A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales

Ignatyuk, V. V.; Mryglod, I. M.; Bryk, Taras

doi:10.5488/cmp.21.13001

Cited by 3 publications

(12 citation statements)

References 30 publications

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“…Thus, a possible solid-like scenario of the fluid dynamics, which has been discussed in Ref. 31 , is not realized in our case.…”

Section: Spectral Functionsmentioning

confidence: 73%

“…In our recent paper 31 we have calculated the VAFs at various values of Γ j , regardless of their relations to the fluid at a particular thermodynamic point. We have presented different regimes of the fluids dynamics (when the system behaves in a solid-like, liquid-like or gas-like manner), modelled in the framework of such an approach.…”

Section: Time Behavior Of the Autocorrelation Functions: Computer Sim...mentioning

confidence: 99%

“…Thus, an attempt to create and verify such an approach is a motivation of our study. A present paper should be considered as a logical continuation of our very recent article 31 , where the basic concept of the effective summing up of the infinite continued fractions has been formulated, and some relevant theoretical results for the VAFs behavior have been obtained. However, in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…However, in Ref. 31 the input parameters of the theory (some kinds of SCFs) had been initially prescribed and did not rely upon the data of experiments or computer simulations.…”

Section: Introductionmentioning

confidence: 99%

“…II, we briefly recall the method of continued fractions for the VAF presentation and calculate the kinetic kernels of the highest order at a physically reasonable assumption adopted in Ref. 31 . In Sec.…”

Section: Introductionmentioning

confidence: 99%

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A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

Ignatyuk,

Mryglod,

Bryk

2019

Preprint

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Velocity autocorrelation functions (VAF) of the fluids are studied on short-and longtime scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the MD data than those of the Markovian approximation.The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode (GCM) theory, the mode coupling theory (MCT), and some other theoretical approaches.

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“…Thus, a possible solid-like scenario of the fluid dynamics, which has been discussed in Ref. 31 , is not realized in our case.…”

Section: Spectral Functionsmentioning

confidence: 73%

Section: Time Behavior Of the Autocorrelation Functions: Computer Sim...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…However, in Ref. 31 the input parameters of the theory (some kinds of SCFs) had been initially prescribed and did not rely upon the data of experiments or computer simulations.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

Ignatyuk,

Mryglod,

Bryk

2019

Preprint

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A simple closure procedure for the study of velocity autocorrelation functions in fluids as a “bridge” between different theoretical approaches

Ignatyuk

Mryglod

Bryk

2018

The Journal of Chemical Physics

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Velocity autocorrelation functions (VAFs) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have a purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the molecular dynamic data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode theory, the mode coupling theory, and some other theoretical approaches.

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Hydrodynamic correlations in isotropic fluids and liquid crystals simulated by multi-particle collision dynamics

Híjar¹

2019

Condens. Matter Phys.

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Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the implementation of multi-particle collision dynamics for isotropic fluids is analysed under the so-called Andersen-thermostatted scheme, a particular algorithm for systems in the canonical ensemble. This method gives rise to hydrodynamic fluctuations that spontaneously relax towards equilibrium. This relaxation process can be described by a linearized theory and used to calculate transport coefficients of the system. The extension of the algorithm for nematic liquid crystals is also considered. It is shown that thermal fluctuations in the average molecular orientation can be described by an extended linearized scheme. Flow fluctuations induce orientation fluctuations. However, orientational changes produce observable effects on velocity correlation functions only when simulation parameters exceed their values from those used in previous applications of the method. Otherwise, the flow can be considered to be independent of the orientation field. and energy. This property allows MPCD to recover, over long simulation times, the hydrodynamic equations of mass, momentum, and heat propagation. In addition, the stochastic character of MPCD produces fluctuations and Brownian forces [7,8].A considerable number of soft condensed matter systems have been successfully simulated under MPCD schemes. Recent examples include sediment-water interface flow [9], bistable biochemical systems [10], and two-dimensional one-component plasma [11], to mention but a few. Furthermore, modified MPCD rules have been used to extend simulations towards complex solvents, e.g., viscoelastic fluids [12] and binary mixtures [13]. Very recently, algorithms for simulating nematic liquid crystals (NLCs) using the principles of MPCD have been also proposed [14,15]. They allow one to reproduce hydrodynamic and elastic characteristics of such phases, still being potentially able to be coupled with microscopic degrees of freedom. These algorithms simulate isotropic-nematic phase transitions, consistent dynamics for annihilation of defects, and molecular reorientation under flow.Here, basic implementations of MPCD for simple liquids and NLCs are considered. Simulations for equilibrium states are presented, where systems are in contact with the thermal bath based on an Andersen thermostat that keeps them at a fixed temperature. In order to exhibit the ability of MPCD to reproduce hydrodynamic behaviour and to emphasise its stochastic character, attention is focused on the analysis of the spectra of hydrodynamic fluctuations produced by the algorithm in both simple liquids and nematics. There is discussed a very good agreement that exists between correlation functions obtained from the numerical implementation with those derived from linearized hydrodynamic models of liquids and LCs. Following the MPCD model for nematics (MPCD-N) i...

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A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales

Cited by 3 publications

References 30 publications

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a “bridge” between different theoretical approaches

Hydrodynamic correlations in isotropic fluids and liquid crystals simulated by multi-particle collision dynamics

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