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.