Vortex patterns in mesoscopic superconducting ellipses and strips

Vortex patterns inside a saperconducting elliptic sample are considered. In the London approximation, the energy of a given configuration is calculate d analytically by the method of Fourier series, in terms of the positions o f the vortices. These positions are determined by numerical minimization of the energy, for given applied held and shape of the ellipse. Vortices appe ar to arrange themselves in particuliar classes of geometrical structures a nd the magnetic fields responsible for the transitions, from one geometry: to the other, are found to be roughly independent of the shape of the ellip se. For a superconducting strip, we find vortex-line transitions which are clearly seen in the magnetization curves. A paramagnetic effect is observed in the case of small samples.