Modeling and study of dynamics of micro-beam coupled to two Josephson junctions

Abstract

In this work, we proposed to study the dynamics of a bi-recessed micro-beam coupled magnetically to two Josephson junctions. After building a model of micro electro mechanical systems (MEMS), the equations of their dynamics are determined. The fixed points of system are analytically checked and their stability is analyzed by using the Routh–Hurwitz criterion. For this purpose, a numerical study utilizing the bifurcation diagram, Lyapunov exponents, phase portraits and time histories is made to analyze the different dyanamic modes of micro-beam coupled to two Josephson junctions. The effect of Josephson junctions on the behavior of the micro-beam is seriously analyzed. It is obtained for each part of the MEMS the various dynamics influenced by certain parameters of the system.

Dynamical analysis and microcontroller implementation of fractal resistive-capacitive shunted Josephson junction

“…Regarding fractal integration, the investigation of unpredicted matrix theory, with special consideration on energy level spectrum and fractal characteristics was exploited by Sani and Behnia [47], and complex association of inductivity from length as the overall contribution of both the 2D and 3D fractal behaviors of respectively the coplanar microwave transmission lines and the W is provided by not only fractal features of CTL twodimensional surface but fractal features of three-dimensional Au grain distribution over skin depth wide was investigated by Torkhov et al [48]. Also, the JJ was observed in different contributions including the investigation of the dynamics exhibited by coupling two JJ to micro-beam [49], evaluations of the dynamics of the long 0-π JJwith applications to digital single flux quantum circuits [50], the comparison of the theoretical evaluation of quantum optical micro maser and JJ-photonics systems [51], the observations ofchaos, transient chaos, the coexistence of solutions, coexistence of attractors, and bursting oscillation just to cite some were observed in the findings of [52], the investigation of the magnetic characteristics of artificial nanoparticles via their hysteresis curves for vibrating sample magnetometerwas carried out by [53], the detail investigation of the hysteresis characteristics of the thermodynamic and magnetocaloric behaviors of a three-layer graphene-like schematic [54], and finally the investigation of the JJ with high critical-temperaturesuperconductors [55].…”

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects

“…The Josephson junction is a suitable choice among many other mechanical devices. This has been the subject of intensive research recently [27][28][29][30][31]. Moreover, there are multiple applications for Josephson junctions in various fields such as engineering, health and communication.…”

“…Moreover, there are multiple applications for Josephson junctions in various fields such as engineering, health and communication. Koudafokê et al studied the influence of a Josephson junction on the dynamic modes of the micro-beam oscillator [27]. They also modeled and analyzed the electro dynamic modes of a self-sustaining active sensor with Josephson junctions [28].…”