Sasuke Miyazima

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.

Fluctuation of biological rhythm in finger tapping

By analyzing biological rhythms obtained from finger tapping, we have investigated the differences of two biological rhythms between healthy and handicapped persons caused by Parkinson, brain infraction, car accident and so on. In this study, we have observed the motion of handedness of all subjects and obtained a slope a which characterizes a power-law relation between frequency and amplitude of finger-tapping rhythm. From our results, we have estimated that the slope a=0.06 is a rough criterion in order to distinguish healthy and handicapped persons.

COLONY OF THE FUNGUS Aspergillus oryzae AND SELF-AFFINE FRACTAL GEOMETRY OF GROWTH FRONTS

A variety of colony shapes of the fungus Aspergillus oryzae under varying environmental conditions such as the nutrient concentration, medium stiffness and incubation temperature are obtained, ranging from a homogeneous Eden-like to a ramified DLA-like pattern. The roughness σ(l, h) of the growth front of the band-shaped colony, where h is the mean front height within l of the horizontal range, satisfies the self-affine fractal relation under favorable environmental conditions. In the most favorable condition of our experiments, its characteristic exponent is found to be a little larger than that of the 2-dimensional Eden model.

Self-affine fractal growth front of Aspergillus oryzae

Aspergillus oryzae have been grown in various environmental conditions and analyzed from the viewpoint of self-affinity. The growth behavior can be described by the Eden model in favorable conditions, and by DLA in unfavorable conditions.

Asymptotic analysis of the model for distribution of high-tax payers

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others [12]–[14]. Our analysis shows an asymptotic power-law of this model with the exponent −5/2 when a total “mass” has a certain critical value. Below the critical value, the system exhibits an ordinary critical behavior, and scaling relations hold. Above the threshold, numerical simulations show that a power-law distribution coexists with a huge “monopolized” member. It is argued that these behaviors are observed universally in conserved aggregation processes, by analizing an extended model.

PERCOLATED CRACKS IN A SOLID CONTAINING MANY INITIAL DEFECTS

Hydrogen-induced fracture of steel is characterized by the formation of internal voids caused by hydrogen precipitation at an inclusion-matrix interface, followed by the formation of microcrack array under the superposed action of internal hydrogen pressure and external forces. The propagation of the hydrogen-induced fracture is considerably random and the fracture develops by stepwise linking of the microcracks. Crack growth in a solid containing many initial defects is studied by Monte Carlo simulation on a square lattice. Each initial defect is assumed to have two crack tips like the Griffith crack and percolated crack patterns in homogeneous medium are investigated. The effect of the density of the initial defects and the lattice size on percolation characteristics is also studied.

FORMATION OF RAMIFIED COLONY OF FUNGUS ASPERGILLUS ORYZAE ON AGAR MEDIA

Ramified colonies of fungus Aspergillus oryzae have been found to grow at a low growth rate on “liquid-like” agar media with low concentrations of agar and glucose. Box-counting fractal dimensions of the individual colony branches have been found to decrease with the time of incubation. Addition of glucose solution in the interior of branched colonies has brought about the production of the hyphal filaments almost only at the apical region of the colony branches. Active growth of the ramified colonies is localized in the peripheral zone, and this growth manner implies that the fungus is exhibiting a positive exploitation.

A generalized diffusion-limited aggregation where aggregate sites have a finite radical time

In this paper, we study a new class of diffusion-limited aggregation, where each aggregate particle adheres to the aggregate and continues to be radical for a finite time τ. When τ=1 and τ=∞, the present model is reduced to a diffusion-limited self-avoiding walk (DLSAW) and to the original (Witten-Sander) diffusion-limited aggregation, respectively. For a finite radical time, the growth crosses over from DLA growth to DLSAW growth. The crossover time increases with increasing τ. To describe this behavior, we developed a simple scaling theory.

From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

We propose a new class of cluster growth models where growth sites have a finite lifetime τ, which contains as special cases the Eden model (τ = ∞) and the kinetic growth walk (τ = 1). For finite but large τ values the growth process can be characterized by a crossover timetX; for times belowtX an Eden-type cluster is formed, while for times abovetX the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with τ. We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).

MEASURING THE TEMPERATURE OF TEXTS

An innovative method for measuring the temperature of texts is introduced by measuring deviation from a standard Maxwell-Boltzmann (M–B) distribution for a corpus of English words. The temperature of English texts for junior and senior high schools in Japan and grades one through 12 in the US are measured and found to be between 148 K and 87 K, when the temperature of ANC (American National Corpus) is assumed to be 100 K as a standard. The temperature of several books by famous authors (Einstein, Darwin, etc.) is also analyzed. The present technique also can be applied to many other topics. Application to mortality rate distribution in Japan is discussed as an example.