Simulation of Dynamical Processes in Long Josephson Junctions: Computation of Current-Voltage Characteristics and Round Error Growth Estimation for a Second-Order Difference Scheme

2020 ◽  
Vol 60 (1) ◽  
pp. 171-178
Author(s):  
S. I. Serdyukova
Keyword(s):  
Difference Scheme ◽  
Josephson Junctions ◽  
Second Order ◽  
Error Growth ◽  
Dynamical Processes ◽  
Order Difference ◽  
Current Voltage ◽  
Current Voltage Characteristics ◽  
Growth Estimation

A Numerical Simulation Algorithm of the Inviscid Dynamics of Axisymmetric Swirling Flows in a Pipe

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
J. Granata ◽  
L. Xu ◽  
Z. Rusak ◽  
S. Wang
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Difference Scheme ◽  
Second Order ◽  
Swirling Flows ◽  
Inviscid Limit ◽  
Simulation Algorithm ◽  
Spatial Integration ◽  
Order Difference ◽  
Breakdown Process

Current simulations of swirling flows in pipes are limited to relatively low Reynolds number flows (Re < 6000); however, the characteristic Reynolds number is much higher (Re > 20,000) in most of engineering applications. To address this difficulty, this paper presents a numerical simulation algorithm of the dynamics of incompressible, inviscid-limit, axisymmetric swirling flows in a pipe, including the vortex breakdown process. It is based on an explicit, first-order difference scheme in time and an upwind, second-order difference scheme in space for the time integration of the circulation and azimuthal vorticity. A second-order Poisson equation solver for the spatial integration of the stream function in terms of azimuthal vorticity is used. In addition, when reversed flow zones appear, an averaging step of properties is applied at designated time steps. This adds slight artificial viscosity to the algorithm and prevents growth of localized high-frequency numerical noise inside the breakdown zone that is related to the expected singularity that must appear in any flow simulation based on the Euler equations. Mesh refinement studies show agreement of computations for various mesh sizes. Computed examples of flow dynamics demonstrate agreement with linear and nonlinear stability theories of vortex flows in a finite-length pipe. Agreement is also found with theoretically predicted steady axisymmetric breakdown states in a pipe as flow evolves to a time-asymptotic state. These findings indicate that the present algorithm provides an accurate prediction of the inviscid-limit, axisymmetric breakdown process. Also, the numerical results support the theoretical predictions and shed light on vortex dynamics at high Re.

EFFECT OF THERMAL NOISE ON THE CURRENT-VOLTAGE CHARACTERISTICS OF JOSEPHSON JUNCTIONS

1996 ◽  
Vol 10 (22) ◽  
pp. 1095-1102 ◽  
Author(s):  
A.K. CHATTAH ◽  
C.B. BRIOZZO ◽  
O. OSENDA ◽  
M.O. CÁCERES
Keyword(s):  
Josephson Junctions ◽  
Thermal Noise ◽  
Planck Equation ◽  
Resonance Problem ◽  
Shapiro Steps ◽  
Periodic Distribution ◽  
Current Voltage ◽  
Current Voltage Characteristics ◽  
Path Integral Method ◽  
Asymptotic Time

We analyze the influence of thermal noise on the Shapiro steps appearing in the current-voltage characteristics of Josephson junctions. We solve the Fokker-Planck equation describing the system by a path integral method in the steepest-descent approximation, previously applied to the stochastic resonance problem. We obtain the Asymptotic Time-Periodic Distribution Pas(ϕ, t), where ϕ∈[0, 2π] and compute from it the voltage [Formula: see text], constructing the I-V characteristics. We find a defined “softening” of the Shapiro steps as temperature increases, for values of the system parameters in the experimentally accessible range.

Current-voltage characteristics of interacting Josephson junctions

1980 ◽  
Author(s):  
A. K. Jain ◽  
J. E. Lukens ◽  
Kin Li ◽  
R. D. Sandell ◽  
C. Varmazis
Keyword(s):  
Josephson Junctions ◽  
Current Voltage ◽  
Current Voltage Characteristics
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