Calculation of the Frequency Dependent Conductivity of a Composite Medium Using Random Walks

Abstract

The Research for my Senior Individualized Project was done in the Physics department at Kalamazoo College. I need to explain my use of vectors and scalars. For example, I used r to denote the position vector of the random walker relative to the starting point and used r to denote the distance from the starting point. In some parts of this paper I called the mean-square displacement of the walker <r2(t)> and in others I called it <r2(t)>. There is no problem in interchanging the scalar r and the vector r, because r2 = IIrll2 = r·r = r2. I only used the vector notation in section 2, where I needed to prove a general fact in 1, 2, or 3 dimensions. In every other section I used scalars. Programs for this paper were written in True Basic and run on a Macintosh II computer.