This paper presented a new Floquet analysis used to calculate the radiation for 1-D and 2-D coupled periodic antenna systems. In this way, an accurate evaluation of mutual coupling can be proven by using a new mutual ...This paper presented a new Floquet analysis used to calculate the radiation for 1-D and 2-D coupled periodic antenna systems. In this way, an accurate evaluation of mutual coupling can be proven by using a new mutual interaction expression that was based on Fourier analysis. Then, this work indicated how Floquet analysis can be used to study a finite array with uniform amplitude and linear phase distribution in both x and y directions. To modelize the proposed structures, two formulations were given in a spectral and spatial domain, where the Moment (MoM) method combined with a generalized equivalent circuit (GEC) method was applied. Radiation pattern of coupled periodic antenna was shown by varying many parameters, such as frequencies, distance and Floquet states. The 3-D radiation beam of the coupled antenna array was analyzed and compared in several steering angles θs and coupling values dx. The simulation of this structure demonstrated that directivity decreased at higher coupling values. The secondary lobs in the antenna radiation pattern affected the main lobe gain by energy dispersal and considerable increasing of side lobe level (SLL) may be achieved. Therefore, the sweeping of the radiation beam in several steering directions affected the electromagnetic performance of the antenna system: the directivity at the steering angle θs = π⁄3 was more damaged and had 19.99 dB while the second at θs = 0 had about 35.11 dB. This parametric study of coupled structure used to concept smart periodic antenna with sweeping radiation beam.展开更多
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e.,...The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.展开更多
Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two d...Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two dimensions in nor mal direction. The existence and the normal hyperbolicity of the 2-dimensional invariant torus and the 3-dimensional invariant torus are given. The phenome non of bifurcation for the 3-dimensional invariant torus from one single periodic orbit is discovered for the first time.展开更多
文摘This paper presented a new Floquet analysis used to calculate the radiation for 1-D and 2-D coupled periodic antenna systems. In this way, an accurate evaluation of mutual coupling can be proven by using a new mutual interaction expression that was based on Fourier analysis. Then, this work indicated how Floquet analysis can be used to study a finite array with uniform amplitude and linear phase distribution in both x and y directions. To modelize the proposed structures, two formulations were given in a spectral and spatial domain, where the Moment (MoM) method combined with a generalized equivalent circuit (GEC) method was applied. Radiation pattern of coupled periodic antenna was shown by varying many parameters, such as frequencies, distance and Floquet states. The 3-D radiation beam of the coupled antenna array was analyzed and compared in several steering angles θs and coupling values dx. The simulation of this structure demonstrated that directivity decreased at higher coupling values. The secondary lobs in the antenna radiation pattern affected the main lobe gain by energy dispersal and considerable increasing of side lobe level (SLL) may be achieved. Therefore, the sweeping of the radiation beam in several steering directions affected the electromagnetic performance of the antenna system: the directivity at the steering angle θs = π⁄3 was more damaged and had 19.99 dB while the second at θs = 0 had about 35.11 dB. This parametric study of coupled structure used to concept smart periodic antenna with sweeping radiation beam.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1120214711332007+2 种基金11172203and 91216111)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120032120007)
文摘The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.
文摘Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two dimensions in nor mal direction. The existence and the normal hyperbolicity of the 2-dimensional invariant torus and the 3-dimensional invariant torus are given. The phenome non of bifurcation for the 3-dimensional invariant torus from one single periodic orbit is discovered for the first time.
