## 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.