This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the F...This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.展开更多
We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional invest...We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional investigation study. Anthropometric parameters, whole body reaction time and one leg with eye closed balance were measured. Whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in 70’s than those in 60’s in both sexes. Two hundred twenty seven men (31.1%) and 533 women (40.1%) were having no medications. In men, whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in subjects with medications than those in subjects without in 60’s. However, significant differences of whole body reaction time and one leg with eye closed balance between subjects with and without medications in men with 70’s and women with 60’s and 70’s were not noted. This standard mean value may provide a useful reference database for evaluating whole body reaction time and one leg with eye closed balance in Japanese elderly subjects.展开更多
For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based o...For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.展开更多
The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmla...The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmlations. The power-law scaling of the translocation time T with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be T - N^a with the exponent a varying from a = 0.71 for relatively short chains to a = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α= 1.27 for the transloeation of double-strand DNA. The distribution of translocation time D（τ） is close to a Gaussian function for duration time τ 〈 τp and follows a falling exponential function for duration time T 〉 wp. For closed knotted polymers, the scaling exponent a is 1.27 for small field force （F = 5） and 1.38 for large field force （F = 10）. The distribution of translocation time D（τ） remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.展开更多
The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cro...The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.展开更多
The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained accor...The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.展开更多
In the aerospace sector,the soft magnetic materials of Hermetically Sealed Electromagnetic Relays(HSERs)are critical in forming magnetic circuits.Conventional soft magnetic materials,primarily magnetic iron,have been ...In the aerospace sector,the soft magnetic materials of Hermetically Sealed Electromagnetic Relays(HSERs)are critical in forming magnetic circuits.Conventional soft magnetic materials,primarily magnetic iron,have been unable to meet the development trend of fast-response,miniaturized,and lightweight aerospace and aviation systems.This paper applies circuit theory and electromagnetics theory to establish a Field-Circuit Coupling Mathematical Model(FCCMM)for dynamic response analysis of HSERs.This model centers on inductance calculation,with the core's permeability and saturation magnetic flux density as critical parameters.Based on this model,for a specific type of HSER,this paper introduced three alloys with key parameters different from magnetic iron,then tested the magnetic characteristic curves of these four soft magnetic materials,followed by simulations to obtain the electromagnetic characteristics of digital mock-ups corresponding to these four materials,compared and validated the dynamic responses corresponding to these four soft magnetic materials finally.Based on the theoretical model analysis results,this paper designed a lightweight coil to minimize response time,made prototypes,set up test systems,and tested dynamic characteristics.The experimental results indicate that the nanocrystalline alloy1K107B exhibits the most significant optimization,reducing the closing time by 40.48%and achieving a weight reduction of 6.53%.展开更多
基金supported by the Mathematical Tianyuan Foundation (No. 10826078)the National Natural Science Foundation of China (No. 60874006)
文摘This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.
文摘We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional investigation study. Anthropometric parameters, whole body reaction time and one leg with eye closed balance were measured. Whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in 70’s than those in 60’s in both sexes. Two hundred twenty seven men (31.1%) and 533 women (40.1%) were having no medications. In men, whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in subjects with medications than those in subjects without in 60’s. However, significant differences of whole body reaction time and one leg with eye closed balance between subjects with and without medications in men with 70’s and women with 60’s and 70’s were not noted. This standard mean value may provide a useful reference database for evaluating whole body reaction time and one leg with eye closed balance in Japanese elderly subjects.
文摘For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 20574052, 20774066, 20974081 and 20934004)the Program for New Century Excellent Talents in University,China (Grant No. NCET-05-0538)the Natural Science Foundation of Zhejiang Province, China (Grant No. Y4090098)
文摘The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmlations. The power-law scaling of the translocation time T with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be T - N^a with the exponent a varying from a = 0.71 for relatively short chains to a = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α= 1.27 for the transloeation of double-strand DNA. The distribution of translocation time D（τ） is close to a Gaussian function for duration time τ 〈 τp and follows a falling exponential function for duration time T 〉 wp. For closed knotted polymers, the scaling exponent a is 1.27 for small field force （F = 5） and 1.38 for large field force （F = 10）. The distribution of translocation time D（τ） remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.
基金supported by the National Natural Science Foundation of China(Grant No.11374133)the Taishan Scholars Project of Shandong Province,China(Grant No.ts2015110055)
文摘The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.
文摘The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.
基金supported by the National Natural Science Foundation of China(No.52177134)。
文摘In the aerospace sector,the soft magnetic materials of Hermetically Sealed Electromagnetic Relays(HSERs)are critical in forming magnetic circuits.Conventional soft magnetic materials,primarily magnetic iron,have been unable to meet the development trend of fast-response,miniaturized,and lightweight aerospace and aviation systems.This paper applies circuit theory and electromagnetics theory to establish a Field-Circuit Coupling Mathematical Model(FCCMM)for dynamic response analysis of HSERs.This model centers on inductance calculation,with the core's permeability and saturation magnetic flux density as critical parameters.Based on this model,for a specific type of HSER,this paper introduced three alloys with key parameters different from magnetic iron,then tested the magnetic characteristic curves of these four soft magnetic materials,followed by simulations to obtain the electromagnetic characteristics of digital mock-ups corresponding to these four materials,compared and validated the dynamic responses corresponding to these four soft magnetic materials finally.Based on the theoretical model analysis results,this paper designed a lightweight coil to minimize response time,made prototypes,set up test systems,and tested dynamic characteristics.The experimental results indicate that the nanocrystalline alloy1K107B exhibits the most significant optimization,reducing the closing time by 40.48%and achieving a weight reduction of 6.53%.
