Time Evolution of the Total Distribution Function of a One-Dimensional System of Hard Rods

Lebowitz, Joel; Percus, J. K.; Sykes, J. F.

doi:10.1103/physrev.171.224

Cited by 82 publications

(40 citation statements)

References 16 publications

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“…It has been shown by Lebowitz, Percus, and Sykes, (14) that F(k, t) for a one-dimensional system of hard rods does not display damped oscillatory behavior unless the velocity distribution contains some d functions. Moreover, even for a d-function distribution, there exists no single velocity (sound velocity) describing the propagation of a disturbance because each particle velocity is conserved.…”

Section: Resultsmentioning

confidence: 97%

Collective modes of one-dimensional lennard-jones systems

Bishop

1982

J Stat Phys

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The density fluctuations of one-dimensional Lennard-Jones systems are investigated by molecular dynamics simulation. The full Lennard-Jones potential is compared to the repulsive Lennard-Jones potential. It is found that the behavior of the density fluctuations at small wave vectors is determined by the repulsive portion of the potential. The variation of the fluctuations with density is explained. It is shown that these systems do not display hydrodynamics.

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Section: Resultsmentioning

confidence: 97%

Collective modes of one-dimensional lennard-jones systems

Bishop

1982

J Stat Phys

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“…The exact analytical treatment of the infinite system of identical hard-core particles on a line 12,13 shows that the relaxation of a test particle in the system deviates from the short-time exponential behavior, and the VAF presents then a very small, negative part whose leading term is of the form (1) with 8 = 3. That is, the situation differs from the one depicted at d = 2, 3, where the tail is positive and the power-law exponent is d/2.…”

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confidence: 99%

Long-time tails in the velocity autocorrelation function of hard-rod binary mixtures

Marro

Masoliver

1985

Phys. Rev. Lett.

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The temporal evolution of binary mixtures of hard rods in a ring is simulated in a computer with random initial velocities ± v. The time the system takes to reach a Maxwellian distribution dramatically diverges as the mass ratio e -• 1 and it also increases, although rather slowly, when e -• oo. A negative "long-time tail," i.e., a slow, power-law decay in the velocity autocorrelation function at large values of the time t, is observed whose behavior changes from t~3 to t~b, 8 < 1, as e is increased from €=1.

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“…The equation of state for the HR system was solved exactly by Tonks 42 and thus, this system is colloquially known as a Tonks gas. Further theoretical studies of the nonequilibrium properties of the HR system have also been performed, notably by Lebowitz et al [43][44][45] and Jepsen. 46 These theoretical predictions have been confirmed by Bishop and Berne, 47 as well as Haus and Raveché, 48 using molecular dynamics simulations.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

Craven

Popov

Hernandez

2015

The Journal of Chemical Physics

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The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system's constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

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Time Evolution of the Total Distribution Function of a One-Dimensional System of Hard Rods

Cited by 82 publications

References 16 publications

Collective modes of one-dimensional lennard-jones systems

Collective modes of one-dimensional lennard-jones systems

Long-time tails in the velocity autocorrelation function of hard-rod binary mixtures

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

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