Collective modes of one-dimensional lennard-jones systems

Bishop, Marvin

doi:10.1007/bf01342191

Cited by 12 publications

(14 citation statements)

References 14 publications

(7 reference statements)

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“…In practice, as pointed out in Refs. [19,20], even in this case the interaction is limited to about 2-3 neighbours. Therefore, we do not expect that the results reported below will be significantly altered when taking into account the interaction among all pairs.…”

Section: The Modelmentioning

confidence: 88%

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The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

2005

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The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest-neighbour Lennard-Jones potential are computed by molecular-dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon-like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneus fragmentation of the crystal-like structure into an ensemble of "clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q 2 behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.PACS. 05.60.-k Transport processes -66.10.Cb Diffusion and thermal diffusion

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Section: The Modelmentioning

confidence: 88%

“…Of particular relevance in what follows is the work of Bishop and collaborators [19,20]. At variance with our model, they considered the case in which the interaction is extended to all particle pairs.…”

Section: Introductionmentioning

confidence: 99%

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

2005

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“…Early results seem to be rather inconclusive about whether it has a finite thermal conductivity or not [24,25].…”

Section: Introductionmentioning

confidence: 99%

Cluster sizes in a classical Lennard-Jones chain

Lee-Dadswell¹,

Barrett²,

Power³

2017

Phys. Rev. E

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The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed.Analytical expressions are obtained for the expected cluster length, K , as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that K increases exponentially with β = 1/k B T and with pressure, P in agreement with previous results in the literature. A method is illustrated for using K (β, P ) to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.

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“…The conventional hydrodynamic theory predicts that a perturbation may induce a heat mode and a sound mode [2], hence the relaxation of a fluctuation may be understood as a combination of such two types of hydrodynamic modes. However, in recent decades, it has been found that the linearized hydrodynamic description may be invalid in low-dimension systems [3][4][5]. Therefore, it is necessary to investigate, by direct simulations, the particular properties of the hydrodynamic modes and show how they manifest themselves in different systems.…”

Section: Introductionmentioning

confidence: 99%

Diffusion of heat, energy, momentum, and mass in one-dimensional systems

et al. 2013

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NNSF of China [10925525, 11275159, 10805036]; SRFDP of China [20100121110021]We study diffusion processes of local fluctuations of heat, energy, momentum, and mass in three paradigmatic one-dimensional systems. For each system, diffusion processes of four physical quantities are simulated and the cross correlations between them are investigated. We find that, in all three systems, diffusion processes of energy and mass can be perfectly expressed as a linear combination of those of heat and momentum, suggesting that diffusion processes of heat and momentum may represent the heat mode and the sound mode in the hydrodynamic theory. In addition, the dynamic structure factor, which describes the diffusion behavior of local mass density fluctuations, is in general insufficient for probing diffusion processes of other quantities because in some cases there is no correlation between them. We also find that the diffusion behavior of heat can be qualitatively different from that of energy, and, as a result, previous studies trying to relate heat conduction to energy diffusion should be revisited. DOI: 10.1103/PhysRevE.87.03215

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Collective modes of one-dimensional lennard-jones systems

Cited by 12 publications

References 14 publications

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

Cluster sizes in a classical Lennard-Jones chain

Diffusion of heat, energy, momentum, and mass in one-dimensional systems

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