Three-dimensional Lennard-Jones Fluids Research Articles

Perspective: How to overcome dynamical density functional theory

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.

Communication: The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three-dimensional Lennard-Jones fluids

We analyze the interrelation between the coexistence curve of the Lennard-Jones fluid and the Ising model in two and three dimensions within the global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)]. In case of two dimensions, we use the exact Onsager result to construct the binodal of the corresponding Lennard-Jones fluid and compare it with the results of the simulations. In the three-dimensional case, we use available numerical results for the Ising model for the corresponding mapping. The possibility to observe the singularity of the binodal diameter is discussed.

Parallel canonical Monte Carlo simulations through sequential updating of particles

In canonical Monte Carlo simulations, sequential updating of particles is equivalent to random updating due to particle indistinguishability. In contrast, in grand canonical Monte Carlo simulations, sequential implementation of the particle transfer steps in a dense grid of distinct points in space improves both the serial and the parallel efficiency of the simulation. The main advantage of sequential updating in parallel canonical Monte Carlo simulations is the reduction in interprocessor communication, which is usually a slow process. In this work, we propose a parallelization method for canonical Monte Carlo simulations via domain decomposition techniques and sequential updating of particles. Each domain is further divided into a middle and two outer sections. Information exchange is required after the completion of the updating of the outer regions. During the updating of the middle section, communication does not occur unless a particle moves out of this section. Results on two- and three-dimensional Lennard-Jones fluids indicate a nearly perfect improvement in parallel efficiency for large systems.

Lyapunov modes in three-dimensional Lennard-Jones fluids

Recent studies on the phase-space dynamics of a one-dimensional Lennard-Jones fluid reveal the existence of regular collective perturbations associated with the smallest positive Lyapunov exponents of the system, called hydrodynamic Lyapunov modes, which previously could only be identified in hard-core fluids. In this work we present a systematic study of the Lyapunov exponents and Lyapunov vectors, i.e. perturbations along each direction of phase space, of a three-dimensional Lennard-Jones fluid. By performing the Fourier transform of the spatial density of the coordinate part of the Lyapunov vector components and then time-averaging this result we find convincing signatures of longitudinal modes, with inconclusive evidence of transverse modes for all studied densities. Furthermore, the longitudinal modes can be more clearly identified for the higher density values. Thus, according to our results, the mixing of modes induced by both the dynamics and the dimensionality induces a hitherto unknown type of order in the tangent space of the model herein studied at high density values.

Spatial updating grand canonical Monte Carlo algorithms for fluid simulation: Generalization to continuous potentials and parallel implementation

Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.

Enhanced septahedral ordering in cold Lennard-Jones fluids

We report molecular dynamics calculations on a two-component, cold, 15,625 particle, three-dimensional Lennard-Jones fluid. We calculated spherical harmonic components Q(LM) for the density of particles in the first coordination shell of each particle, as well as their spherical invariants <Q2L>, time-correlation functions, and wavelet density decompositions. The spherical invariants show that noncrystalline septahedral (<Q27>) ordering is important, especially at low temperature. While < Q210> could arise from icosahedral ordering, its behavior so closely tracks that of the nonicosahedral <Q211> that alternative origins for <Q210> need to be considered. Time correlation functions of spherical harmonic components are bimodal, with a faster temperature-independent mode and a slow, strongly temperature-dependent mode. Volume wavelet decompositions show that when T is reduced, the correlation length of <Q27> increases, especially below T=0.7 , but that the correlation length of <Q25> is independent of T .

Surface tension of the three-dimensional Lennard-Jones fluid from histogram-reweighting Monte Carlo simulations

The surface tension of the full three-dimensional Lennard-Jones potential is calculated from grand canonical Monte Carlo simulations with the finite-size scaling methodology outlined by Binder [Phys. Rev. A 25, 1699 (1982)]. Surface tensions are determined for the range of reduced temperatures T*=0.95–1.312 and are found to be in good agreement with molecular-dynamics calculations. A critical temperature Tc*=1.311±0.002 is established by locating the T* where the surface tension of the infinite system size vanishes. In addition, with this method it is possible to determine the critical exponent 2ν. For the Lennard-Jones fluid we found 2ν=1.42±0.08, which differs from the accepted value of 2ν=1.26.

Vapour - Liquid Equilibrium Properties for Two- and Three-dimensional Lennard-Jones Fluids from Equations of State

Vapour–liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour–liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state.

The high temperature approximation and linearity of the thermodynamic properties on the WCA perturbation parameter

Abstract We carried out extensive computer simulations to obtain the radial distribution function, potential energy per particle and pressure for three-dimensional Lennard-Jones fluids. Each thermodynamic state (265 in total) was simulated for five values of the perturbative parameter of the Weeks-Chandler-Andersen theory. The results show that, for the Helmholtz free energy, the high temperature approximation works very well for all the temperatures and densities studied here, for the potential energy it is good at moderate and high densities for all temperatures, whereas for the pressure it is generally not good. In accordance with other works, for the radial distribution function the high temperature approximation can be used at high densities only. The linearity of the thermodynamic properties, with respect to the perturbative parameter of this theory was also analysed. The results show that the Helmholtz free energy, potential energy per particle and pressure are linear in the mentioned parameter for all densities and temperatures.

Computer Simulation of Vapor-Liquid Phase Separation

Abstract A late-time growth law of domains undergoing vapor-liquid phase separation is studied for two- and three-dimensional Lennard-Jones fluids by molecular dynamics simulations. The characteristic domain size shows a power law growth in a late stage with the growth exponent of ½ for both two- and three-dimensional fluids. This study concerns also the relationship between statistical properties of domain patterns and temperatures. The asymptotic form factor of each system is obtained using scaling and the asymptotic tail of the form factor is analyzed. This tail is related to the domain-wall structure. At low system temperatures, the form factor satisfies Porod's law; the asymptotic tail decreases as S(k) ∼ k −(D+ 1) where D is the system dimensionality. However, it is found that the decay of the asymptotic tail becomes slower than that of the Porod tail at higher temperatures in both two- and three-dimensional systems. This indicates that the dimension of the domain wall is fractal and increases with ...

Computer simulation of vapor-liquid phase separation in two- and three-dimensional fluids. II. Domain structure.

Fluids undergoing phase separation exhibit complicated domain patterns. In this study we perform molecular-dynamics simulations for two- and three-dimensional Lennard-Jones fluids in order to investigate the relationship between statistical properties of domain structure and system temperature. The asymptotic form factor of each pattern is obtained using scaling and its temperature dependence studied. In particular the asymptotic tail of the form factor is analyzed. This tail is related to the domain-wall structure. At low system, temperatures, the form factor satisfies Porod's law; its asymptotic tail decreases as S(k)\ensuremath{\sim}${\mathit{k}}^{\mathrm{\ensuremath{-}}(\mathit{D}+1)}$ where D is the system dimensionality. However, it is found that the decay of the asymptotic tail becomes slower than that of the Porod tail at higher temperatures in both the two- and three-dimensional systems. This indicates that the dimension of the domain wall is fractal and increases with increasing system temperature.

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field (β = 1/2 in the immediate vicinity of the critical point to Ising-like (β= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.