An Improved Architecture of Sixth Subharmonic Mixers in E-Band

An improved architecture of sixth subharmonic mixers is proposed in this paper. In order to meet the need of low conversion loss, antiparallel diodes are selected and the length of four open/shorted microstrip stubs at both sides of the antiparallel diodes are carefully designed. For any important idle frequency components which can’t be reused by the four stubs, reactive terminations are presented by adjusting the length of main RF and LO microstrip. The tested results indicate the lowest conversion loss is 26.1 dB at the radio frequency of 72 GHz, with fixed LO at 12 GHz. The proposed circuit architecture is suitable for the implementation of subharmonic mixers in E-band as well as other millimeter and submillimeter-wave regions where high quality and high frequency LOs are difficult to realize. Supported in part by National Natural Science Foundation of China (NSFC) under Grants 60621002 and in part by NSFC under Grants 60471017.     

Ion acoustic subharmonic excitation in a plasma

Ion acoustic subharmonic excitation in a plasma, with ion-neutral collision frequency greater than the frequency of excitation, is theoretically investigated. Two-fluid theory with source term is used to describe the system. The system exhibits either subharmonic excitation of orders 1/2 and 1/3, or subharmonic excitation of orders 1/3, 1/4 and 1/5. The resonance frequency range and the amplitude of second harmonic for each case is calculated. A comparison with experimental data can be used to obtain the values of the parameters describing the source term.     

A weak-type inequality of subharmonic functions

We prove the weak-type inequality , , between a non-negative subharmonic function and an -valued smooth function , defined on an open set containing the closure of a bounded domain in a Euclidean space , satisfying , and , where is a constant. Here is the harmonic measure on with respect to 0. This inequality extends Burkholder's inequality in which and , a Euclidean space.

     

Solitary waves and chaos in nonlinear visco-elastic rod

The dynamics behavior of a nonlinear visco-elastic rod subjected to axially periodic load is investigated theoretically and numerically. The weak longitudinal periodic load is distributed uniformly along the rod. Firstly, equation of motion of the rod is derived. Utilizing perturbation technique, we acquire Kdv type equation describing strain wave in the rod. By use traveling wave method, the elliptic cosine wave solution and the solitary wave solution in the rod are provided. Then, Melnikov method is applied to analyze the dynamic behaviour of the rod qualitatively. The explicit conditions for the onset of chaotic dynamics are yielded. With the help of the Poincare map method, phase trajectory and time-displacement history diagrams, the theoretical results obtained are checked.     

Dynamic stability of axially accelerating Timoshenko beam: Averaging method

This study investigates dynamic stability in transverse parametric vibrations of an axially accelerating tensioned beam of Timoshenko model on simple supports. The axial speed is assumed as a harmonic fluctuation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a finite set of ordinary differential equations. The method of averaging is applied to analyze the instability phenomena caused by subharmonic and combination resonance. Numerical examples demonstrate the effects of the mean axial speed, bending stiffness, rotary inertia and shear modulus on the instability boundaries.     

Some properties of conjugate harmonic functions in a half-space

We prove a multi-dimensional analog of the theorem of Hardy and Littlewood about the logarithmic bound of the Lp-average of the conjugate harmonic functions, 0<p?1. We also give sufficient conditions for a harmonic vector to belong to , 0<p?1.     

Periodic shock-emission from acoustically driven cavitation clouds: A source of the subharmonic signal

Single clouds of cavitation bubbles, driven by 254 kHz focused ultrasound at pressure amplitudes in the range of 0.48–1.22 MPa, have been observed via high-speed shadowgraphic imaging at 1 × 10⁶ frames per second. Clouds underwent repetitive growth, oscillation and collapse (GOC) cycles, with shock-waves emitted periodically at the instant of collapse during each cycle. The frequency of cloud collapse, and coincident shock-emission, was primarily dependent on the intensity of the focused ultrasound driving the activity. The lowest peak-to-peak pressure amplitude of 0.48 MPa generated shock-waves with an average period of 7.9 ± 0.5 μs, corresponding to a frequency of f₀/2, half-harmonic to the fundamental driving. Increasing the intensity gave rise to GOC cycles and shock-emission periods of 11.8 ± 0.3, 15.8 ± 0.3, 19.8 ± 0.2 μs, at pressure amplitudes of 0.64, 0.92 and 1.22 MPa, corresponding to the higher-order subharmonics of f₀/3, f₀/4 and f₀/5, respectively. Parallel passive acoustic detection, filtered for the fundamental driving, revealed features that correlated temporally to the shock-emissions observed via high-speed imaging, p(two-tailed) < 0.01 (r = 0.996, taken over all data). Subtracting the isolated acoustic shock profiles from the raw signal collected from the detector, demonstrated the removal of subharmonic spectral peaks, in the frequency domain. The larger cavitation clouds (>200 μm diameter, at maximum inflation), that developed under insonations of peak-to-peak pressure amplitudes >1.0 MPa, emitted shock-waves with two or more fronts suggesting non-uniform collapse of the cloud. The observations indicate that periodic shock-emissions from acoustically driven cavitation clouds provide a source for the cavitation subharmonic signal, and that shock structure may be used to study intra-cloud dynamics at sub-microsecond timescales.     

Nonlinear stochastic analysis of subharmonic response of a shallow cable

The paper deals with the subharmonic response of a shallow cable due to time variations of the chord length of the equilibrium suspension, caused by time varying support point motions. Initially, the capability of a simple nonlinear two-degree-of-freedom model for the prediction of chaotic and stochastic subharmonic response is demonstrated upon comparison with a more involved model based on a spatial finite difference discretization of the full nonlinear partial differential equations of the cable. Since the stochastic response quantities are obtained by Monte Carlo simulation, which is extremely time-consuming for the finite difference model, most of the results are next based on the reduced model. Under harmonical varying support point motions the stable subharmonic motion consists of a harmonically varying component in the equilibrium plane and a large subharmonic out-of-plane component, producing a trajectory at the mid-point of shape as an infinity sign. However, when the harmonical variation of the chordwise elongation is replaced by a narrow-banded Gaussian excitation with the same standard deviation and a centre frequency equal to the circular frequency of the harmonic excitation, the slowly varying phase of the excitation implies that the phase difference between the in-plane and out-of-plane displacement components is not locked at a fixed value. In turn this implies that the trajectory of the displacement components is slowly rotating around the chord line. Hence, a large subharmonic response component is also present in the static equilibrium plane. Further, the time variation of the envelope process of the narrow-banded chordwise elongation process tends to enhance chaotic behaviour of the subharmonic response, which is detectable via extreme sensitivity on the initial conditions, or via the sign of a numerical calculated Lyapunov exponent. These effects have been further investigated based on periodic varying chord elongations with the same frequency and standard deviation as the harmonic excitation, for which the amplitude varies in a well-defined way between two levels within each period. Depending on the relative magnitude of the high and low amplitude phase and their relative duration the onset of chaotic vibrations has been verified.     

Period doubling bifurcations for families of maps on ℝ n

Infinite sequences of period doubling bifurcations in one-parameter families (1-pf) of maps enjoy very strong universality properties: This is known numerically in a multitude of cases and has been shown rigorously for certain 1-pf of maps on the interval. These bifurcations occur in 1-pf of analytic maps at values of the parameter tending to a limit with the asymptotically geometric ratio 1 /4.6692 ....In this paper we indicate the main steps of a proof that the same is true for 1-pf of analytic maps from ⁿ to ⁿ , whose restriction to ⁿ is real.Work supported by the Fonds National Suisse, and by the National Science Foundation under Grant PHY-79-16812.     

Periodic and subharmonic solutions of a class of superquadratic Hamiltonian systems

Periodic solutions and infinitely distinct subharmonic solutions are obtained for a class of nonconvex and nonautonomous superquadratic Hamiltonian systems by using the minimax methods in critical point theory.