In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitud...In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.展开更多
It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system ha...It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).展开更多
The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equa...The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.展开更多
Inexistence and existence of limit cycles in a predator-prey model with undercrowding effect are studied.The number of limit cycles obtained by Zheng Weiwei in 2000 is corrected.
In this paper, we prove that a planar quadratic systems with a 3rd-order weak focus has at most one limit cycle, and a planar quadratic system with a 2nd-order weak focus has at most two limit cycles.
Nanostructured dielectric metasurfaces offer unprecedented opportunities to control light-matter momentum exchange,and thereby the forces and torques that light can exert on matter.Here we introduce optical metasurfac...Nanostructured dielectric metasurfaces offer unprecedented opportunities to control light-matter momentum exchange,and thereby the forces and torques that light can exert on matter.Here we introduce optical metasurfaces as components of ultracompact untethered microscopic metaspinners capable of efficient light-induced rotation in a liquid environment.Iluminated by weakly focused light,a metaspinner generates torque via photon recoil through the metasurfaces'ability to bend light towards high angles despite their sub-wavelength thickness,thereby creating orbital angular momentum.We find that a metaspinner is subject to an anomalous transverse lateral optical gradient force that acts in concert with the classical gradient force.Consequently,when two or more metaspinners are trapped together in a laser beam,they collectively orbit the optical axis in the opposite direction to their spinning motion,in stark contrast to rotors coupled through hydrodynamic or mechanical interactions.The metaspinners delineated herein not only serve to llustrate the vast possibilities of utilizing optical metasurfaces for fundamental exploration of optical torques,but they also represent potential building-blocks of artificial active matter systems,light-driven micromachinery,and general-purpose optomechanical devices.展开更多
In this paper we study the variation of limit cycles around different foci when a coefficient in the equation of the quadratic differential system varies.
For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary...For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.展开更多
In this paper, we investigate the maximal number of limit cycles surrounding a first order weak focus for the quadratic differential system. And proved such a system has at most two limit cycles under some certain con...In this paper, we investigate the maximal number of limit cycles surrounding a first order weak focus for the quadratic differential system. And proved such a system has at most two limit cycles under some certain conditions.展开更多
基金supported by the National Key Research and Development Program of China(No.2022YFA1603401)National Natural Science Foundation of China(Nos.12035010 and 12342501)+1 种基金Beijing Outstanding Young Scientist Program(No.JWZQ20240101006)the Tsinghua University Dushi Program.
文摘In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.
文摘It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).
文摘The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.
文摘Inexistence and existence of limit cycles in a predator-prey model with undercrowding effect are studied.The number of limit cycles obtained by Zheng Weiwei in 2000 is corrected.
基金Supported by the National Natural Science Foundation of China (19671071).
文摘In this paper, we prove that a planar quadratic systems with a 3rd-order weak focus has at most one limit cycle, and a planar quadratic system with a 2nd-order weak focus has at most two limit cycles.
基金Open access funding provided by Chalmers University of Technology.
文摘Nanostructured dielectric metasurfaces offer unprecedented opportunities to control light-matter momentum exchange,and thereby the forces and torques that light can exert on matter.Here we introduce optical metasurfaces as components of ultracompact untethered microscopic metaspinners capable of efficient light-induced rotation in a liquid environment.Iluminated by weakly focused light,a metaspinner generates torque via photon recoil through the metasurfaces'ability to bend light towards high angles despite their sub-wavelength thickness,thereby creating orbital angular momentum.We find that a metaspinner is subject to an anomalous transverse lateral optical gradient force that acts in concert with the classical gradient force.Consequently,when two or more metaspinners are trapped together in a laser beam,they collectively orbit the optical axis in the opposite direction to their spinning motion,in stark contrast to rotors coupled through hydrodynamic or mechanical interactions.The metaspinners delineated herein not only serve to llustrate the vast possibilities of utilizing optical metasurfaces for fundamental exploration of optical torques,but they also represent potential building-blocks of artificial active matter systems,light-driven micromachinery,and general-purpose optomechanical devices.
文摘In this paper we study the variation of limit cycles around different foci when a coefficient in the equation of the quadratic differential system varies.
基金Supported by the National Natural Science Foundation of China(No.11371373 and 10831003)
文摘For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.
文摘In this paper, we investigate the maximal number of limit cycles surrounding a first order weak focus for the quadratic differential system. And proved such a system has at most two limit cycles under some certain conditions.
