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

Classical Group Field Theory

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored) defined over a tensor product of the same group, we address the issue of translation and dilatation symmetries and the corresponding Noether theorem. The energy momentum tensor and dilatation current are derived and their properties identified for each case