thesis abstract
## KINETIC PROPERTIES OF STOCHASTIC PROCESSES [ PostScript ]

### Author: Eli Ben-Naim

### Advisor: Sidney Redner, Boston University Physics Department

In this thesis, kinetic and steady state properties of a range of
stochastic and nonequilibrium models are investigated. A typical
process is specified by a transport mechanism and a reaction mechanism
and this leads naturally to simple ``toy-like'' models.
In the first part, the kinetics of ballistically-controlled reactions
with continuous initial particle velocity distributions are studied. A
non-universal power-law decay is found for both the concentration and
the velocity, with the characteristic exponents governed by the
form of the initial velocity distribution. For the case where particles
annihilate upon contact, a mean-field theory provides good estimates for
the decay kinetics. A ballistic
aggregation model, inspired by one-lane traffic flows, is solved and the
qualitative behavior of the reaction process is determined. The
contribution of diffusion to the annihilation process with a bimodal
initial velocity distribution is also studied. Using scaling arguments
and series analysis techniques, it is shown that introduction of
diffusion, even if small, alters the asymptotic behavior of the
concentration of particles.

In the second part, a steady state model of the inhomogeneous
two-species annihilation reaction, *A+B--> 0*, is presented. In this
model, two different species *A* and *B* are injected with equal fluxes at
the opposite boundaries of a finite system. Analytical results for the
concentration profile are obtained by solving the reaction-diffusion
equations. The dependence of the reaction rate on the flux is found and
this result is applied to the time-dependent reaction model.

In the third part, collective properties of adsorption-desorption models
in one dimension are studied. The steady state of a reversible parking
process, where monodisperse particles adsorb and desorb
on a one-dimensional substrate, is solved.
The system exhibits a weak dependence on the adsorption rate in the
desorption-controlled regime. To understand this behavior, an
irreversible model incorporating immediate adsorption as well as
desorption is introduced. A slow approach to the fully occupied state is
found by heuristic arguments and by simulations. Furthermore, a cluster
approximation technique is suggested to analyze the critical nature of a
one-dimensional irreversible adsorption-desorption model.