- 著者
- Arimitsu T. Arimitsu N.
- 出版者
- American Physical Society
- 雑誌
- Physical review E (ISSN:1063651X)
- 巻号頁・発行日
- vol.61, no.3, pp.3237-3240, 2000-03
- 被引用文献数
- 86 110
The analysis of the fully developed turbulence with the help of the binomial multiplicative process is reinvestigated from the standpoint of Tsallis nonextensive statistics in order to provide some insight in understanding the underlying physical meaning of the Tsallis ensemble. The formula is derived which relates Tsallis index q with the intermittency exponent μ that is a manifestation of multifractality of the sizes of eddies. It is shown that the probability density function of the local dissipation of turbulent kinetic energy can be represented by a distribution function of the type in Tsallis statistics with the index q determined by the experimentally observable quantity μ through the derived formula.
- 著者
- Kobayakawa T. S. Hatsugai Y. Kohmoto M.
- 出版者
- American Physical Society
- 雑誌
- Physical review E (ISSN:1063651X)
- 巻号頁・発行日
- vol.51, no.6, pp.5365-5370, 1995-06
- 被引用文献数
- 9 9
Recently, the smoothed correlation between the density of eigenvalues of Hermitian random matrices was found to be universal, that is, independent of the probability distribution from which the random matrices are taken. We study this universal correlation numerically by ensemble averaging, using the Monte Carlo sampling method. Although the density of eigenvalues and the ‘‘bare’’ correlation between the density of eigenvalues are certainly not universal, we find that the smoothed correlation indeed shows a universal behavior. The orthogonal and the symplectic ensembles are also studied numerically. The smoothed correlation is shown to be universal in these cases.
- 著者
- Arimitsu Toshihico Arimitsu Naoko
- 出版者
- American Physical Society
- 雑誌
- Physical review E (ISSN:1063651X)
- 巻号頁・発行日
- vol.50, no.1, pp.121-137, 1994-07
- 被引用文献数
- 6 16
A general formula of the time-resolved optical spectrum for transient resonant light scattering is derived systematically by means of the operator algebra within the formalism of nonequilibrium thermo field dynamics (NETFD). The formula is applied to an analytically solvable model of the localized electron and phonon system, i.e., second-order light scattering due to the optically active three electronic states whose intermediate state is dynamically modulated by the phonon interaction mode. The derivation of the analytical expression for a four-point function, needed to obtain the spectrum, is performed with the help of the algebraic manipulations in NETFD, which showed the advantage of its methodology with respect to nonequilibrium transient phenomena. The three-dimensional profiles of the Raman and luminescence components in the time-resolved spectrum in the model are presented to show how the stochastic character comes out in the fast modulation limit, and how the dynamical behavior of the phonon system causing the modulation of the intermediate electronic state comes out in the slow modulation limit.
- 著者
- Yoshida Kyo Kaneda Yukio
- 出版者
- American Physical Society
- 雑誌
- Physical review E (ISSN:1063651X)
- 巻号頁・発行日
- vol.63, pp.016308, 2000-12
- 被引用文献数
- 17 20
A model of randomly advected solenoidal field is presented. The model is formally derived by a linearization of the Navier-Stokes equation with respect to the perturbation to a basic state and by assuming the characteristic time scale of the basic state to be very short. The model includes a nonlocal (in space) effect through a pressurelike term that keeps the advected field solenoidal, but still yields exact equations for multipoint moments. The advecting field is assumed to be statistically homogeneous and isotropic with zero mean and structure function with exponent xi. An analysis is made of the scaling of the steady second-order moments of the solenoidal field in two dimensions. The scaling exponent zeta(l) of the isotropic part (l=0) and the anisotropic part for the angular wave number l=2 is obtained analytically or numerically. The scaling of the isotropic part does not depend on whether the pressurelike term is present or not while the scaling of the anisotropic part is affected by the pressurelike term. There are two homogeneous similarity solutions with real positive exponents zeta(2) when xi>xi(c)(2) approximately 1.3. The same kind of analysis is also applied to a simplified two-point closure equation.