Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions

Verlet, Loup

doi:10.1103/physrev.165.201

Cited by 1,164 publications

(436 citation statements)

References 19 publications

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“…The Newton's equations of motion are integrated using a Fincham's leap-frog algorithm (rotational) [30] and a Verlet Velocity algorithm (translational) [31]. The kinematic tangential relative displacement, ξ (t), is updated using an Euler's algorithm.…”

Section: Modelmentioning

confidence: 99%

Force analysis of clogging arches in a silo

et al. 2013

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In this work, we examine a quasi-2D silo that clogs due to the spontaneous formation of stable arches. We validate a numerical scheme comparing the morphology of clogging arches with previous experimental findings. Additionally, we inspect the forces that act on particles, both on those in the bulk of the silo as well as those belonging to the arches formed above the outlet. In the silo, we have found that normal forces are higher close to the wall, in contrast to the central part of the silo, where normal forces are notably lower. Besides, it is revealed that normal forces on particles belonging to the clogging arches are significantly larger than in their surroundings. In a particle of the arch, the magnitude of the force strongly depends on the angle subtended from its center to the contact points with its two neighbors in the arch. Indeed, for angles exceeding 180 • , the larger the angle, the lower the normal force and the higher the tangential one. On the contrary, for smaller angles the behavior is reversed, so the normal forces increase with the angle. Finally, we present a comparison of the normal and tangential force distributions for the particles within the arch and in the bulk. All this shows the special nature of the forces developed in clogging arches, which suggests that direct extrapolations of bulk properties should not be taken for granted.

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Section: Modelmentioning

confidence: 99%

Force analysis of clogging arches in a silo

et al. 2013

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“…Our calculations are focussed on four values of n. First, n = 6 which is long ranged and the classical model for simple liquids [38,39]. This potential has been extensively studied and therefore is suitable to validate the methods used.…”

Section: Studying Phase Behaviour In Computeromentioning

confidence: 99%

“…The structure factors were obtained by both direct Fourier transformation of the density-density correlation function [44] and by Fourier transformation of the pair correlation function [42]. The algorithms were tested on the Hard Sphere system and the Lennard Jones 12-6 system for which accurate values are available in literature [38,39,43].…”

Section: Studying Phase Behaviour In Computeromentioning

confidence: 99%

Strong weak and metastable liquids structural and dynamical aspects of the liquid state

Vliegenthart

Lodge

Lekkerkerker

1999

Physica A: Statistical Mechanics and its Applications

109

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Structural and dynamical properties of a model liquid system were studied as a function of the range of the interaction using computer simulations. We observed the usual strong dependency of the global phase diagram on the range of attraction. In systems with long range attractive interactions the structure of the liquid state down to the triple point is determined by the short range repulsive forces. For short ranged attractive interactions however the attraction has a noticeable effect. Although the gas-liquid transition becomes metastable as the attractive range becomes shorter, the change in dynamics in these systems when passing the hidden binodal is gradual rather then abrupt.

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“…We made use of direct Fourier transform 8 while Zoppi et al use an extrapolation of g(r) to large distances by means of the formula suggested by Verlet. 13 To enable a direct comparison of both sets of data we have followed the same procedure employed by Zoppi et al 12 The large-r part of the g(r)'s have been fitted to a decaying sine function 12,13 and the fitted function extrapolated to rϭ30 Å previous to Fourier inversion. The results given in Fig.…”

Section: ͑2͒mentioning

confidence: 99%

Microscopic structure factor of liquid parahydrogen: Monte Carlo and molecular dynamics simulations

et al. 2002

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We present a comparison of results on the microscopic structure of liquid parahydrogen as calculated by path-integral Monte Carlo and path-integral-centroid-molecular-dynamics simulations. The radial distribution functions calculated using both approaches are found to be in good agreement. The disagreement between published estimates for the static structure factor are found to arise from different approximations followed for the Fourier transform of heavily truncated data. A comparison of the structure of the real liquid with that of a classical analog is also made and shows that the latter would freeze at the experimental liquid density. Liquid parahydrogen is therefore stabilized by the action of large quantum effects. DOI: 10.1103/PhysRevB.66.212202 PACS number͑s͒: 67.20.ϩk, 61.12.Ϫq, 61.20.Ja The continued interest on the properties of liquid hydrogen stems from different reasons. First, it is known to be one of the dominant constituents of the giant planets 1 where it is found in various states of aggregation stretching over a vast range of densities and temperatures. Second, laboratory efforts to cross the insulator→metal transition resulting in the production of metallic hydrogen continue apace 2 and finally, apart from its use as a cryogenic liquid or as a fuel element in spacecraft technology, the material still constitutes a promising energy source since it is environmentally safe and has a high caloric content.The fundamental difficulties in dealing with this liquid arise from the light masses of its constituent particles and the relatively low temperatures where the liquid exists under its saturated vapor pressure. This makes quantum effects prominent and its first manifestation is the appearance of a discrete spectrum of transitions between molecular rotational levels. The quantum nature of such motions imposes some symmetry constraints to the total molecular wave function. This means that the rotational states and the nuclear spin states of the two protons forming the H 2 molecule are not independent. Coupling of nuclear spin states (Iϭ0 for a molecule having antiparallel proton spins and Iϭ1 for parallel spin states͒ leads to two distinguishable species, para-H 2 (p-H 2 ) and ortho-H 2 (o-H 2 ), respectively. This results in special characteristics of the interaction potential between H 2 molecules. Such constraints imply that p-H 2 molecules interact with its neighbors through an isotropic potential since the total wave function, and therefore the electronic charge distribution, will have spherical symmetry, whereas o-H 2 shows a strong angular dependence of such interactions due to the action of a finite electric quadrupole moment.The liquid structure function of p-H 2 as quantified by the g(r) radial distribution function is now beginning to be understood mostly by recourse to computer simulations where the quantum degrees of freedom are explicitly taken into consideration. A preliminary report on results from pathintegral-centroid-molecular-dynamics ͑PICMD͒ Simulations ͑Ref. 3͒ has shown ...

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Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions

Cited by 1,164 publications

References 19 publications

Force analysis of clogging arches in a silo

Force analysis of clogging arches in a silo

Strong weak and metastable liquids structural and dynamical aspects of the liquid state

Microscopic structure factor of liquid parahydrogen: Monte Carlo and molecular dynamics simulations

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