Universality of Zipf's Law

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows that the behavior of the model is very robust and universal.Comment: 5 eps files included. To be published in J. Phys. Soc. Jp

Homogeneous nucleation in spatially inhomogeneous systems

Homogeneous nucleation of a vapor in the presence of the loss of clusters by diffusion and thermophoretic drift is investigated. Analytical results are obtained for the cluster size distribution and the rate of nucleation by solving the modified kinetic equation for nucleation. The implications of cluster loss by diffusion and phoretic drift on the onset of the homogeneous nucleation of silicon vapor in the horizontal epitaxial chemical vapor deposition reactor is discussed. The range of conditions under which the loss of subcritical clusters by diffusion and drift becomes important for the interpretation of diffusion cloud chamber experimental data of the onset conditions of the homogeneous nucleation of vapors is also delineated

Binary nucleation in acid–water systems. II. Sulfuric acid–water and a comparison with methanesulfonic acid–water

This work presents a systematic investigation of binary nucleation rates for sulfuric acid and water and the effect of temperature on these rates at isothermal, subsaturated conditions. The results from nucleation rate measurements for the sulfuric acid (H2SO4)–water system are discussed and compared to those previously presented for methanesulfonic acid (MSA)–water [B. E. Wyslouzil, J. H. Seinfeld, R. C. Flagan, and K. Okuyama, J. Chem. Phys. (submitted)]. Experiments were conducted at relative humidities (Rh) ranging from 0.006<Rh<0.65, relative acidities (Ra) in the range of 0.04<Ra<0.46, and at three temperatures, T=20, 25, and 30 °C, in the continuous flow mixing-type apparatus described in Paper I. Particles were formed by binary nucleation and grew by condensation as the mixed stream flowed through an isothermal glass tube. Number concentrations observed at the exit of the nucleation and growth tube as a function of Rh and Ra are extremely sensitive to the binary nucleation rate, and from these data the nucleation rate was estimated as a function of saturation level and temperature. Particle size distributions were also measured using a specially constructed differential mobility analyzer. As anticipated, the H2SO4 particles formed by nucleation and growth are much smaller than those formed in the MSA–water experiments, but particle size distribution measurements confirm that most of the particles formed are being observed. The ratio of experimental to theoretical nucleation rates, Jexpt/Jtheor, was found to be a strong function of the predicted number of acid molecules in the critical nucleus for both the H2SO4–water and MSA–water systems