This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a ...This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.展开更多
An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized in...An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.展开更多
This paper introduces the finding of a unified Lorenz-like system.By gradually tuning the only parameter d,the reported system belongs to Lorenz-type system in the sense defined by Clikovsky.Meanwhile,this system belo...This paper introduces the finding of a unified Lorenz-like system.By gradually tuning the only parameter d,the reported system belongs to Lorenz-type system in the sense defined by Clikovsky.Meanwhile,this system belongs to Lorenz-type system,Lu-type system,Chen-type system with d less than,equivalent to and greater than 1.5,respectively,according to the classification defined by Yang.However,this system can only generate a succession of Lorenz-like attractors.Some basic dynamical properties of the system are investigated theoretically and numerically.Moreover,the tracking control of the system with exponential convergence rate is studied.Theoretical analysis and computer simulation show that the proposed scheme can allow us to drive the output variable x\ to arbitrary reference signals exponentially,and the guaranteed exponential convergence rate can be estimated accurately.展开更多
Turbulent control and drag reduction in a channel flow via a bidirectional traveling wave induced by spanwise oscillating Lorentz force have been investigated in the paper.The results based on the direct numerical sim...Turbulent control and drag reduction in a channel flow via a bidirectional traveling wave induced by spanwise oscillating Lorentz force have been investigated in the paper.The results based on the direct numerical simulation(DNS)indicate that the bidirectional wavy Lorentz force with appropriate control parameters can result in a regular decline of near-wall streaks and vortex structures with respect to the flow direction,leading to the effective suppression of turbulence generation and significant reduction in skin-friction drag.In addition,experiments are carried out in a water tunnel via electro-magnetic(EM)actuators designed to produce the bidirectional traveling wave excitation as described in calculations.As a result,the actual substantial drag reduction is realized successfully in these experiments.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 60674059
文摘This paper establishes two theorems for two time-delayed （chaotic） discrete systems to achieve timedelayed generalized synchronization （TDGS）. These two theorems uncover the genera/forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.
基金the National Natural Science Foundation of China (Grant Nos. 10974179 and 61178016)Zhejiang Provincial Natural Science Foundation of China (Grant No. Y1090073)the Key Project of the Education Commission of Zhejiang Province of China (Grant No.Z201120128)
文摘An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.
基金Supported by the Research Foundation of Education Bureau of Hunan Province of China under Grant No.13C372Jiangsu Provincial Natural Science Foundation of China under Grant No.14KJB120007the Outstanding Doctoral Dissertation Project of Special Funds under Grant No.27122
文摘This paper introduces the finding of a unified Lorenz-like system.By gradually tuning the only parameter d,the reported system belongs to Lorenz-type system in the sense defined by Clikovsky.Meanwhile,this system belongs to Lorenz-type system,Lu-type system,Chen-type system with d less than,equivalent to and greater than 1.5,respectively,according to the classification defined by Yang.However,this system can only generate a succession of Lorenz-like attractors.Some basic dynamical properties of the system are investigated theoretically and numerically.Moreover,the tracking control of the system with exponential convergence rate is studied.Theoretical analysis and computer simulation show that the proposed scheme can allow us to drive the output variable x\ to arbitrary reference signals exponentially,and the guaranteed exponential convergence rate can be estimated accurately.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172140 and 11202102)the Specialized Research Fund for Doctoral Program of Higher Education(Grant No.20123219120050)the EU FP6 Framework Program AVERT and the Faculty of Engineering,University of Nottingham
文摘Turbulent control and drag reduction in a channel flow via a bidirectional traveling wave induced by spanwise oscillating Lorentz force have been investigated in the paper.The results based on the direct numerical simulation(DNS)indicate that the bidirectional wavy Lorentz force with appropriate control parameters can result in a regular decline of near-wall streaks and vortex structures with respect to the flow direction,leading to the effective suppression of turbulence generation and significant reduction in skin-friction drag.In addition,experiments are carried out in a water tunnel via electro-magnetic(EM)actuators designed to produce the bidirectional traveling wave excitation as described in calculations.As a result,the actual substantial drag reduction is realized successfully in these experiments.
