Signal properties of radio frequency SQUID with a finite amplitude of the second harmonic in the current-phase relationship

2001 ◽  
Vol 11 (1) ◽  
pp. 1114-1117
Author(s):  
E. Ilichev ◽  
Ya.S. Greenberg ◽  
R.P.J. Ijsselsteijn ◽  
V. Schultze ◽  
H.E. Hoenig ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Second Harmonic ◽  
Phase Relationship ◽  
Finite Amplitude ◽  
Current Phase

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

2016 ◽  
Vol 30 (08) ◽  
pp. 1650096 ◽  
Author(s):  
Shuzeng Zhang ◽  
Xiongbing Li ◽  
Hyunjo Jeong
Keyword(s):  
Rayleigh Waves ◽  
General Equation ◽  
Wave Motion ◽  
Numerical Solutions ◽  
Second Harmonic ◽  
Approximate Equation ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Quasilinear Theory ◽  
Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

scholarly journals Interferometric Measurement of the Current-Phase Relationship of a Superfluid Weak Link

2014 ◽  
Vol 4 (3) ◽  
Author(s):  
S. Eckel ◽  
F. Jendrzejewski ◽  
A. Kumar ◽  
C. J. Lobb ◽  
G. K. Campbell
Keyword(s):  
Weak Link ◽  
Phase Relationship ◽  
Current Phase ◽  
Interferometric Measurement ◽  
Relationship Of

scholarly journals Manipulation of Cooper Pair Entanglement in Hybrid Topological Josephson Junctions

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 44
Author(s):  
Gianmichele Blasi ◽  
Fabio Taddei ◽  
Vittorio Giovannetti ◽  
Alessandro Braggio
Keyword(s):  
Critical Current ◽  
Cooper Pair ◽  
Phase Relationship ◽  
Scattering Matrix ◽  
Entangled States ◽  
Current Phase ◽  
Matrix Approach ◽  
Non Local ◽  
Relationship Of ◽  
Direct Quantification

The non-local manipulation of spin-entangled states by means of local gating in two parallel 2D topological insulators properly connected to two superconducting electrodes is studied. We calculate analytically the current-phase relationship of the Josephson current making use of the scattering matrix approach and we identify the various local and non-local scattering mechanisms. We show that the Josephson critical current, remarkably, allows a direct quantification of the entanglement manipulation.

Formation and recurrence of ion wave solitons

1975 ◽  
Vol 13 (2) ◽  
pp. 217-230 ◽  
Author(s):  
S. Watanabe
Keyword(s):  
Exact Solution ◽  
Numerical Analysis ◽  
Nonlinear Wave ◽  
Vries Equation ◽  
Dispersive Medium ◽  
Second Harmonic ◽  
Sine Wave ◽  
Finite Amplitude ◽  
Initial State ◽  
Coupled Mode

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.

Current-Phase Relationship in Short Superconducting Weak Links

1970 ◽  
Vol 25 (25) ◽  
pp. 1738-1738 ◽  
Author(s):  
A. Baratoff ◽  
J. A. Blackburn ◽  
B. B. Schwartz
Keyword(s):  
Phase Relationship ◽  
Weak Links ◽  
Current Phase

On the shape and breaking of finite amplitude internal gravity waves in a shear flow

1978 ◽  
Vol 85 (1) ◽  
pp. 7-31 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Shear Flow ◽  
Internal Waves ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Mixing Layer ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Depth Interval ◽  
Plane Shear

This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.

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