4,327 research outputs found
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
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