T * in .
文摘A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金National Natural Science Foundation of China （20095251024）
文摘This article seeks to outline an integrated and practical geometric optimization design system （GODS） incorporating hybrid graphical electromagnetic computing-wedge modeling （GRECO-WM） scheme and the genetic algorithm （GA） for calculating the radar cross section （RCS） and optimizing the geometric parameters of a large and complex target respectively. A new wedge modeling （WM） scheme is presented for calculating the high-frequency RCS of wedge with only one visible facet based on the method of equivalent currents （MEC）. The applications of GODS to 2D cross-section and 3D surface are respectively implemented by choosing an average of monostatic RCS values corresponding to a series of incident angles over a frequency band as the optimum objective function. And the results demonstrate that the RCS can be effectively and conveniently reduced by the GODS presented in this article.
基金supported by the Ministry of Education of Singapore under Grant No.R265-000-277-112
文摘A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.
文摘A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.
基金Supported by the National Natural Science Foundation of China(61272300)
文摘Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.
基金supported by the National Natural Science Foundation of China(61573014)the Fundamental Research Funds for the Central Universities(JB180702)
文摘A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repair finished. When the system failure, the repairman repair it immediately. The time interval of the preventive repair and the failure correction is described with the extended geometric process. Different from the available replacement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T,N) is considered. The explicit expression of the long-run average cost rate function C(T,N) of the system is derived. Through alternatively minimize the cost rate function C(T,N), the optimal replacement policy (T?,N?) is obtained, and it proves that the optimal policy is unique. Numerical cases illustrate the conclusion, and the sensitivity analysis of the parameters is carried out.
基金Supported by the China NSF for Distinguished Young Scholars under Grant No.10925104
文摘It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.
基金supported by the National Natural Science Foundation of China under Grant No. 60573008
文摘Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2014AM030)。
文摘We study theoretically the geometric phase of a double-quantum-dot(DQD) system measured by a quantum point contact(QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer.In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero,which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment,the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.
基金Project supported by the National Natural Science Foundation of China(Grant No.61773010)Taishan Scholar Foundation of Shandong Province of China(Grant No.ts20190938)。
文摘In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system.By using numerical measures,complex dynamical behaviors of the memristive laser system are uncovered.It appears the alternating appearance of quasi-periodic and chaotic oscillations.The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy.Interestingly,initial-values-oriented extreme multi-stability patterns are found,where the coexisting attractors have the same Lyapunov exponents.In addition,the introduction of a memristor greatly improves the complexity of the laser system.Moreover,to control the amplitude and offset of the chaotic signal,two kinds of geometric control methods including amplitude control and rotation control are designed.The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics.Finally,a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.
基金Project supported by the National Natural Science Foundation (Grant Nos 10574022 and 10575022)the Funds of the Natural Science of Fujian Province, China (Grant No Z0512006)
文摘We propose a scheme for the implementation of remote controlled-NOT gates and entanglement swapping via geometric phase gates in ion-trap systems. The proposed scheme uses the two ground states of the A-type ions as memory instead of the vibrational mode. And the system is robust against the spontaneous radiation and the dephasing.
文摘A coordinate system of the original image is established using a facial feature point localization technique. After the original image transformed into a new image with the standard coordinate system, a redundant watermark is adaptively embedded in the discrete wavelet transform（DWT） domain based on the statistical characteristics of the wavelet coefficient block. The coordinate system of watermarked image is reestablished as a calibration system. Regardless of the host image rotated, scaled, or translated（RST）, all the geometric attacks are eliminated while the watermarked image is transformed into the standard coordinate system. The proposed watermark detection is a blind detection. Experimental results demonstrate the proposed scheme is robust against common and geometric image processing attacks, particularly its robustness against joint geometric attacks.
基金Project supported by the National Natural Science Foundation of China(Grant No.12201555)China Postdoctoral Science Foundation(Grant No.2021M702864)。
文摘We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.
基金supported by National Natural Science Foundation of China (NSFC-11775219, 11775222, 11505186, 11575185 and 11575186)the National Key Research and Development Program (2016YFA0400600, 2016YFA0400601 and 2016YFA0400602)+3 种基金the ITER-China Program (2015GB111003, 2014GB124005)Chinese Scholar Council (201506340103)China Postdoctoral Science Foundation (2017LH002)the GeoA lgorithmic Plasma Simulator (GAPS) Project
文摘Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.
基金supported by the Special Funds of the National Natural Science Foundation of China(Grant Nos.11247006 and 11247207)the Scientific Research Foundation of Jiangxi Provincial Education Department(Grant Nos.GJJ12355 and GJJ13651)the Natural Science Foundation of Jiangxi Province,China(Grant Nos.20122BAB212004 and 20132BAB212008)
文摘We analyze the dynamics of geometric measure of discord （GMOD） and measurement-induced non-locality （MIN） in the presence of initial system-reservoir correlations without Born and Markov approximation. Although the initial system-environment states have the same reduced density matrices for both the system and environment, the effects of different initial system-environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.
基金Project supported by the National Basic Research Program of China(Grant No.2014CB921201)the National Natural Science Foundation of China(Grant Nos.11434008 and 11574380)
文摘We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit＇s ground state and first-excited state along different circular trajectories in phase space. We identify the resonator＇s phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit It-phase gate with a process fidelity of 0.851± 0.001.
基金supported by the National Natural Science Foundation of China(61573014)the Fundamental Research Funds for the Central Universities(JB180702).
文摘The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.
