We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency.

A population of eight non-overlapping domain decomposition methods for solving elliptic differential equations are viewed and formulated as iterated interface relaxation procedures. A comprehensive review of the underlying mathematical ideas and the computational characteristics is given. The existing theoretical results are also reviewed and high level descriptions of the various algorithms are presented. The effectiveness of these methods on I-dimensional differential problems is investigated by presenting and discussing preliminary performance evaluation data.

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results are in terms of elliptic functions for the case of inline geometry, and are in agreement with the numerical calculations, explaining also the strong hysteretic phenomena typically seen in the calculation of the maximum tunnelling current. This suggests a different experimental approach based on the use, instead of the external magnetic field, of the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behaviour and unfold the overlapping Imax (H ) curves.