arXiv subjects

Mitsuhiro Kawasaki

Publications and source records attributed to Mitsuhiro Kawasaki.

9 recordsLinked to original sources

arXiv2005

Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom

For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be calculated using only one UPO sampled from the ensemble. Evidence to support this conclusion is obtained by generating the ensemble by Monte Carlo calculation for a statistical mechanical model described by a space-time Hamiltonian that is expressed in terms of Floquet exponents of UPOs. This result allows us to interpret the recent interesting discovery that statistical properties of turbulence can be obtained from only one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].

nlin.CD↗

arXiv2003

Statistics for transition of a plasma turbulence with multiple characteristic scales

Subcritical transition of an inhomogeneous plasma where turbulences with different characteristic space-time scales coexist is analyzed with methods of statistical physics of turbulences. We derived the development equations of the probability density function (PDF) of the spectrum amplitudes of the fluctuating electro-static potential. By numerically solving the equations, the steady state PDFs were obtained. Although the subcritical transition is observed when the turbulent fluctuations are ignored, the PDF shows that the transition is smeared out by the turbulent fluctuations. It means that the approximation ignoring the turbulent fluctuations employed by traditional transition theories could overestimate the range where hysteresis is observed and statistical analyses are inevitably needed.

physics.plasm-ph↗

arXiv2003

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 $ρ(w_i)\sim {w_i}^{α-1} (0 < α\leq 1)$. More precisely, the frequency-dependence of the disorder-averaged admittance $<χ>$ disagrees with that of the admittance $χ$ of any sample. It implies that the Cole-Cole plot of $<χ>$ 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.

cond-mat.dis-nn↗

arXiv2002

The Real-Space Renormalization Group Applied to Diffusion in Inhomogeneous Media

The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a discretized real space and hence it can be easily combined with numerical studies for partial differential equations.

cond-mat.dis-nn↗

arXiv2002

Transition Probability to Turbulent Transport Regime

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.

physics.plasm-ph↗

arXiv2002

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 (FDT). 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.

cond-mat.dis-nn↗

arXiv2002

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.

physics.plasm-ph↗

arXiv2000

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

A random walk model in a one dimensional disordered medium with an oscillatory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered medium. It is rigorously shown that an admittance which is equal to the Fourier-Laplace transform of the first-passage time distribution is non-self-averaging when the disorder is strong. The low frequency behavior of the disorder-averaged admittance, $<χ> -1 \sim ω^μ$ where $μ< 1$, does not coincide with the low frequency behavior of the admittance for any sample, $χ- 1 \sim ω$. It implies that the Cole-Cole plot of $<χ>$ appears at a different position from the Cole-Cole plots of $χ$ of any sample. These results are confirmed by Monte-Carlo simulations.

cond-mat.dis-nn↗

arXiv2000

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.

cond-mat.dis-nn↗