Contactless manipulation of multi-scale objects using the acoustic vortex(AV) tweezers offers tremendous perspectives in biomedical applications.However,it is still hindered by the weak acoustic radiation force(ARF) a...Contactless manipulation of multi-scale objects using the acoustic vortex(AV) tweezers offers tremendous perspectives in biomedical applications.However,it is still hindered by the weak acoustic radiation force(ARF) and torque(ART)around the vortex center.By introducing the elevation angle to the planar transducers of an N-element ring array,the weakfocused acoustic vortex(WFAV) composed of a main-AV and N paraxial-AVs is constructed to conduct a large-scale object manipulation.Different from the traditional focused AV(FAV) generated by a ring array of concave spherical transducers,a much larger focal region of the WFAV is generated by the main lobes of the planar transducers with the size inversely associated with the elevation angle.With the pressure simulation of the acoustic field,the capability of the rotational object driving in the focal plane for the WFAV is analyzed using the ARF and the ART exerted on an elastic ball based on acoustic scattering.With the experimental system built in water,the generation of the WFAV is verified by the scanning measurements of the acoustic field and the capability of object manipulation is also analyzed by the rotational trapping of floating particles in the focal plane.The favorable results demonstrate the feasibility of large-scale rotational manipulation of objects with a strengthened ART and a reduced acousto-thermal damage to biological tissues,showing a promising prospect for potential applications in clinical practice.展开更多
A sufficient condition for fcth Lyapunov value to be zero for planar polynomial vector fields is given, which extends the result of "jumping property’ of Lyapunov values obtained by Wang Duo to more general case...A sufficient condition for fcth Lyapunov value to be zero for planar polynomial vector fields is given, which extends the result of "jumping property’ of Lyapunov values obtained by Wang Duo to more general cases. A concrete example that the origin cannot be weak focus of order 1, 2, 4, 5, 8 is presented.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
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
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.
For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical ...For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is (M(n)=?)? This problem relates to Hilbert’s 16th problem closely. Inequality M(3)≥7 have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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11934009,11974187,and 12004187)the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BK20161013 and BK20200724)。
文摘Contactless manipulation of multi-scale objects using the acoustic vortex(AV) tweezers offers tremendous perspectives in biomedical applications.However,it is still hindered by the weak acoustic radiation force(ARF) and torque(ART)around the vortex center.By introducing the elevation angle to the planar transducers of an N-element ring array,the weakfocused acoustic vortex(WFAV) composed of a main-AV and N paraxial-AVs is constructed to conduct a large-scale object manipulation.Different from the traditional focused AV(FAV) generated by a ring array of concave spherical transducers,a much larger focal region of the WFAV is generated by the main lobes of the planar transducers with the size inversely associated with the elevation angle.With the pressure simulation of the acoustic field,the capability of the rotational object driving in the focal plane for the WFAV is analyzed using the ARF and the ART exerted on an elastic ball based on acoustic scattering.With the experimental system built in water,the generation of the WFAV is verified by the scanning measurements of the acoustic field and the capability of object manipulation is also analyzed by the rotational trapping of floating particles in the focal plane.The favorable results demonstrate the feasibility of large-scale rotational manipulation of objects with a strengthened ART and a reduced acousto-thermal damage to biological tissues,showing a promising prospect for potential applications in clinical practice.
基金National Natural Science Foundation of China,State Education Commission of China and Tsinghua University.
文摘A sufficient condition for fcth Lyapunov value to be zero for planar polynomial vector fields is given, which extends the result of "jumping property’ of Lyapunov values obtained by Wang Duo to more general cases. A concrete example that the origin cannot be weak focus of order 1, 2, 4, 5, 8 is presented.
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.
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.
文摘For any second order autonomous differential system with a polynomial of degree n on its right-hand side, what the maximum order of fineness of its weak focal point, weak saddle point in real domain and weak critical singular point in complex domain is (M(n)=?)? This problem relates to Hilbert’s 16th problem closely. Inequality M(3)≥7 have
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.
