The superperiod of the nonlinear weighted string (FPU) problem

Tuck, J.L.; Menzel, Matthias

doi:10.1016/0001-8708(72)90024-2

Cited by 76 publications

(42 citation statements)

References 18 publications

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“…Unfortunately, it has not been possible to extend the SB simulations to shear rates where significant normal pressure differences and nonequipartition of the kinetic energy occur, y*-2, as the very high temperatures generated lead to fluid particles penetrating the wall. Attempts to "stiffen" the boundaries by using higher values of k proved counterproductive as this leads to a reduction in the rate of energy transfer between the fluid and the boundary particles and a consequent increase in the fluid temperature This decoupling behavior is well known for system with disparate characteristic frequencies [31]. Another possibility might be to modify the interaction potential between the wall and fluid particles in order to reduce penetration, but we have not explored this method.…”

Section: A Comparisons Between the Two Methodsmentioning

confidence: 99%

Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method

1992

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The homogeneous-shear (HS} technique has been used extensively to study shear How, but it uses artificial methods to remove the viscous heat generated. In reality the viscous heat is removed from the system by conduction out through the boundaries. This inevitably leads to characteristic gradients in temperature, density, and shear rate. While at low shear rates these effects may be neglected, and the use of HS justified, at high shear rates they certainly cannot, and doubts remain as to the validity of HS in this regime. In this study we make careful comparisons between HS and a more-realistic slidingboundary method. HS gives very similar results when conditions corresponding to different regions within the sliding system are used. The use of HS simulations at shear rates where energy is generated at a rate faster than can be realistically removed by any natural process is called into question.PACS number(s): 47.50.+d, 47.25.Ei, 44.90.+c, 66.20.+d

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Section: A Comparisons Between the Two Methodsmentioning

confidence: 99%

Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method

1992

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“…(For a chain of 32, atoms the initial state was almost recovered on a time-scale associated with about 158 periods of the harmonic oscillators.) Subsequent computations by James Tuck and Mary Tsingou Menzel [2] showed that, on a longer time-scale, the system exhibited superrecurrences. This phenomenon remained a complete puzzle until Zabusky and Kruskal mapped the discrete lattice problem onto the nonlinear Korteweg-de Vries equation and showed [3], via numerical computation, that this system also exhibited a similarly unusual recurrence phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Quantized intrinsically localized modes of the Fermi–Pasta–Ulam lattice

Basu¹,

Riseborough

2012

Philosophical Magazine

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We have examined the quantized n ¼ 2 excitation spectrum of the FermiPasta-Ulam lattice. The spectrum is composed of a resonance in the twophonon continuum and a branch of infinitely long-lived excitations which splits off from the top of the two-phonon creation continuum. We calculate the zero-temperature limit of the many-body wavefunction and show that this mode corresponds to an intrinsically localized mode (ILM). In one dimension, we find that there is no lower threshold value of the repulsive interaction that must be exceeded if the ILM is to be formed. However, the spatial extent of the ILM wavefunction rapidly increases as the interaction is decreased to zero. The dispersion relation shows that the discrete n ¼ 2 ILM and the resonance hybridize as the center of mass wavevector q is increased towards the zone boundary. The many-body wavefunction shows that as the zone boundary is approached, there is a destructive resonance which occurs between pairs of sites separated by an odd number of lattice spacings. We compare our theoretical results with the recent experimental observation of a discrete ILM in NaI by Manley et al.

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“…The simplest dynamics problem of this kind is a variant of Fermi's anharmonic chain studies. 5 It is the Newtonian motion of a nearest-neighbor harmonic chain, in which the motion of the ith particle responds to forces linear in the relative displacements of its neighbors:…”

Section: The Simplest Problem a One-dimensional Harmonic Chainmentioning

confidence: 99%

“…This computational particle description is called molecular dynamics, and originated about 50 years ago at the Los Alamos, Livermore, and Brookhaven National Laboratories. [5][6][7][8][9] The computational requirement is to solve the particle equations of motion, mr = mv = F atomistic + F boundary + F constraints + F driving , ͑1͒…”

Section: Introductionmentioning

confidence: 99%