# Accession Number:

## AD0673234

# Title:

## WALKS ON A RANDOM BINARY VELOCITY FIELD.

# Descriptive Note:

## Doctoral thesis,

# Corporate Author:

## JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MECHANICS

# Personal Author(s):

# Report Date:

## 1966-02-01

# Pagination or Media Count:

## 229.0

# Abstract:

This is a study of a class of one-dimensional random walks in which probabilities are assigned not to the walking particle, but to the random binary velocity field on which the particle moves. Since there exists a unique transformation from velocity field to trajectory, the statistics of the walk may be obtained by examining the transformation. Motivation for studying these walks comes from the problem of the dispersion of a particle-attached containment in a turbulent fluid given some statistical information about the velocity field, what may one say about the statistics of the dispersing particle. Experiments were done, with the aid of a digital computer, on two types of velocity fields 1 fields generated by a filtering or averaging process, and 2 fields generated by two first order Markov chains. An analytical solution is given for the second case, while for the more general class of filtered fields as well as for any binary velocity fields satisfying certain symmetry requirements, the initial behavior of a walking particle is related to the velocity field. Another class of random walks in which probabilities are assigned directly to the walking particle is examined. These are more nearly like the classical random walk except that the sequence of particle velocities forms a first, second, or third order Markov chain. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Nuclear Physics and Elementary Particle Physics