Journal ArticleDOI
The Induction Phenomenon and Ergodicity in the Anharmonic Lattice Vibration
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In this article, it was shown that the induction phenomenon in the exchange of energies of normal modes found by computer experiments is an inherent property of the anharmonic lattice vibration and its behavior obeys the time reversal even after the elapse of the induction period.Abstract:
It is shown that the induction phenomenon in the exchange of energies of normal modes found by computer experiments is an inherent property of the anharmonic lattice vibration and its behavior obeys the time reversal even after the elapse of the induction period. The instability of the normal modes when one mode is excited initially is related to the induction phenomenon, and is discussed by the application of the instability region of the Mathieu function. The exponential orbital separation is also shown to take place after the elapse of the induction period. This guarantees the C-property of the anharmonic lattice vibration.read more
Citations
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Exact solutions in the FPU oscillator chain
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Low-Dimensional Solutions in the Quartic Fermi–Pasta–Ulam System
TL;DR: In this article, general expressions for the type I subsets of the Fermi-Pasta-Ulam (FPU)-β system were derived for the induction phenomenon.
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Ergodicity and Time-Scales for Statistical Equilibrium in Classical Dynamical Systems
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Reversible approach to statistical equilibrium in a nonlinear chain: an ensemble study
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Metastable states and energy flow pathway in square graphene resonators.
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References
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Journal ArticleDOI
Computer Studies on the Approach to Thermal Equilibrium in Coupled Anharmonic Oscillators. II. One-Dimensional Case
Hajime Hirooka,Nobuhiko Saitô +1 more
TL;DR: One-dimensional anharmonic lattices with quadratic as well as quartic potentials between nearest neighbors are treated on computer to see the long-time behaviors of the vibration.
Journal ArticleDOI
Nonlinear coupled oscillators: Modal equation approach
TL;DR: In this paper, a one-dimensional system of equimass particles coupled by identical nonlinear springs is studied, where the equations of motion are expressed in terms of the normal coordinates of the corresponding linear system.
Journal ArticleDOI
Computer Experiments on Ergodic Problems in Anharmonic Lattice Vibrations
TL;DR: In this paper, a short review of the present status of the ergodic theories is also given and the interrelations among various results of various results are clarified, and the apparent randomness which the system exhibits after elapsing the induction period is, strictly speaking, quasi-stochastic.
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