Section for Mathematical Physics
Abstract: One of the most successful applications of the sine-Gordon (sG) equation pertains to the dynamics of fluxons in long Josephson junctions in one spatial dimension. In an oscillating mode the power output from one junction is very weak and in some technical applications it is desirable to enhance the power output by coupling several long Josephson junctions together in a stack. This leads to studies of phase locking of fluxons for maximum power output and the stability of such phase locked states. By introducing a piecewise linear approximation to the nonlinear sine() term we have been able to obtain accurate simple analytical results of the dynamics of coupled Joesphson junctions.
A particular promising result concerns the dynamics of fluxons travelling through a curved planar Josephson junction. The region with finite curvature manifests itself as a potential barrier whose height and width depends on the curvature and of the radius of the waveguide. The kink transmission, reflection and trapping has been investigated. The kink may be captured when a driving force, provided by a magnetic field, is applied to the kink. This study shows that by changing the geometry of waveguides one can efficiently control the dynamics of nonlinear excitations. This feature could be applied to electronic devices for storing binary data.
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Start date: January 2000
End date: December 2002