In the first part of this article we review the theory of flux motion in conventional superconductors. We then describe the recent developments in the theory of vortex motion in the mixed state of high-T c superconductors. In particular, a unified theory of vortex motion in the presence of thermal fluctuations and pinning centres is introduced in detail. Applications of this theory are presented to account for such experimentally observed phenomena as the scaling behaviour, sign reversal of the Hall resistivity and properties of the complex resistivity. Moreover, theoretical investigations on the thermomagnetic effects such as the Nernst and Seebeck effects, and the Ettinghausen effect are also addressed. Such an analysis using the single-vortex-motion model could provide an understanding of many physical properties of high-T c superconductors.

The nonlinear a.c. response of the flux motion in type II superconductors is studied using a single flux motion model. We have performed a numerical simulation and evaluated the a.c. response against frequency. Three cases of applied current are considered a single-frequency ax. current, an a.c. current of two frequencies and a d.c. plus an a s . current. We find that, when the Lorentz driving force is greater than the pinning force, there exists a crossover frequency below which a strong nonlinear a.c:response is exhibited. We also find that the value of this crossover frequency has a linear relation with the ratio of the Lorentz and the pinning forces.