DIFFUSION EQUATION FOR ONE-DIMENSIONAL UNBIASED HOPPING

A computer simulation is presented of a one-dimensional particle migra tion by local hopping of Chandrasekhar type with no local bias but wit h hopping rates which vary with position in the system. Of the two pos sible diffusion equations to represent the process, one is clearly sho wn to be wrong while the other gives an accurate representation of the evolution of the system. The cases of both reflecting and absorbing b oundaries are considered, and in the latter case a sum-rule previously derived for this type of random migration is verified. The concept of local particle traffic is introduced. Arguments are presented to show that the spatial traffic distribution gives a better insight into som e aspects of particle activity than the probability distribution. (C) 1997 American Association of Physics Teachers.