The order parameter of superconducting pairs penetrating an inhomogeneous magnetic material can acquire a long range triplet component (LRTC) with non-zero spin projection. This state has been predicted and generated recently in proximity systems and
Josephson junctions. We show using an analytically derived domain wall of an exchange spring how the LRTC emerges and can be tuned with the twisting of the magnetization. We also introduce a new kind of Josephson current reversal, the triplet $0-pi$ transition, that can be observed in one and the same system either by tuning the domain wall or by varying temperature.
Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appea
r: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.
