Kazuo Tokiwano

Exponential Characteristics of Power Spectral Densities Caused by Chaotic Phenomena

Power spectral densities (PSDs) were calculated by the maximum entropy method (MEM) for three types of chaotic time series numerically generated from the Lorenz, Rossler and Duffing models. Every PSD indicated exponential decay until it levels off at a limit determined by the accuracy of the present computation. This exponential chracteristics were universally found in all chaotic time series irrespective of the data length as well as the time range of data. The values of the coefficient of exponent were 3.26, 5.72 and 7.36 for 6000-point data of the Lorenz, Rossler and Duffing models, respectively, and they slightly increased as the data length shortened. The exponential form was also recognized in the MEM-PSD for the Lorentzian-type time series as in theory.

A Detailed Study of Power Spectral Density for Rossler System

Power spectral densities (PSDs) calculated by the maximum entropy method (MEM) for Rossler system indicated exponential decay with a large number of well-defined spectral lines. The spectral lines were confirmed to indicate a complete bifurcation up to the fifth-order period-doubling. An extremely anomalous behavior was recognized in the region of c =4.18–4.21 which is considered to be a transition region. The contribution of the power of the fundamental mode to the total power was overwhelmingly large: it becomes larger than 90%. A prediction of time series including chaotic ones was performed and the satisfactory results obtained. It will be discussed that the fluctuations due to amplitude instability of time series in the periodic solutions generate, resulting in the continuous component of PSD structured through the subharmonic cascade process, and this continuous region is restructured in the inverse cascade process (the socalled broad continuum in the chaotic mixing).

New Method of Time Series Analysis and Its Application to Wolf's Sunspot Number Data. II: Periodicities of The Daily Sunspot Numbers

The daily sunspot numbers data from 1979 October 1 to 1993 December 31 were analyzed using a new method of time series analysis proposed by the authors, and the long- and short-term periodicities were investigated. A three-dimensional (3D) spectral array of the normalized power spectral densities (PSDs) obtained by the segment time series analysis revealed the temporal behavior of the 27- and 155-d periodicities in the solar activity minimum. In the normalized 3D spectral array, the solar rotation cycle of 27-d accompanied by its multiplets was confirmed to migrate gradually from the low frequency region toward the high frequency region in the solar activity minimum as the solar activity increases, while the 155-d periodicity exists in the solar activity maximum only. Moreover, the behavior of the daily sunspot numbers variation was conjectured to be deterministic chaos, based on the exponential characteristics of the PSDs and the subharmonic relations of the spectral lines.

Restoration of Scanning Tunneling Microscope Images by means of Two-Dimensional Maximum Entropy Method

We present a new technique for the restoration of scanning tunneling microscopy (STM) images, which is a two-dimensional extension of a recently developed statistical approach based on the one-dimensional least-squares method (LSM). An STM image is regarded as a realization of a stochastic process and assumed to be a composition of an underlying image and noise. We express the underlying image in terms of a two-dimensional generalized trigonometric polynomial suitable for representing the atomic protrusions in STM images. The optimization of the polynomial is performed by the two-dimensional LSM combined with the power spectral density function estimated by means of the maximum entropy method (MEM) iterative algorithm for two-dimensional signals. The restored images are obtained as the optimum least-squares fitting polynomial which is a continuous surface. We apply this technique to modeled and actual STM data. Results show that the present method yields a reasonable restoration of STM images.

Molecular Dynamics Study of Dense Fluids

A computer experiment has been performed to investigate dynamical properties of a fluid system composed of 864 particles interacting through a modified Lennard-Jones-type potential. The velocity autocorrelation functions are computed and discussed in comparison with the Enskog predictions. The correlation functions are found to be very similar to those of the effective hard sphere fluids after the lapse of about 8 successive collisions. The slow power-law decaying behavior in the time correlation function is observed for a fluid composed of particles interacting with a harshly repulsive core and an attractive potential.