Tsuneyasu Okabe

Molecular Dynamics Studies of Yttria Stabilized Zirconia. I. Structure and Oxygen Diffusion

The structure and dynamical properties of oxygen conductor yttria stabilized zirconia, (ZrO 2 ) 1- x (Y 2 O 3 ) x , are investigated for three dopant concentrations of 4.85, 10.2 and 22.7 mol%Y 2 O 3 using a method of molecular dynamics simulation. It is shown that a Y–O nearest neighbor distance is longer than that for Zr–O, and an oxygen coordination number for Y ion is a little larger than that for Zr ion in all dopant concentrations. The self-diffusion constant of O ions, D , shows a maximum at 10.2 mol%Y 2 O 3 with increasing the dopant concentration. These results are in agreement with experimental measurements. It is shown that dopant Y ions play an important role in such notable behavior of oxygen diffusion.

LYAPUNOV INSTABILITY IN ONE-DIMENSIONAL LENNARD-JONES SYSTEM

We study a transition from quasiperiodic to stochastic motion in one-dimensional classical systems consisting of N particles with the nearest-neighbor Lennard–Jones interaction, extensively by computer simulation. We find a new feature in the change of the Lyapunov spectrum and the maximal Lyapunov exponent by changing its energy in the intermediate region between quasiperiodic and stochastic motions. The characteristics of the Lennard–Jones system in the intermediate region is considered by means of properties of Hessian matrix of potential function. The applicability of random matrix approximation for high energy region is also investigated, comparing with the case of soft-core potential.

Instability of One-Dimensional Lennard–Jones System — Particle Density Dependence

We report dynamical instability of one-dimensional system with the nearest-neighbor Lennard–Jones interaction. A presence of new certain region between weakly and strongly chaotic region has been found in energy dependence of the maximal Lyapunov exponent. It is numerically shown that the presence of the region is enhanced by decrease of the particle density. The characteristics of the Lennard–Jones system, which are different from the FPU and soft-core system, are explained by means of a local instability of the potential surface. In addition, the relation between the presence of the new region and spatio-temporal pattern is also discussed in the low density cases.

1⧹f Type Fluctuations in One-dimensional Lennard–Jones Chain

Abstract We report some features found around the stochastic transition from quasiperiodic to stochastic motions in a one-dimensional classical system, consisting of particles with nearest-neighbor Lennard Jones interaction, by computer simulation. In and around the transition region, between regular and stochastic motions, 1⧹f α (0 ⩽ a ⩽ 2) type fluctuations of the total kinetic energy can be well observed, even for the system with a small degree of freedom with an increase of the total energy per one particle, which weakly depends on the number of particles. The system size dependence of the critical frequency from which the 1⧹f α type fluctuations begin to appear is also investigated. The non-stationary fluctuations corresponding to the 1⧹f α type power spectral density can be also characterized by Allan variance.

Statistical Properties of Self-Diffusion in AgI in a Classically Mesoscopic Regime.

The distribution p ( x , t ) of time-developing Cartesian component of particle displacement, x = x ( t )- x (0), starting from δ-function is studied extensively in a superionic conductor AgI in a classically mesoscopic regime using the method of molecular dynamics calculation. The distribution law is modified from that of the Gaussian process, and is found to have the form p ( x , t )∝exp {- a x β / t α }, ( a >0, 0 ≤α≤1, 0 ( t )∝ t 2α/β seems to be t -linear, i.e., 2α/β≃1, in the molten and/or α phase. At the melting point or the superionic transition point, two different distributions of this type seem to compete with each other.

DYNAMICAL INSTABILITY IN THE FEW-PARTICLE LENNARD–JONES CHAIN

We show the energy-dependence of maximal Lyapunov exponent in the one-dimensional Lennard–Jones system consisting of three or four particles with a periodic boundary condition. The robustness of the plateau region, in which the energy-dependence is insensitive, is shown for few-particle systems. It is also shown that the plateau region is roughly characterized by the collision property of the particles. Moreover, the Poincare section corresponding to the energy dependence is given.

HOW IS SYMPLECTIC INTEGRATOR APPLICABLE TO MOLECULAR DYNAMICS

We systematically investigate how symplectic integrator schemes are effective when applied to molecular dynamics method. The performances are estimated from a point of view of the total energy conservation by investigating molecular dynamics of one-component Lennard–Jones system in constant volume and constant temperature and pressure. It is shown that numerical simulations by the symplectic integrator scheme are better than those by classical schemes for a long-time simulation even in the case of large step size. The performances of various orders of symplectic integrator are evaluated.

DYNAMICAL INSTABILITY OF ONE-DIMENSIONAL MORSE SYSTEM

Dynamical instability in an one-dimensional many-body system with Morse-type interaction potential is studied by computer simulation. The dynamical instability of the Morse system is caused by two kinds of instability. One is the parametric instability caused by the stochastic fluctuation of positive curvature of a Riemannian manifold and the other is the local instability approximated by the local negative eigenvalues of the Hessian matrix for the potential function. We investigate the energy dependence of the maximal Lyapunov exponent in order to emphasize the characteristic dynamical instability of the Morse system and compare the characteristics with results have been reported in Fermi–Pasta–Ulam system and Lennard–Jones system. We also investigate the energy dependence of the particle diffusion in the Morse system.

Lyapunov Analysis of One-Dimensional Lennard-Jones System

We have already reported energy-dependence of maximum Lyapunov exponent (MLE) in one-dimensional Lennard-Jones (LJ) system. 1), 2) As a result, the energydependence is classified into four characteristic regions as the energy of the system increases: (1) quasiperiodic, (2) weakly chaotic, (3) plateau and (4) strongly chaotic regions. 1) 3) The existence of the plateau region, in which the energy-dependence is insensitive, is a remarkable feature of LJ system, different from Fermi-Pasta-Ulam (FPU) and soft-core system. (See Fig. 1.) In this report, we give the details of the characteristics of dynamical property in the plateau region, by calculating distribution of local MLE with comparing with FPU system.

ENERGY DEPENDENCE OF DYNAMICAL INSTABILITY IN ONE-DIMENSIONAL LENNARD–JONES SYSTEM

We have reported energy dependence of maximal Lyapunov exponent in one-dimensional Lennard–Jones (LJ) system in previous papers [Int. J. Mod. Phys.B12, 901 (1998); Mod. Phys. Lett.B12, 615 (1998)]. The existence of the plateau region, in which the energy dependence is insensitive, has been shown as a remarkable feature of the LJ system, different from FPU and soft-core system. In this paper, we investigate the details of the characteristics of dynamical property in the plateau region, by means of Lyapunov spectra and distribution of local maximal Lyapunov exponents.