TABLE OF CONTENTS The theory of the random motion of a particle through space has a variety of uses. Two important applications are to molecular or atomic diffusion, and to the statistics of long chain molecules. To clarify the concept of random flight, consider a particle that, starting from a fixed point R o = 0, can move a distance r in any direction. After the first jump, the particle can again move in any direction, but with the same distance r. That is, the motion of the particle consists of a number of N sequential jumps in an arbitrary direction, but all having the same magnitude. The particle is said to have executed a random flight of N equal-sized steps that are defined by the set of vectors { r} N ? r 1, r 2, r 3, , r N, each having a magnitude r, after which it has moved a distance R.
Each step is called a jump, and the distance from the starting point after N jumps is called the total displacement. An example of a random flight in two dimensions is shown in figure 13.1. For a general random flight, the jump distances do not necessarily all have the same magnitude.
Two important properties of a random flight that arise in physical applications are the scalar distance R = R between the starting...
