Long-time behavior of the velocity autocorrelation function for moderately dense, soft-repulsive, and Lennard-Jones fluids

Data-driven coarse-grained modeling of polymers in solution with structural and dynamic properties conserved

We present data-driven coarse-grained (CG) modeling for polymers in solution, which conserves the dynamic as well as structural properties of the underlying atomistic system. The CG modeling is built upon the framework of the generalized Langevin equation (GLE). The key is to determine each term in the GLE by directly linking it to atomistic data. In particular, we propose a two-stage Gaussian process-based Bayesian optimization method to infer the non-Markovian memory kernel from the data of the velocity autocorrelation function (VACF). Considering that the long-time behaviors of the VACF and memory kernel for polymer solutions can exhibit hydrodynamic scaling (algebraic decay with time), we further develop an active learning method to determine the emergence of hydrodynamic scaling, which can accelerate the inference process of the memory kernel. The proposed methods do not rely on how the mean force or CG potential in the GLE is constructed. Thus, we also compare two methods for constructing the CG potential: a deep learning method and the iterative Boltzmann inversion method. With the memory kernel and CG potential determined, the GLE is mapped onto an extended Markovian process to circumvent the expensive cost of directly solving the GLE. The accuracy and computational efficiency of the proposed CG modeling are assessed in a model star-polymer solution system at three representative concentrations. By comparing with the reference atomistic simulation results, we demonstrate that the proposed CG modeling can robustly and accurately reproduce the dynamic and structural properties of polymers in solution.

Density dependence of the dynamical processes governing the velocity autocorrelation function of a quantum fluid

We present an exponential mode analysis of the dynamical processes determining the time behavior of the Kubo velocity autocorrelation function (KVAF) of fluid para-H_{2}, as obtained by ring polymer molecular dynamics simulations at various fluid densities. The mechanisms contributing to the decay of the KVAF are thoroughly characterized at a slightly supercritical temperature, in a density interval ranging from the critical point to the fluid-solid transition. We show that the quantum nature of the system does not influence the specific phenomena and decay channels through which a loss in velocity correlation takes place, since these are the same as found in classical fluids. Similarly, a dynamical crossover is observed with increasing density, signaling the onset of a transverse-like dynamics like in classical systems. We also investigate the effect of density on the processes contributing to the most relevant property of a quantum fluid, namely, the large values of the total and zero-point kinetic energy arising through the Heisenberg uncertainty principle.

Dynamical Origin of the Total and Zero-Point Kinetic Energy in a Quantum Fluid

By applying an exponential mode analysis to ring polymer molecular dynamics simulations of dense fluid parahydrogen, we find that the dynamical processes establishing the time behavior of the Kubo velocity autocorrelation function display the same nature as those already observed in high-density classical fluids. This result permits us to demonstrate that the exponential mode decomposition is a unique tool to identify which dynamical processes lead to one of the most notable properties of quantum fluids: the large value of the mean kinetic energy per particle and the importance of the zero-temperature quantum effects in determining it.

Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions

Through molecular dynamics simulations, we examined the hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius aHD was quantified from the Stokes-Einstein relation. The aHD value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, aHD is similar to the size of bare fullerene when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. A hydrodynamic long-time tail t-3/2 is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particle size. However, the VACF at shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of the VACF around the sound-propagation timescale over the particle size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.

Friction and diffusion of a nano-colloidal disk in a two-dimensional solvent with a liquid-liquid transition

We report on the friction and diffusion of a single mobile nano-colloidal disk, whose size and mass are one and two orders of magnitude, respectively, greater than the molecules of the host solvent; all particles are restricted to move in a two-dimensional space. Using molecular dynamics simulations, the variation of the transport coefficients as a function of the thermodynamic state of the supporting fluid, in particular, around those states in the neighbourhood of the liquid-liquid phase coexistence, is investigated. The diffusion coefficient is determined through the fit of the mean-square displacement at long times and with the Green-Kubo relationship for the velocity autocorrelation function, whereas the friction coefficient is computed from the correlation of the fluctuating force. From the determination of the transport properties, the applicability of the Stokes-Einstein relation in two dimensions around the second critical point is discussed.

Molecular hydrodynamics: Vortex formation and sound wave propagation

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.

Density of states and dynamical crossover in a dense fluid revealed by exponential mode analysis of the velocity autocorrelation function

Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [Phys. Rev. E 92, 042166 (2015)PLEEE81539-375510.1103/PhysRevE.92.042166] to cover higher-density and lower-temperature states, we show that the recently demonstrated multiexponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multiexponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wave vectors.

Self-consistent molecular dynamics calculation of diffusion in higher n-alkanes

Diffusion is one of the key subjects of molecular modeling and simulation studies. However, there is an unresolved lack of consistency between Einstein-Smoluchowski (E-S) and Green-Kubo (G-K) methods for diffusion coefficient calculations in systems of complex molecules. In this paper, we analyze this problem for the case of liquid n-triacontane. The non-conventional long-time tails of the velocity autocorrelation function (VACF) are found for this system. Temperature dependence of the VACF tail decay exponent is defined. The proper inclusion of the long-time tail contributions to the diffusion coefficient calculation results in the consistency between G-K and E-S methods. Having considered the major factors influencing the precision of the diffusion rate calculations in comparison with experimental data (system size effects and force field parameters), we point to hydrogen nuclear quantum effects as, presumably, the last obstacle to fully consistent n-alkane description.

Time dependence of the velocity autocorrelation function of a fluid: An eigenmode analysis of dynamical processes

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.

Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.

Superdiffusion in quasi-two-dimensional Yukawa liquids

The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa systems are investigated by molecular dynamics simulations. Using both the asymptotic behavior of the mean-squared displacement of the particles and the long-time tail of the velocity autocorrelation function as indicators of superdiffusion, we confirm the existence of a transition from normal diffusion to superdiffusion in systems changing from a three-dimensional to a two-dimensional character. A connection between superdiffusion and dimensionality is established by the behavior of the projected pair distribution function.

Stokes-Einstein relation for pure simple fluids

The authors employed the equilibrium molecular dynamics technique to calculate the self-diffusion coefficient and the shear viscosity for simple fluids that obey the Lennard-Jones 6-12 potential in order to investigate the validity of the Stokes-Einstein (SE) relation for pure simple fluids. They performed calculations in a broad range of density and temperature in order to test the SE relation. The main goal of this work is to exactly calculate the constant, here denominated by alpha, present in the SE relation. Also, a modified SE relation where a fluid density is raised to a power in the usual expression is compared to the classical expression. According to the authors' simulations slip boundary conditions (alpha=4) can be satisfied in some state points. An intermediate value of alpha=5 was found in some regions of the phase diagram confirming the mode coupling theory. In addition depending on the phase diagram point and the definition of hydrodynamics radius, stick boundary condition (alpha=6) can be reproduced. The authors investigated the role of the hydrodynamic radius in the SE relation using three different definitions. The authors also present calculations for alpha in a hard-sphere system showing that the slip boundary conditions hold at very high density. They discuss possible explanations for their results and the role of the hydrodynamic radius for different definitions in the SE relation.

Dynamical signatures of freezing: stable fluids, metastable fluids, and crystals

Mean squared displacements and velocity auto correlation functions are calculated using molecular dynamics for hard spheres under a range of conditions (i) for the equilibrium fluid below freezing; (ii) for the metastable fluid above freezing; and (iii) for the hard sphere crystal, both in the metastable region between freezing and melting, and in the stable region above melting. In addition, simulations are carried out for a metastable Lennard-Jones system. The results confirm recent studies that indicated the disappearance of the classical Alder long-time tail, and show that they apply to systems other than the metastable hard sphere fluid. The implications of these results for our understanding of crystallization and the glass transition are discussed.

Long-time behavior of the velocity autocorrelation function at low densities and near the critical point of simple fluids

Numerous theoretical and numerical works have been devoted to the study of the algebraic decrease at large times of the velocity autocorrelation function of particles in a fluid. The derivation of this behavior, the so-called long-time tail, generally based on linearized hydrodynamics, makes no reference to any specific characteristic of the particle interactions. However, in the literature doubts have been expressed about the possibility that by numerical simulations the long-time tail can be observed in the whole fluid phase domain of systems in which the particles interact by soft-core and attractive pair potentials. In this work, extensive and accurate molecular-dynamics simulations establish that the predicted long-time tail of the velocity autocorrelation function exists in a low-density fluid of particles interacting by a soft-repulsive potential and near the liquid-gas critical point of a Lennard-Jones system. These results contribute to the confirmation that the algebraic decay of the velocity autocorrelation function is universal in these fluid systems.

Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This second of a series of four papers presents the results for the self-diffusion coefficient, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. The uncertainty of the self-diffusion data is estimated to be 1% in the gas region and 0.5% at high-density liquid states. With the very accurate data, even fine details in the shape of the self-diffusion isotherms are resolved, and the previously little-investigated behavior of the self-diffusion coefficient at low-density gaseous states is analyzed in detail. Finally, aspects of the mass transport mechanisms on the molecular scale are explored by an analysis of the velocity autocorrelation functions.