arXiv subjects
Publications and source records attributed to W. Sakikawa.
By calculating the non-equilibrium parameter of the probability distribution function and the singularity spectrum of multifractal we have quantified the dynamical heterogeneity in strongly correlated many-body systems.
On the basis of the lattice Boltzmann method we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. First in the analysis of the mean-field behavior of the velocity field using the exit-time statistics we have verified Kolmogorov's scaling and Taylor's hypothesis for the first time in the simulation for the Navier-Stokes equation. Second in the analysis of the intermittent velocity fluctuations using a non-equilibrium probability distribution function and the wavelet denoising we have clarified that the coherent vortices sustain the power-law velocity correlation in the non-equilibrium state.
We have shown that the epsilon-entropy determined from the time-series of the velocity fluctuation in a forced turbulence simulated by the lattice Boltzmann method obeys the Kolmogorov scaling.
The dynamical heterogeneity in supercooled liquids measured by a molecular dynamics simulation has been quantified on the basis of the multifractal formalism. The singularity spectrum becomes broader as the glass transition is approached. This behavior is similar to that observed in the case of the Anderson-localization transition.
The distribution of the fractal dimension of the two-dimensional Ising model at the critical temperature measured by the Monte-Carlo simulation is discussed. At small spatio-temporal scales it exhibits a multifractal behavior and is well fitted by a non-Gaussian distribution derived from the Rényi or Tsallis entropy.