Tomomasa Nagamine

Power-law distribution of family names in Japanese societies

We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.

Family Name Distribution in Japanese Societies

We have studied on the empirical distributions of Japanese family name appearing in a telephone directory, and found the good power-law behaviors on their distributions. In this paper we propose a possible model of family name distribution based on the mixture of diffusion-limited aggregation (DLA) and percolation growths.

Growth properties of Eden model with acceleration sites

One plus one dimensional growth of an Eden model with acceleration sites is investigated by simulations, where the acceleration sites which are distributed at random before the process starts become immediately Eden cells if the surface of Eden cluster touches them. The critical concentration of acceleration sites where the growth rate of the average cluster height diverges is found as pc=0.592±0.005 corresponding to the site percolation threshold of the square lattice. The exponent which characterizes this divergence near the percolation threshold have been found as ν=1.33±0.08. An effective roughness exponent α which characterizes the surface morphology is found to belong to the same universality class as the Eden model for p<pc. At the critical concentration, the present system changes to hold a self-similar surface.

AN INTERFACE OBTAINED BY COLLISION OF TWO INDEPENDENT ROUGH SURFACES : INVASION BY BURNING OF PAPER

Abstract The growing surface at a fire front has the property of self-affinity. We start fires from two opposite edges of rectangular paper and obtain two independent rought surfaces with roughness exponent α = 0.73 and growth exponent β ′ = 0.47. The two independent fronts later collide in the central region of the paper to form an interface with roughness exponent α ′ = 0.67 and growth exponent β ′ = 0.22.

FRACTAL PROPERTIES OF THE EDEN COLLISION INTERFACE

Abstract We have simulated the growth of the Eden collision interface produced by the collision of two independent rough growth surfaces made by the Eden process and measured the cluster size s and the number of the clusters n s of the collision interface. Here, we have assumed the scaling form of s and n s as n s ≈ N γ f(s/N ɛ ) , where N = Σ s · n s . We have obtained good scaling. Furthermore, we have also considered the scaling relation 2ɛ + γ = 1.

SURFACE GROWTH OF BINARY EDEN MODEL AT PERCOLATION THRESHOLD CONCENTRATION

We extend the Eden model to the binary system of two kinds of sites with different noise reduction parameters n and m(⩾n). The new model called binary Eden model connects the original Eden model (n=m=1) to the percolation model (n=1 and m=∞). From our numerical simulation on a square lattice of a lattice edge width L, the surface width W(L,m) is found to satisfy the scaling relation at the percolation threshold concentration. Moreover, the surface length s(L,m) is also found to obey the same type scaling relation.

Fractal property of Eden growth morphology with acceleration effect

Fundamental growth process of Eden model has been used in many simulational studies of growing surfaces and the roughness exponent αE=12 and growth exponent βE=13[2] are well known. In this study we have added acceleration effect to the Eden model and examined universality class. We have simulated the growing Eden surface for several concentrations of acceleration sites p so as to observe changing morphology with p. As the simulation is limited to a finite lattice, we have to estimate exponents for infinite lattice size by simulating several lattice sizes Lx×Ly. At the conclusion we have estimated roughness and growth exponents for infinite lattice size and obtained αA∞≃αE=12 and βA∞≃βE=13 which are similar to those of normal Eden model for all concentrations of acceleration sites.