Date of Award


Document Type


Degree Name

Master of Science in Materials Science and Engineering (MSMSE)


Mathematical Sciences

First Advisor

Maamar Benkraouda

Second Advisor

Bashir Suleiman

Third Advisor

Hassan Ghamlouche


The high temperature superconductors are very promising materials in a wide range of applications, starting from the electricity power supply. They play a lifesaving function through imaging systems. Even major internet and communication advances depend on these materials.

Superconductivity in these materials occurs particularly in the copper-oxide planes. However, since these materials are type-II superconductors, magnetic fields can penetrate these materials in quantized amounts of flux called vortices without destroying completely superconductivity, but producing some resistance, due to vortex motion. In order to overcome the resistance problem, vortices must be pinned to prevent their motion and hence eliminate the resistance.

In this thesis, we will model the magnetic pancake vortices in a finite stack of superconducting layers. Pinning centers are uniformly distributed in each layer but the strength of these pinning centers is random from one layer to another to see their effect on the conductivity of the superconducting layers.

In chapter two, we apply equal but oppositely directed de currents to the outermost layers, where two different cases are considered (1) free-pinning sample and (2) pinned sample. Decoupling current as function of the applied magnetic field as well as number superconducting layers is shown.

In chapter three, dc current is applied to one of the outermost layers. Velocities of outermost layers as well as displacement difference between the top layer and the layer below it are calculated. Moreover, time averaged voltages due to the motion of pancakes is computed for outermost layers. In addition, magnetic flux flow rate at the top layer and flux flow rate difference between outermost layers are shown. All these calculations are done in presence and absence of vortex pinning.

In chapter four, ac current is applied to the top layer. Velocities of top and bottom layers as well as displacement difference between the top layer and the layer below it are shown. In addition, flux flow rate difference between outermost layers as a function of time is computed and ac losses are shown.