We study the time scale T to equipartition in a [Formula Presented] lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam β model). We take the initial energy to be either in a single mode γ or in a package of low-frequency modes centered at γ and of width δγ, with both γ and δγ proportional to N. These initial conditions both give, for finite energy densities [Formula Presented] a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density [Formula Presented] A theory of the scaling with [Formula Presented] is presented and compared to the numerical results in the range [Formula Presented]. © 1999 The American Physical Society.
Finite times to equipartition in the thermodynamic limit / De Luca, J.; Lichtenberg, A. J.; Ruffo, S.. - In: PHYSICAL REVIEW E. - ISSN 1063-651X. - 60:4(1999), pp. 3781-3786. [10.1103/PhysRevE.60.3781]
Finite times to equipartition in the thermodynamic limit
Ruffo S.
1999-01-01
Abstract
We study the time scale T to equipartition in a [Formula Presented] lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam β model). We take the initial energy to be either in a single mode γ or in a package of low-frequency modes centered at γ and of width δγ, with both γ and δγ proportional to N. These initial conditions both give, for finite energy densities [Formula Presented] a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density [Formula Presented] A theory of the scaling with [Formula Presented] is presented and compared to the numerical results in the range [Formula Presented]. © 1999 The American Physical Society.File | Dimensione | Formato | |
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