Amplitude stochastic response of Rayleigh beams to randomly moving loads

We consider the problem of the nonlinear response of a Rayleigh beam to the passage of a train of forces moving with stochastic velocity. The Fourier transform and the theory of residues are used to estimate the mean square amplitude of the beam, while the stochastic averaging method gives the stationary probability density function of the oscillations amplitude. The analysis shows that the effect of the load random velocities is highly nonlinear, leading to a nonmonotonic behavior of the mean amplitude versus the intensity of the stochastic term and of the load weight. The analytic approach is also checked with numerical simulations. The effect of loads number on the system response is numerically investigated.     

High-T c Josephson junctions for electronic applications

Summary The current status of the electronic applications of high-T _c Josephson junctions is briefly reviewed. Recent results obtained by the authors on devices employing step-edge junctions are reported. In particular the design of a microwave oscillator based on a parallel array of junctions is discussed and preliminary experimental results are presented. Paper presented at the ?VII Congresso SATT? Torino, 4–7 October 1994.     

Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω _J becomes equal to the natural frequency ω_rc of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.     

Mutual inductance effects in rf driven planar Josephson junctions arrays

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed an explicit set of differential equations. We have found that the discretization parameter - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full model with mutual inductances, while the limits for very large and very small values of they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., small ) as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large ). Received 9 November 1998 and Received in final form 6 April 1999     

Stability of the synchronization manifold in nearest neighbor nonidentical van der Pol-like oscillators

We investigate the stability of the synchronization manifold in a ring and in an open-ended chain of nearest neighbor coupled self-sustained systems, each self-sustained system consisting of multi-limit cycle van der Pol oscillators. Such a model represents, for instance, coherent oscillations in biological systems through the case of an enzymatic-substrate reaction with ferroelectric behavior in a brain waves model. The ring and open-ended chain of identical and nonidentical oscillators are considered separately. By using the Master Stability Function approach (for the identical case) and the complex Kuramoto order parameter (for the nonidentical case), we derive the stability boundaries of the synchronized manifold. We have found that synchronization occurs in a system of many coupled modified van der Pol oscillators, and it is stable even in the presence of a spread of parameters.     

Coherence and stochastic resonance in a birhythmic van der Pol system

We consider the response to uncorrelated noise and harmonic excitation of a birhythmic van der Pol-type oscillator. This system, as opposed to the standard van der Pol oscillator, is characterized by two stable orbits. The noisy oscillator can be analytically mapped, with the technique of stochastic averaging, onto an ordinary bistable system with a bistable (quasi)potential. The birhythmic oscillator can also be numerically characterized through the diagnostics of coherent resonance and the signal-to-noise-ratio. The analysis shows the presence of noise-induced coherent states, influenced by the different time scales of the oscillator.