Hiroto Kuninaka

Statistical Features of Complex Systems –Toward Establishing Sociological Physics–

Complex systems have recently attracted much attention, both in natural sciences and in sociological sciences. Members constituting a complex system evolve through nonlinear interactions among each other. This means that in a complex system the multiplicative experience or, so to speak, the history of each member produces its present characteristics. If attention is paid to any statistical property in any complex system, the lognormal distribution is the most natural and appropriate among the standard or “normal” statistics to overview the whole system. In fact, the lognormality emerges rather conspicuously when we examine, as familiar and typical examples of statistical aspects in complex systems, the nursing-care period for the aged, populations of prefectures and municipalities, and our body height and weight. Many other examples are found in nature and society. On the basis of these observations, we discuss the possibility of sociological physics.

Anomalous behavior of the coefficient of normal restitution in oblique impact

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice model for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed unity and has a peak against the incident angle in our simulation. We also explain this behavior based upon a phenomenological theory.

Characteristics of population distributions in municipalities

Population characterizes collective behaviors of human beings. In this paper we investigate cumulative population distribution of municipalities (cities, towns, and villages) of Japan to show that each of them can be represented by a characteristic distribution function. We also introduce a numerical model for population dynamics to explain the origin of the distributions. From our analysis it has become clear that each distribution originates from the lower and upper bounds of population in the definitions of cities and towns.

Simulation of cohesive head-on collisions of thermally activated nanoclusters

Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions has a peak at a colliding speed due to the competition between the cohesive interaction and the repulsive interaction of colliding clusters. Some aspects of the collisions can be understood by the theory of Brilliantov [Phys. Rev. E 76, 051302 (2007)], but many aspects are found from the simulation. In particular, we find that there are some anomalous rebounds in which the restitution coefficient is larger than unity. The phase diagrams of rebound processes against impact speed and the cohesive parameter can be understood by a simple phenomenology.

Simulation and theory of the impact of two-dimensional elastic disks ☆

Abstract The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. This suggests that the elastic model cannot be used in the quasi-static limit. A new quasi-static theory of impacts is proposed, in which the effect of thermal diffusion is dominant. The abrupt decrease of COR has been found due to the plastic deformation of the disk, which is assisted by the initial internal motion.

Size Distribution of Bacterial Cells in Homogeneously Spreading Disk-like Colonies by Bacillus subtilis

We have experimentally investigated size distribution of bacterial cells at the circumference of homogeneously spreading disk-like colonies formed by Bacillus subtilis, and found that the size distribution of bacterial cells shows lognormal. We have developed a phenomenological model based on the experimental results for the growth process of bacterial cells and confirmed that the model reproduces a lognormal distribution of bacterial cell size which is very close to our experimental result. Our results indicate that both the lognormal distributions of cell cycle and cell growth rate are essential for the lognormal distribution of bacterial cell size.

Why Does Zipf's Law Break Down in Rank-Size Distribution of Cities?

We study the rank-size distribution of cities in Japan by data analysis and computer simulation. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has an independent power exponent. In addition, the power exponent of the head part of the distribution changes with time and Zipfs law holds only for a restricted period. We show that Zipfs law broke down owing to the great Showa and Heisei mergers and recovered owing to population growth in middle-sized cities after the great Showa merger.

Theory of the Inelastic Impact of Elastic Materials

We review recent developments in the theory of impact of macroscopic elastic materials. This review includes (i) standard theories for normal and oblique impacts, (ii) some typical approaches to simulate impact problems and (iii) results from our numerical simulations which clarify the mechanism of anomalous restitution in an oblique impact, where the restitution coefficient may exceed unity.

Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background

The statistics of isothermal lines and loops of the cosmic microwave background (CMB) radiation on the sky map is studied and the fractal structure is confirmed in the radiation temperature fluctuation. We estimate the fractal exponents, such as the fractal dimension D e of the entire pattern of isothermal lines, the fractal dimension D c of a single isothermal line, the exponent ζ in Korcaks law for the size distribution of isothermal loops, the two kind of Hurst exponents, H e for the profile of the CMB radiation temperature, and H c for a single isothermal line. We also perform fractal analysis of two artificial sky maps simulated by a standard model in physical cosmology, the WMAP best-fit Λ cold dark matter (ΛCDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ΛCDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by H e ≃0.2...

Statistical Properties of Height of Japanese Schoolchildren

We study height distributions of Japanese schoolchildren based on the statictical data which are obtained from the school health survey by the ministry of education, culture, sports, science and technology, Japan . From our analysis, it has been clarified that the distribution of height changes from the lognormal distribution to the normal distribution in the periods of puberty.