Global aspects of turbulence induced by heteroclinic cycles in competitive diffusion Lotka-Volterra equation

This paper presents detailed numerical results of the competitive diffusion Lotka-Volterra equation (May-Leonard type). First, we derive the global phase diagrams of attractors in the parameter space including the system size, where transition lines between simple attractors are clearly obtained in accordance with the results of linear stability analysis, but the transition borders become complex when multi-basin structures appear. The complex aspects of the transition borders are studied in the case when the system size decreases. Next, we show the statistical aspects of the turbulence with special attention to the onset of the supercritical Hopf bifurcation. Several characteristic quantities, such as correlation length, correlation time, Lyapunov spectra and Lyapunov dimension, are investigated in detail near the onset of turbulence. Our data show the critical scaling law near the onset only in the restricted parameter domain. However even when the critical indices are not determined accurately, it is shown that the empirical scaling relations are obtained in a wide parameter domain far from the onset point and those scaling indices satisfy several relations. These scaling relations are discussed in comparison with the result derived by the phase reduction method. Lastly, we make a conjecture about the stability of an ecosystem based on the bifurcation diagram: the ecosystem obeying the Lotka-Volterra equation in the case of May-Leonard type is stabilized more as the system size increases.     

Self-Modulation of Scattering Intensity from a Silica Sphere Coated with a Sol-Gel Film Doped with J-Aggregates

A micrometer-sized nonlinear optical resonator constituted of a silica microsphere coated with J-aggregates has been fabricated by the sol-gel process. We determined the scattering light spectrum and discuss the application of the observed effect for the realization of an optical switching element. Optical evaluation of the sphere has been performed in the attenuated-total-reflection (ATR) configuration. We excited a whispering gallery mode and measured the nonlinear ATR signal dependence on excitation intensity. The experimental result agrees very well with the simulation results obtained using the Mie theory and the finite-difference time-domain method taking into account optical Kerr nonlinearity. The permittivity of the film of J-aggregates was measured by ATR method at several wavelengths and the value at the desired wavelength was determined by extrapolation using the Lorentz function.     

Study by X-ray crystallography and Mössbauer spectroscopy of CeFe(CN)6·5H2O and GdFe(CN)6·4H2O

From the X-ray crystallographic point of view, the environment of Fe in CeFe(CN)₆·5H₂O has higher octahedral symmetry than that in GdFe(CN)₆·4H₂O. The single Mössbauer absorption peak for CeFe(CN)₆·5H₂O indicates that the three t_2g levels are close to each other in energy due to a near-perfect octahedral Fe(CN)₆ unit. The doublet peak of of GdFe(CN)₆·4H₂O can be explained by assuming that the three t_2g levels are widely separated as a result of the distortion of the octahedral Fe(CN)₆ unit.     

Microscopic theory of formation of macroscopic order

A general microscopic theory for the formation process of macroscopic order is proposed. The existence of a finite on-set time is shown in our framework. The relation between the previous scaling theory and the present one is also discussed.     

Waveform Measurement of Ultra-Short Optical Pulses Based on Two-Photon Absorption in Si-Image Sensor

We demonstrate a novel waveform mesurement system of ultra-short optical pulses based on the two-photon absorption process in a Si-image sensor. Using an interferometer with a tilt mirror in the reference path, the relative time difference between the signal and reference pulses is spatially distributed on the Si-image sensor, so the intensity auto-correlation is monitored as an image at a time without using moving parts. This system can create or remove an interference fringe pattern overlapped on the auto-correlation image by controlling the polarization states of the laser pulse, which is useful for measuring the crossing angle between the signal and reference beams as well as avoiding contamination of the interference fringe into the auto-correlation image. We successfully measured optical pulses less than 100 fs from a fiber ring laser with a temporal resolution of 0.4 fs. The obtained waveform agreed well with that observed with a conventional second harmonic generation (SHG) based auto-correlator.     

The applicability of the defocusing technique in organic mass spectrometry

Defocusing techniques for detecting metastable ions of rather complex molecules were investigated and a generalised procedure, which provides efficient methods in the analysis of fragmentation pathways of complex compounds, was established. Additionally, a new method to differentiate between the transition in the first and the third field free regions, was developed.     

Synthesis of 24,24-difluoro- and 24ξ-fluoro-25-hydroxyvitamin D3

From cholenic acid 24,24-difluoro-25-hydroxyvitamin D₃ and 24ξ-fluoro-25-hydroxyvitamin D₃ were prepared.     

Migdal-Kadanoff renormalization group approach to the spin-1/2 anisotropic Heisenberg model

The spin-1/2 anisotropic Heisenberg model is studied by generalizing the Migdal-Kadanoff renormalization transformations to quantum spin systems. An approximate one-dimensional decimation is employed besides the potential-moving approximation in this generalization. It is shown that these approximations are valid at high temperatures. The results obtained from these approximations suggest that the two-dimensional spin-1/2X-Y model shows the critical behavior similar to that expected for the classicalX-Y and planar models.     

Renormalization group approach to the one-dimensional hubbard model

An approximate decimation method is applied to the one-dimensional half-filled Hubbard model. The specific heat, the entropy and the magnitude of local moments are calculated. The results are in good agreement with those obtained by Shiba at high temperatures.