The mass resolution of the ordinary ion trap mass spectrometer derived from the quadrupole mass spectrometer usually ranges from hundreds to thousands.In this study,the fine secular frequency resonance oscillation was...The mass resolution of the ordinary ion trap mass spectrometer derived from the quadrupole mass spectrometer usually ranges from hundreds to thousands.In this study,the fine secular frequency resonance oscillation was observed with a rectilinear ion trap mass spectrometer.The FWHM of the responding resonance secular frequency of benzene was 0.012 kHz.The corresponding mass resolution was 8600 m/Δm for benzene(m/z=78).The mass spectrometer with secular frequency scanning has a linear response to benzene in the concentration range from 200 ppbv to 10000 ppbv.This study shows a new feature of the secular frequency scanning for ion trap mass spectrometers.展开更多
The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental res...The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental results demonstrate the efficiency and effectiveness of the proposed method.展开更多
A parametric study of a high-power-density dual resonator for achieving low frequency broadband electromagnetic energy harvesting is reported.The dual resonator consists of a rectilinear oscillator(R_LO)performing mag...A parametric study of a high-power-density dual resonator for achieving low frequency broadband electromagnetic energy harvesting is reported.The dual resonator consists of a rectilinear oscillator(R_LO)performing magnetic levitation and a rotary oscillator(R_TO)performing electromagnetic coupling through a stator and a rotor.Both oscillators,coupled by magnetic forces generated by a set of arc permanent magnets,radially magnetized and centro-symmetrically fixed onto the R_LO and the rotor of the R_TO achieve the reciprocating-to-rotary motion conversion and frequency up-conversion.Specifically,the dual resonator is able to convert stochastic reciprocating motion into controllable rotation,provide intrinsic frequency up-conversion,use non-contact magnetic coupling to provide near loss-free energy transfer and be configured into specific applications to obtain and maintain high-energy orbits of multi-stable energy harvesting.While solely focusing on developing a dual resonator provides substantial benefits,its dynamic behavior is unclear,thus electromagnetic-dynamic governing equations are derived,and a curve fitting model of restoring torque of R_TO under different repulsive magnets configurations are developed to predict key characteristics and to improve performance of the electromechanical system.Power analysis is carried out for providing aquantitative guidance of customizing the harvester to achieve an optimal power density.展开更多
In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed...In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.展开更多
The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steine...The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steiner, for RSMT construction based on ant colony optimization （ACO）. An RSMT is constructed with ants＇ movements in Hanan grid, and then the constraint of Hanan grid is broken to accelerate ants＇ movements to improve the performance of the algorithm. This algorithm has been implemented on a Sun workstation with Unix operating system and the results have been compared with the fastest exact RSMT algorithm, GeoSteiner 3.1 and a recent heuristic using batched greedy triple construction （BGTC）. Experimental results show that ACO-Steiner can get a short running time and keep the high performance. Furthermore, it is Mso found that the ACO-Steiner can be easily extended to be used to some other problems, such as rectilinear Steiner minimal tree avoiding obstacles, and congestion reduction in global routing.展开更多
This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-...This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10-20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points.展开更多
This paper investigates the optimal transfer trajectories from a circular parking orbit towards the apocenter of a rectilinear ellipse,where the spacecraft reaches a quasi-stationary condition relative to an inertial ...This paper investigates the optimal transfer trajectories from a circular parking orbit towards the apocenter of a rectilinear ellipse,where the spacecraft reaches a quasi-stationary condition relative to an inertial reference frame.The spacecraft is equipped with a propulsion system that provides a circumferential continuous propulsive acceleration,that is,an acceleration whose direction is perpendicular to the primary body-spacecraft line.The performance index to minimize is the total flight time,and an indirect method is used to analyze the transfer trajectories.In this context,the optimal transfer performance is obtained as a function of the spacecraft propulsive acceleration magnitude through an interpolation procedure of numerical simulations.The results obtained with a continuous thrust propulsion system are also compared with those derived from a multi-impulse transfer.Finally,the paper investigates a heliocentric mission scenario in which the spacecraft minimizes the flight time required to reach a rectilinear ellipse with a given value of the aphelion radius.展开更多
We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that ...We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...展开更多
In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and ...In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and vertical segments and having at mort k bends? Any such graph is said tobe k--rectilinear. No matter what k is, an obvious necessary condition for k-rectilinearity is that thedegree of each vertex does not exceed four.Our main result is that every planar graph H satisfying this condition is 3--rectilinear:in fact,it is 2--rectilinear with the only exception of the octahedron. We also outline a polynomial-timealgorithm which actually constructs a plane embedding of H with at most 2 bends (3 bends if H isthe octahedron) on each edge. The resulting embedding has the property that the total number ofbends does not exceed 2n, where n is the number of vertices of H.展开更多
This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimi...This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.展开更多
基金supported by the National Natural Science Foundation of China(No.22076184)Fundamental Research Funds for the Central Universities,Beijing Municipal Science&Technology Commission(Z181100003818008).
文摘The mass resolution of the ordinary ion trap mass spectrometer derived from the quadrupole mass spectrometer usually ranges from hundreds to thousands.In this study,the fine secular frequency resonance oscillation was observed with a rectilinear ion trap mass spectrometer.The FWHM of the responding resonance secular frequency of benzene was 0.012 kHz.The corresponding mass resolution was 8600 m/Δm for benzene(m/z=78).The mass spectrometer with secular frequency scanning has a linear response to benzene in the concentration range from 200 ppbv to 10000 ppbv.This study shows a new feature of the secular frequency scanning for ion trap mass spectrometers.
文摘The definition and formula of flexibility of arbitrary rectilinear blocks are introduced and LFF principles are extended to handle arbitrary rectilinear blocks and blocks with relative constraints.The experimental results demonstrate the efficiency and effectiveness of the proposed method.
基金partially supported by the U.S.Office of Navy Research (No.N000141410230)partially supported by the Department of Energy ARPA-E (No. DOE-AR0000531)
文摘A parametric study of a high-power-density dual resonator for achieving low frequency broadband electromagnetic energy harvesting is reported.The dual resonator consists of a rectilinear oscillator(R_LO)performing magnetic levitation and a rotary oscillator(R_TO)performing electromagnetic coupling through a stator and a rotor.Both oscillators,coupled by magnetic forces generated by a set of arc permanent magnets,radially magnetized and centro-symmetrically fixed onto the R_LO and the rotor of the R_TO achieve the reciprocating-to-rotary motion conversion and frequency up-conversion.Specifically,the dual resonator is able to convert stochastic reciprocating motion into controllable rotation,provide intrinsic frequency up-conversion,use non-contact magnetic coupling to provide near loss-free energy transfer and be configured into specific applications to obtain and maintain high-energy orbits of multi-stable energy harvesting.While solely focusing on developing a dual resonator provides substantial benefits,its dynamic behavior is unclear,thus electromagnetic-dynamic governing equations are derived,and a curve fitting model of restoring torque of R_TO under different repulsive magnets configurations are developed to predict key characteristics and to improve performance of the electromechanical system.Power analysis is carried out for providing aquantitative guidance of customizing the harvester to achieve an optimal power density.
文摘In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.
基金This work was partially supported by the National Natural Science Foundation of China （NSFC） under Grant No. 60373012, and the Specialized Research Fund for the Doctoral Program of Higher Education （SRFDP） of China under Grant No. 20050003099. Some preliminary results of this work were presented at IEEE International Conference on Communications, Circuits and Systems （ICCCAS）, Chengdu, China, 2004.
文摘The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steiner, for RSMT construction based on ant colony optimization （ACO）. An RSMT is constructed with ants＇ movements in Hanan grid, and then the constraint of Hanan grid is broken to accelerate ants＇ movements to improve the performance of the algorithm. This algorithm has been implemented on a Sun workstation with Unix operating system and the results have been compared with the fastest exact RSMT algorithm, GeoSteiner 3.1 and a recent heuristic using batched greedy triple construction （BGTC）. Experimental results show that ACO-Steiner can get a short running time and keep the high performance. Furthermore, it is Mso found that the ACO-Steiner can be easily extended to be used to some other problems, such as rectilinear Steiner minimal tree avoiding obstacles, and congestion reduction in global routing.
基金the National Natural Science Foundation of China under Grant Nos.10401038,60373012 and 70221001the Key Project of Chinese Ministry of Education under Grant No.106008
文摘This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10-20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points.
文摘This paper investigates the optimal transfer trajectories from a circular parking orbit towards the apocenter of a rectilinear ellipse,where the spacecraft reaches a quasi-stationary condition relative to an inertial reference frame.The spacecraft is equipped with a propulsion system that provides a circumferential continuous propulsive acceleration,that is,an acceleration whose direction is perpendicular to the primary body-spacecraft line.The performance index to minimize is the total flight time,and an indirect method is used to analyze the transfer trajectories.In this context,the optimal transfer performance is obtained as a function of the spacecraft propulsive acceleration magnitude through an interpolation procedure of numerical simulations.The results obtained with a continuous thrust propulsion system are also compared with those derived from a multi-impulse transfer.Finally,the paper investigates a heliocentric mission scenario in which the spacecraft minimizes the flight time required to reach a rectilinear ellipse with a given value of the aphelion radius.
基金Specialized Research Fund for the Doctoral Program of Higher Education (No.20050141011)
文摘We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...
文摘In the design of certain kinds of electronic circuits the following question arises:given a non-negative integer k, what graphs admit of a plane embedding such that every edge is a broken lineformed by horizontal and vertical segments and having at mort k bends? Any such graph is said tobe k--rectilinear. No matter what k is, an obvious necessary condition for k-rectilinearity is that thedegree of each vertex does not exceed four.Our main result is that every planar graph H satisfying this condition is 3--rectilinear:in fact,it is 2--rectilinear with the only exception of the octahedron. We also outline a polynomial-timealgorithm which actually constructs a plane embedding of H with at most 2 bends (3 bends if H isthe octahedron) on each edge. The resulting embedding has the property that the total number ofbends does not exceed 2n, where n is the number of vertices of H.
文摘This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.
