Mitsuhiro Kawasaki

Transition in multiple-scale-lengths turbulence in plasmas

The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale lengths coexist. Statistical nonlinear interactions between semimicro and micro modes are first kept in the analysis as the drag, noise and drive. The nonlinear dynamics determines both the fluctuation levels and the cross field turbulent transport for the fixed global parameters. A quenching or suppressing effect is induced by their nonlinear interplay, even if both modes are unstable when analyzed independently. Influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of the internal transport barrier. The thermal fluctuation of the scale length of λD is assumed to be statistically independent. The hierarchical structure is constructed according to the scale lengths. Transitions in turbulence are found and phase diagrams with cusp type catastrophe are obtained. Dynamics is followed. Statistical properties of the su...

On transition in plasma turbulence with multiple scale lengths

A statistical theory of plasma turbulence which is composed of multiple-scale fluctuations is examined. Influences of statistical noise and variance of rapidly changing variable in an adiabatic approximation are investigated. It is confirmed that the contributions of noise and variance remain higher order corrections. Transition rate of the turbulence with multiple scale lengths is obtained under the refined adiabatic approximation.

Transition probability to turbulent transport regime

Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analysed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains hysteresis characteristics. Transition rates between two states are analysed. Transition from turbulent state to thermal noise state occurs in the entire region between subcritical bifurcation point and linear stability boundary.

Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation.

The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized fluctuation-dissipation theorem. We show that there are two experimental time regimes characterized by different thermal properties. In the first regime where the waiting time is much longer than the measurement time, the principle of minimum work holds even though a system is out of equilibrium. In the second regime where both the measurement time and the waiting time are long, the thermal properties are completely different from properties in equilibrium. For the single-correlation-scale systems such as p-spin spherical spin glasses, contrary to a fundamental assumption of thermodynamics, the work done in an infinitely slow operation depends on the path of change of the external field even when the waiting time is infinite. On the other hand, for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model, the work done in an infinitely slow operation is independent of the path. Our results imply that in order to describe thermodynamic properties of systems with aging it is essential to consider the experimental time scales and history of a system as a state variable is necessary.

Absence of self-averaging in the complex admittance for transport through disordered media

Random walk models in one-dimensional disordered media with an oscillatory input current are investigated theoretically as generic models of the boundary perturbation experiment. It is shown that the complex admittance obtained in the experiment is not self-averaging when the jump rates w i are random variables with the power-law distribution ρ(w i )∼w α - 1 i (0 disagrees with that of the admittance Χ of any sample. It implies that the Cole-Cole plot of shows a different shape from that of the Cole-Cole plots of Χ of each sample. The condition for absence of self-averaging is investigated with a toy model in terms of the extended central limit theorem. Higher-dimensional media are also investigated and it is shown that the complex admittance for two-dimensional or three-dimensional media is also non-self-averaging.

Stochastic Transition between Turbulent Branch and Thermodynamic Branch of an Inhomogeneous Plasma

Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains submarginal characteristics. Probability density functions and transition rates between two states are analyzed. Transition from turbulent branch to thermodynamic branch occurs in almost entire region between subcritical bifurcation point and linear stability boundary.

Stochastic Transition of a Turbulent Plasma

Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analyzed with statistical theory. Time‐development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains hysteresis characteristics. Transition rates between two states are analyzed. Transition from turbulent state to thermal noise state occurs in entire region between subcritical bifurcation point and linear stability boundary.

The Rejuvenation Effect in the Two-State Random Energy Model

Theoretical analyses of the random energy model with only two states and its extension with a hierarchy of only two levels show that these models reproduce out-of-equilibrium phenomena observed in experiments of glassy materials; the rejuvenation effect (the chaos effect), i.e. the abrupt jump and subsequent relaxation of the out-of-phase susceptibility as if the system rejuvenates when the temperature is lowered, and the power-law relaxation of the two-time correlation function. Our results suggest that also in an assembly of small systems with relaxation times distributed broadly some of these interesting out-of-equilibrium phenomena can be observed.