Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.Comment: 6 pages, 2 figure

Independent Component Analysis of Spatiotemporal Chaos

Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.

Two-dimensional structures of ferroelectric domain inversion in LiNbO3 by direct electron beam lithography

We report on the fabrication of domain-reversed structures in LiNbO3 by means of direct electron beam lithography at room temperature without any static bias. The LiNbO3 crystals were chemically etched after the exposure of electron beam and then, the patterns of domain inversion were characterized by atomic force microscopy (AFM). In our experiment, an interesting phenomenon occurred when the electron beam wrote a one-dimensional (1-D) grating on the negative c-face: a two-dimensional (2-D) dotted array was observed on the positive c- face, which is significant for its potential to produce 2-D and three-dimensional photonic crystals. Furthermore, we also obtained 2-D ferroelectric domain inversion in the whole LiNbO3 crystal by writing the 2-D square pattern on the negative c-face. Such a structure may be utilized to fabricate 2-D nonlinear photonic crystal. AFM demonstrates that a 2-D domain-reversed structure has been achieved not only on the negative c-face of the crystal, but also across the whole thickness of the crystal.Comment: 17 pages, 4 figure

Can Gravitational Waves Prevent Inflation?

To investigate the cosmic no hair conjecture, we analyze numerically 1-dimensional plane symmetrical inhomogeneities due to gravitational waves in vacuum spacetimes with a positive cosmological constant. Assuming periodic gravitational pulse waves initially, we study the time evolution of those waves and the nature of their collisions. As measures of inhomogeneity on each hypersurface, we use the 3-dimensional Riemann invariant ${\cal I}\equiv {}~^{(3)\!}R_{ijkl}~^{(3)\!}R^{ijkl}$ and the electric and magnetic parts of the Weyl tensor. We find a temporal growth of the curvature in the waves' collision region, but the overall expansion of the universe later overcomes this effect. No singularity appears and the result is a ``no hair" de Sitter spacetime. The waves we study have amplitudes between $0.020\Lambda \leq {\cal I}^{1/2} \leq 125.0\Lambda$ and widths between $0.080l_H \leq l \leq 2.5l_H$, where $l_H=(\Lambda/3)^{-1/2}$, the horizon scale of de Sitter spacetime. This supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To [email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9

Two Boosted Black Holes in Asymptotically de Sitter Space-Time - Relation between Mass and Apparent Horizon Formation -

We study the apparent horizon for two boosted black holes in the asymptotically de Sitter space-time by solving the initial data on a space with punctures. We show that the apparent horizon enclosing both black holes is not formed if the conserved mass of the system (Abbott-Deser mass) is larger than a critical mass. The black hole with too large AD mass therefore cannot be formed in the asymptotically de Sitter space-time even though each black hole has any inward momentum. We also discuss the dynamical meaning of AD mass by examining the electric part of the Weyl tensor (the tidal force) for various initial data.Comment: 15 pages, accepted for publication in PR

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB6_6

A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.Comment: 4 pages, 5 figure