K. Kudo’s research while affiliated with Kindai University and other places

Oxide layers formed by micro-arc oxidation (MAO) using direct current electrolysis and pulse electrolysis were characterized by scanning electron microscopy. X-ray diffraction, energy-dispersive X-ray spectroscopy and adhesive strength measurements. Ti oxide films fabricated by pulse electrolysis were found to have a significantly higher adhesive strength than those fabricated by direct current electrolysis. This can be explained by the different interface adhesive strengths between the two Ti oxide layers and the Ti substrate, as revealed by cross-sectional SEM micrographs. In addition, the dependences of the voltage and the current on the electrolysis time were investigated. [doi: 10.2320/matertrans.M2010227]

We present a model of rule-changing cellular automata (CA) to study dynamical structure of CA in detail. In our model calculation the edge of chaos is observed on the basis of the source rule 22 which yields the most interesting behavior. We find that the edge of chaos is generated through competition between two rule-changing behaviors. These rule-changing behaviors are analyzed quantitatively by using the mutual information as a measure ofcomplexity. It is noted that the mutual information has the maximum value near the edge of chaos because of competition.

A relation of radon (Rn) daughters concentration in the air to meteorological parameters is investigated. The atmospheric radon daughter concentration and the related meteorological parameters are treated as a simple time series data. The power sprctrum of radon daughter concentration and temperature after fourier transfer are fit to 1/f closely. This fact confirms that the common dynamics exist between the variations of the parameters.

The rule changeable elementary cellular automata are proposed analogous to the ecological system. In this model we find the behavioral diversity for a suitable threshold value x on chaotic source rule. The behavioral diversity is characterized by block entropy and joint entropy. Our behavioral diversity plays just as “edge of chaos” for spatial and temporal evolution.

Dynamics of two coupled van der Pol type inverted pendulums are studied. A phase transition is observed between synchronized phase and asynchronized phase. Behavior of angular correlation near critic2Ll point is observed. Exact critical point and critical exponent are obtained by obeserving convergent time.

The diversity of entropy, as a measure of complexity, for data traffic on Internet has been studied. We also calculated the measure of artificial sequences, such as periodic, random, mixed, cellular automata generated and logistic map generated sequences, to compare with that of data traffic on the Internet. As a result, we find, the measure of data traffic is larger than those produced by other artificial sequences.

Measures of complexity hitherto proposed are classified into two, i.e. first order complexity C 1 and second order complexity C 2. It is difficult to comprehend complexity of self-organization by means of these measures. We have proposed a way to analyze the mechanism of self-organization on the basis of the convolution model to make the relation between the states of total system and subsystems. The state of total system is convoluted by the states of subsystems in some phase space, while the state of subsystem is given by convolution of the states of total system as the feedback effect in the process of time development. It has been pointed out that complexity of self-organization results from antagonistic relationality between total system and subsystems to set these systems in the respective appropriate states.

Nonlinear complex open systems show great diversity in the process of self-organization, and that diversity increases as complexity increases. The measurement of complexity and the origins of the diversity of such complex systems are the focus of interdisciplinary studies extending across a wide range of scientific disciplines that include applied mathematics, physics, chemistry, biology, psychology, ecology, sociology, and economics. Previous investigations have concentrated either on complexity or on diversity, but not both. This volume makes clear the relation between complexity and diversity with examples drawn from various disciplines. Compiles here are presentations from the Complexity and Diversity workshop held in Fugue, Japan, in August 1996. The contributions are the results of research in mathematical systems, physical systems, living systems, and social systems, and are contained in the four corresponding sections of the book. Mathematical expressions for the theory of complexity as a fundamental method along with realistic examples for application of systematic methods provide the reader with ready access to the latest topics in complex systems.

On the basis of statistical thermodynamics we represent the free energy and the partition function of intermittent multifractal systems. It is pointed out that even in the case of chaotic system in which the value of minimum free energy cannot be determined because of thermal fluctuations, we can obtain the partition function by using the effective free energy defined in the dominant region of power law indices. We analyze one-scale Cantor set in the fluctuation mode to show a typical example of this system.

We obtain the mutual information of Ising systems, which shows singular behavior near the critical point. We connect the mutual information with the magnetization and the correlation function. The mutual information is a suitable measure for the critical behavior of Ising systems.