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

Marro, Joaquín; Masoliver, Jaume

doi:10.1103/physrevlett.54.731

Cited by 16 publications

(7 citation statements)

References 17 publications

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“…Theoretical studies [16] and simulation for various systems and molecular interactions [17,18,11,[19][20][21][22][23] Thus, determination of the VAF asymptotic behavior in dense systems remains a challenge. which complete understanding cannot be revealed by using traditional experimental techniques.…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical studies [16] and simulation for various systems and molecular interactions [17,18,11,[19][20][21][22][23] reinforced the hypothesis of the power law time dependence of the LTT, but with limitations posed by a finite time interval of simulations and the uncertainty of extrapolation to an infinite number of interacting particles [24]. These studies give comprehensive understanding of the LTT in a hard disk/sphere system, in contrast to the systems with more realistic continuous interaction like a Lennard-Jones potentials, where the LTT appears only in intermediate densities, almost in the gaseous state, while in dense systems other dynamical effects on shorter time scales, such as backscattering due to bouncing of atoms of near neighbours, effectively hide the LTT [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

et al. 2018

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The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a t −3/2 long time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations. PACS. 76.60.Lz Spin echoes and 83.10.Mj Molecular dynamics, Brownian dynamics and 33.20.-t Molecular spectra

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

et al. 2018

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“…The problem of optimal relaxation in a one-dimensional binary gas mixture was first studied numerically in [15] through molecular dynamics simulation of a system of hard rods. Investigations have subsequently concentrated on the homogeneous (space-independent) Boltzmann equation, describing the evolution of the velocity distributions of both species F i (v, t) (i = 1, 2) as a coupled system…”

Section: Elastic Binary Mixtures and Beyondmentioning

confidence: 99%

“…Therefore, there must exist some optimal ratio in the interval ]1, ∞[ over which the relaxation rate is always finite. Following numerical observations for a binary mixture of hard rods [15], this problem has been solved for Maxwellian particles (see below) by two different techniques [16][17][18][19], leading to the same result: an optimal mass ratio of m 2 /m 1 = 3 + 2 √ 2 ≃ 5.82. This result has been extended to species with different concentrations in [20], using a method that may be generalized to an arbitrary number of discrete species.…”

Section: Introductionmentioning

confidence: 99%

Polydispersity and Optimal Relaxation in the Hard Sphere Fluid

Barbier

Trizac

2014

J Stat Phys

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We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the result that no such continuous dispersion in fact minimizes the relaxation time, as the global optimum is characterized by a finite number of species. This optimal mixture is found to depend on the dimension d of space, ranging from five species for d = 1 to a single one for d ≥ 4. The role of the collisional kernel is also discussed, and extensions to dissipative systems are shown to be possible.

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“…Observing tagged particle dynamics constitutes a simple way of probing the complex dynamics of an interacting many body system and has been studied both theoretically [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] and experimentally [24,25,26,27,28,29]. Much of the theoretical studies on tagged particle diffusion have focused on one-dimensional systems and discussed two situations where the microscopic particle dynamics is (i) Hamiltonian [1,2,3,4,5,6,7,8,9,10,11] or (ii) stochastic [12,13,14,15,16,17,18,19,20,…”

Section: Introductionmentioning

confidence: 99%

Tagged Particle Diffusion in One-Dimensional Systems with Hamiltonian Dynamics-II

et al. 2015

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We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal distribution. The correlation functions are studied in finite systems, and their forms examined at short and long times. Various one-dimensional systems are studied. Results of numerical simulations for the Fermi-Pasta-Ulam chain are qualitatively similar to results for the harmonic chain, and agree unexpectedly well with a simple description in terms of linearized equations for damped fluctuating sound waves. Simulation results for the alternate mass hard particle gas reveal that -in contradiction to our earlier results [1] with smaller system sizes -the diffusion constant slowly converges to a constant value, in a manner consistent with mode coupling theories. Our simulations also show that the behaviour of the Lennard-Jones gas depends on its density. At low densities, it behaves like a hard-particle gas, and at high densities like an anharmonic chain. In all the systems studied, the tagged particle was found to show normal diffusion asymptotically, with convergence times depending on the system under study. Finite size effects show up at time scales larger than sound traversal times, their nature being system-specific.

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

Cited by 16 publications

References 17 publications

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method

Polydispersity and Optimal Relaxation in the Hard Sphere Fluid

Tagged Particle Diffusion in One-Dimensional Systems with Hamiltonian Dynamics-II

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