Published Papers - MIYAGUCHI Tomoshige

Nonlinear dynamics of magnetic field lines

Tomoshige Miyaguchi, Makoto Hosoda, Katsuyuki Imagawa, Katsuhiro Nakamura

Nonlinear Phenomena in Complex Systems   13 ( 1 ) 79 - 84   2010

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Nonlinear dynamics of magnetic field lines generated by simple electric current elements are investigated. In general, the magnetic field lines show behavior similar to that of the Hamiltonian systems
in fact, they can be generally transformed into 1.5 degrees of freedom Hamiltonian systems and obey the KAM theorem. In the case where unperturbed systems are described by two action (slow) and one angle (fast) variables, however, it is found that the periodic orbits of the unperturbed systems vanish for arbitrarily small symmetry-breaking perturbations (a breakdown of the KAM theorem). The mechanism of this phenomenon is investigated by weak nonlinear stability analysis.

Singular Behavior of Slow Dynamics of Single Excitable Cells

Takahiro Harada, Tomomi Yokogawa, Tomoshige Miyaguchi, Hiroshi Kori

BIOPHYSICAL JOURNAL ( CELL PRESS )  96 ( 1 ) 255 - 267   2009.01

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In various kinds of cultured cells, it has been reported that the membrane potential exhibits fluctuations with long-term correlations, although the underlying mechanism remains to be elucidated. A cardiac muscle cell culture serves as an excellent experimental system to investigate this phenomenon because timings of excitations can be determined over an extended time period in a noninvasive manner through visualization of contractions, although the properties of beat-timing fluctuations of cardiac muscle cells at the single-cell level remains to be fully clarified. In this article, we report on our investigation of spontaneous contractions of cultured rat cardiac muscle cells at the single-cell level. It was found that single cells exhibit several typical temporal patterns of contractions and spontaneous transitions among them. Detrended fluctuation analysis on the time series of interbeat intervals revealed the presence of 1/f(beta) noise at sufficiently large timescales. Furthermore, multifractality was also found in the time series of interbeat intervals. These experimental trends were successfully explained using a simple mathematical model, incorporating correlated noise into ionic currents. From these findings, it was established that singular fluctuations accompanying 1/f(beta) noise and multifractality are intrinsic properties of single cardiac muscle cells.

DOI

Escape time statistics for mushroom billiards

Tomoshige Miyaguchi

PHYSICAL REVIEW E ( AMER PHYSICAL SOC )  75 ( 6 )   2007.06

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Chaotic orbits of the mushroom billiards display intermittent behaviors. We investigate statistical properties of this system by constructing an infinite partition on the chaotic part of a Poincare surface, which illustrates details of chaotic dynamics. Each piece of the infinite partition has a unique escape time from the half disk region, and from this result it is shown that, for fixed values of the system parameters, the escape time distribution obeys a power law 1/t(esc)(3).

DOI

Spectral analysis and an area-preserving extension of a piecewise linear intermittent map

Tomoshige Miyaguchi, Yoji Aizawa

PHYSICAL REVIEW E ( AMER PHYSICAL SOC )  75 ( 6 )   2007.06

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We investigate the spectral properties of a one-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius-Perron operator has two simple real eigenvalues 1 and lambda(d)is an element of(-1,0) and a continuous spectrum on the real line [0,1]. From these spectral properties, we also found that this system exhibits a power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.

DOI

Transport Properties of a Piecewise Linear Transformation and Deterministic Levy Flights(Condensed Matter and Statistical Physics)

Tomoshige MIYAGUCHI, Department of Applied Physics Faculty of Science and Engineering Waseda University

Progress of theoretical physics = Progress of theoretical physics ( Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan )  115 ( 1 ) 31 - 41   2006.01

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The transport properties of a 1-dimensional piecewise linear dynamical system are investigated through the spectrum of its Frobenius-Perron operator. For a class of initial densities, eigenvalues and eigenfunctions of the Frobenius-Perron operator are obtained explicitly. It is also found that in the long length wave limit, this system exhibits normal diffusion and super diffusion called Levy flight. The diffusion constant and stable index are derived from the eigenvalues.

DOI

Anomalous Diffusion in a Hamiltonian System

Tomoshige MIYAGUCHI, Yoji AIZAWA, Department of Applied Physics Faculty of Science and Engineering Waseda University, Department of Applied Physics Faculty of Science and Engineering Waseda University

Progress of theoretical physics = Progress of theoretical physics ( Published for the Research Institute for Fundamental Physics by Physical Society of Japan )  109 ( 1 ) 145 - 149   2003.01

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We investigate transport properties of a Hamiltonian system with two degrees of freedom. We found that, for a range of parameter values, transport is superdiffusive, and we numerically comfirmed that this is caused by stickiness of ballistic mode islands. We also note that a Poincare map of our system has properties similar to those of Levy flight.

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Dynamical systems that produce the Lévy flights

Tomoshige Miyaguchi, Yoji Aizawa

Progress of Theoretical Physics ( Yukawa Institute for Theoretical Physics )  10 ( 4 ) 697 - 704   2001

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We introduce a one-dimensional map producing flights of arbitrary length and explain that the orbits and the density functions that evolve under this map have the same properties as Lévy flight. We derive an approximated Frobenius-Perron equation and prove that this equation converges to the Lévy diffusion equation.

DOI