Event-driven Molecular Dynamics Research Articles

Simulation of rarefied gas flow inside the satellite air intake in ultra-low Earth orbit

The key problem for the long-term operation of the satellite in ultra-low Earth orbits (ULEO) and its safety is to provide the propulsion system with a sufficient amount of working fluid. Gas from the atmosphere can be used as the working fluid, for which the satellite is equipped with an air intake. In this paper, the problem of rarefied gas flow in such an air intake in ultra-low Earth orbit (140 km) was solved. Using the method of event-driven molecular dynamics (EDMD), we studied how the narrowing of the effective aerodynamic cross-section after the air intake (in the ionization chamber) can affect the compression ratio and the flow field. It was shown that the flow field in the air intake depends significantly on the geometry of the subsequent sections of the device, therefore it is incorrect to model the flow in the air intake separately from the rest of the internal tract of the propulsion system, as it was done in the literature earlier.

Hamiltonian limited valence model for liquid polyamorphism

Liquid-liquid phase transitions have been found experimentally or by computer simulations in many compounds such as water, hydrogen, sulfur, phosphorus, carbon, silica, and silicon. Limited valence model implemented via event-driven molecular dynamics algorithm provides a simple generic mechanism for the liquid-liquid phase transitions in all these diverse cases. Here, we introduce a variant of the limited valence model with a well defined Hamiltonian, i.e., a unique algorithm by which the potential energy of the system of particles can be computed solely from the coordinates of the particles and is thus equivalent to a complex multi-body potential. We present several examples of the model which can be used to reproduce liquid--liquid phase transition in systems with maximum valence z = 1 (hydrogen), z = 2 (sulfur) and z = 4 (water), where z is the maximum number of bonds an atom is allowed to have. For z = 1, we find a set of parameters for which the system has a liquid-liquid and an isostructural solid-solid critical points. For z = 4, we find a set of parameters for which the phase diagram resembles that of water with a wide region of negative thermal expansion coefficient (density anomaly) extending into the metastable region of negative pressures. The limited valence model can be modified to forbid not only too large valences but also too low valences. In the case of sulfur, we forbid the formation of monomers, thus restricting the valence v of an atom to be within an interval 1 = vmin ≤ v ≤ vmax ≡ z = 2.

Density and confinement effects on fluid velocity slip

Understanding the velocity slip of fluids in channels of molecular length scales is essential for accurately manipulating their flow in engineering applications, such as in water desalination or, by reversing the process, osmotic power generation. This study addresses two major open questions, namely (a) the range of validity of the Navier-Stokes equations with slip boundary conditions in describing fluid flows within channels of molecular confinement, and (b) the effect of fluid density and confinement as well as surface properties, such as microscopic roughness and curvature, on fluid slippage along walls. Using a hard-sphere fluid model and describing the fluid-wall interactions by the Maxwell scattering kernel, an event-driven molecular dynamics simulation study was performed in planar and cylindrical channels of different sizes and accommodation coefficients with varying fluid densities. The results show that the well-known criterion for the slip solution, which is valid in rarefied conditions, also holds for a dense gas, i.e., the predictive accuracy improves with decreasing Knudsen numbers, as long as the channel size is larger than about ten molecular diameters. We also find that the key quantity influencing the friction coefficient of a fluid is the peak density at the walls, rather than the nominal density, the fluid confinement, or the channel curvature, as found in previous studies. In particular, higher nominal densities lead to higher density peaks, and therefore a decrease in slip, while tighter confinements lead to lower density peaks, and therefore an increase in slip, regardless of channel geometry. Furthermore, the velocity slip depends on the microscopic roughness via the Smoluchowski factor. These findings are a stepping stone towards a deeper understanding of the molecular mechanisms underlying fluid velocity slip in molecular-scale channels. Published by the American Physical Society 2024

Cold atom-ion systems in radio-frequency multipole traps: Event-driven molecular dynamics and stochastic simulations

Cold atom-ion systems in radio-frequency multipole traps: Event-driven molecular dynamics and stochastic simulations

Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

Transport coefficients like shear, bulk and longitudinal viscosities are sensitive to the intermolecular interaction potential and finite size effects when are numerically determined. For the hard-sphere (HS) fluid, such transport properties are determined almost exclusively with computer simulations. However, their systematic determination and analysis throughout shear stress correlation functions and the Green-Kubo formalism can not be done due to discontinuous nature of the interaction potential. Here, we use the pseudo hard-sphere (PHS) potential to determine pressure correlation functions as a function of volume fraction in order to compute mentioned viscosities. Simulation results are compared to available event-driven molecular dynamics of the HS fluid and also used to propose empirical corrections for the Chapman–Enskog zero density limit of shear viscosity. Moreover, we show that PHS potential is a reliable representation of the HS fluid and can be used to compute transport coefficients. The molecular simulation results of the present work are valuable for further exploration of HS-type fluids or extend the approach to compute transport properties of hard-colloid suspensions.

Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases.

The importance of roughness in the modeling of granular gases has been increasingly considered in recent years. In this paper, a freely evolving homogeneous granular gas of inelastic and rough hard disks or spheres is studied under the assumptions of the Boltzmann kinetic equation. The homogeneous cooling state is studied from a theoretical point of view using a Sonine approximation, in contrast to a previous Maxwellian approach. A general theoretical description is done in terms of d_{t} translational and d_{r} rotational degrees of freedom, which accounts for the cases of spheres (d_{t}=d_{r}=3) and disks (d_{t}=2,d_{r}=1) within a unified framework. The non-Gaussianities of the velocity distribution function of this state are determined by means of the first nontrivial cumulants and by the derivation of non-Maxwellian high-velocity tails. The results are validated by computer simulations using direct simulation Monte Carlo and event-driven molecular dynamics algorithms.

The outflow of gas mixture into vacuum, periodically interrupted by bodies moving towards the jet

The problem about the unsteady outflow of a mixture of gases into a vacuum, periodically interrupted by bodies moving toward the jet, was studied. This problem was considered as a possible gas separation technique. The unsteady flow of the gas mixture was simulated using the event-driven molecular dynamics (EDMD) approach under the following conditions: (1) moving boundaries, (2) a wide range of Knudsen number, (3) a wide range of Mach number, (4) violation of equilibrium between rotational and translational degrees of freedom. The problem of periodically interrupted flow was solved as close to reality as possible, taking into account the finite gap between the stator and the moving runner blades. The dependences of the molar fraction and flow rate of the resulting mixture on the system parameters were obtained. As a result, a number of practically important recommendations for the design of such systems have been formulated.

Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag.

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog–Fokker–Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.

Tethered hard spheres: A bridge between the fluid and solid phases.

The thermodynamics of hard spheres tethered to a Face-Centered Cubic (FCC) lattice is investigated using event-driven molecular-dynamics. The particle-particle and the particle-tether collision rates are related to the phase space geometry and are used to study the FCC and fluid states. In tethered systems, the entropy can be determined by at least two routes: (i) through integration of the tether collision rates with the tether length rT or (ii) through integration of the particle-particle collision rates with the hard-sphere diameter σ (or, equivalently, the density). If the entropy were an entirely analytic function of rT and σ, these two methods for calculating the entropy should lead to the same results; however, a non-analytic region exists as an extension of the solid-fluid phase transition of the untethered hard-sphere system, and integration paths that cross this region will lead to values for the entropy that depend on the particular path chosen. The difference between the calculated entropies appears to be related to the communal entropy, and the location of the non-analytic region appears to be related to conditions where the regions of phase space associated with the FCC configuration become separated from those associated with the disordered fluid. The non-analytic region is finite in extent, vanishing below rT/a ≈ 0.55, where a is the lattice spacing, and there are many continuous paths that connect the fluid and solid phases that can be used to determine the crystal free energy with respect to the fluid.

Transition Gas Flow Between Two Parallel Plates with a Slit-Type Obstacle of Various Geometry by Event Driven Molecular Dynamics Simulation

In this study, pressure-driven flow through a slit-type obstacle with various length (L) and height (H) placed in between two parallel plates was investigated by Event Driven Molecular Dynamics (EDMD) simulation. Mach number, temperature and pressure distributions were obtained along the channel in the transition regime. The change in these macroscopic properties and flow rate were examined for different cases created by changing Knudsen number (Kn) of the gas, the geometry of the slit and the outlet/inlet pressure ratio of the flow. Collision of gas molecules with plates and the obstacle were modeled with diffuse reflection boundary condition. The flow rate showed a sudden change in the transition regime and significant differences in the molecular regime depending on the pressure ratio. Except for the Kn, H and L dimensions were found to be effective in Mach disc formation. Pressure drops at the exit of the slit were shaped differently in normalized pressure profiles depending on Kn, H and L dimensions. In addition, the structure of the vortices formed at the entrance and exit of the slit varies depending on Kn. Some of the results obtained were confirmed to be consistent with the similar studies in the literature.

Normal and anomalous diffusion in the disordered wind-tree model.

Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities ρ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient D, as obtained from the simulation, with that predicted by kinetic theory where D^{-1} is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times t grows like t^{1-2ρ/3}. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.

Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids

The Ornstein–Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be λ=1.5. In particular, for both fluids, we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Verlet, “Integral equations for classical fluids. II. Hard spheres again,” Mol. Phys. 42, 1291–1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state and accurate computer simulation results; at high densities, i.e., close to the freezing transition, expected (small) deviations are seen. In the case of the square-well fluid, good agreement is observed at low and high densities when compared with event-driven molecular dynamics computer simulations. For intermediate densities, the explored closure relations vary in terms of accuracy. Our findings suggest that a modification of the optimization problem to include, for example, additional thermodynamic consistency criteria could improve the results for the type of fluid here explored.

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag.

Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equationand event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes it necessary to revise the usual definition of the thermal Mpemba effect, which is shown to be better described in terms of the relaxation of the local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations.

Diffusional characteristics of a Newtonian event-chain Monte Carlo in hard disk systems

The equilibration and relaxation times of the physical properties of time correlation functions have historically been of fundamental importance in terms of molecular simulation. An efficient algorithm for the acceleration of equilibration, termed the ‘event-chain Monte Carlo’ has been investigated over the past decade. Recently, by adding the collision rule often used in event-driven molecular dynamics, a Newtonian event-chain Monte Carlo was developed. In this event-chain Monte Carlo and variants thereof, optimal performance strongly depends on chain length, physical properties, and system size; the microscopic mechanism in play remains elusive. To identify key factors affecting equilibration, we investigated the diffusional characteristics per event (collision) for each algorithm, focusing systematically on the diffusion coefficients and pair dispersions in two-dimensional hard disk systems.

Efficient event-driven simulations of hard spheres.

Hard spheres are arguably one of the most fundamental model systems in soft matter physics, and hence a common topic of simulation studies. Event-driven simulation methods provide an efficient method for studying the phase behavior and dynamics of hard spheres under a wide range of different conditions. Here, we examine the impact of several optimization strategies for speeding up event-driven molecular dynamics of hard spheres and present a light-weight simulation code that outperforms existing simulation codes over a large range of system sizes and packing fractions. The presented differences in simulation speed, typically a factor of five to ten, save significantly on both CPU time and energy consumption and may be a crucial factor for studying slow processes such as crystal nucleation and glassy dynamics.

Aeroseparation of gas mixture during supersonic outflow in vacuumed reservoir with skimmer

Present paper presents the theoretical study of aeroseparation effect. Simulation is performed using the event-driven molecular dynamics (EDMD) method. Considered problem is a noble gas mixture outflow into vacuum through convergent–divergent micronozzle. In present paper two practical aspects were studied: (1) enhancement of binary mixture separation by adding third light carrier component; (2) influence of position, orientation and shape of flow separator (skimmer) located in the outlet (vacuumed) reservoir on separation efficiency. It was shown that, despite separation results of actual skimmers differ from predictions of virtual ones located in the same place, those predictions can still be used to evaluate the performance of real skimmers. It is also shown that position, orientation and shape of skimmer can influence separation performance but can be chosen in a way to minimize the deviation from predictions made using virtual skimmers.

Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by $|{x}_{1}{|}^{2p}+|{x}_{2}{|}^{2p}+{|{x}_{3}|}^{2p}\ensuremath{\le}1$, where $p\ensuremath{\in}(0,\ensuremath{\infty})$ is a deformation parameter indicating to what extent the shape deviates from a sphere. As $p$ increases from the sphere point ($p=1$), the superball tends to a cuboidal shape and approaches a cube in the $p\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. As $p\ensuremath{\rightarrow}0.5$, it approaches an octahedron, becomes a concave body with octahedral symmetry for $p<0.5$, and approaches a three-dimensional cross in the limit $p\ensuremath{\rightarrow}0$. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction $\ensuremath{\phi}$, average contact number $\overline{Z}$) vary nonanalytically as $p$ diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with $0.85\ensuremath{\le}p\ensuremath{\le}1.50$. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors $S(Q)$ and spectral densities ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)$, as the wave number $Q$ tends to zero, and find that these packings are effectively hyperuniform for all values of $p$ examined. We show that the mean width $\overline{w}$ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution $F(\ensuremath{\delta})$ and find that the pore sizes tend to decrease as $|1\ensuremath{-}p|$ increases. From $F(\ensuremath{\delta})$, we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of $p$. Additionally, we compute the diffusion ``spreadability'' $\mathcal{S}(t)$ [Torquato, Phys. Rev. E 104, 054102 (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-$Q$ power law scaling of the spectral density ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)\ensuremath{\sim}{Q}^{\ensuremath{\alpha}}$ with an exponent $\ensuremath{\alpha}$ that ranges from 0.64 at the sphere point to 0.32 at $p=1.50$, and decreases as $|1\ensuremath{-}p|$ increases. Each of the structural characteristics computed here exhibits an extremum at the sphere point and varies nonanalytically as $p$ departs the sphere point. We find the nonanalytic behavior in $\ensuremath{\phi}$ on either side of the sphere point is nearly linear, and determine that the rattler fraction ${\ensuremath{\phi}}_{R}$ decreases rapidly as $|1\ensuremath{-}p|$ increases. Our results can be used to help inform the design of colloidal or granular materials with targeted densities and transport properties.

Heat transfer in a rarefied gas between profiled surfaces moving relative to each other

The heat transfer in a rarefied gas between two solid surfaces moving relative to each other was studied. The problem was solved for nitrogen using the event-driven molecular dynamics (EDMD) method under the following conditions: (1) а wide range of flow regimes (Kn=0.05−20), (2) high relative velocity of surfaces, comparable to the thermal velocity of gas molecules, (3) significant difference in surface temperatures, (4) rotational degrees of freedom in gas molecules and (5) complex geometry of solid surfaces. Special attention was paid to the heat removal from the hot surface, namely the quantitative assessment of the reduction of heat removal due to viscous friction and effect of the transverse profiling of surfaces on the heat transfer between them.

Mpemba effect in an anisotropically driven granular gas

The Mpemba effect refers to the counterintuitive relaxation wherein a hotter system equilibrates faster than a cooler system when quenched to a cold temperature. Even though the effect has been illustrated for isotropically driven granular gases, a prototypical system far from equilibrium, its existence requires non-stationary initial states, limiting experimental realisation. In this paper, we demonstrate the existence of the Mpemba effect in anisotropically driven granular gases, even when quenched from initial states that are stationary. Our theoretical predictions, based on kinetic theory, for the regular, inverse and strong Mpemba effects agree well with results of event-driven molecular dynamics simulations of hard discs.

Molecular dynamics study of six-dimensional hard hypersphere crystals.

Six-dimensional hard hypersphere systems in the A6, D6, and E6 crystalline phases have been studied using event-driven molecular dynamics simulations in periodic, skew cells that reflect the underlying lattices. In all the simulations, the systems had sufficient numbers of hyperspheres to capture the first coordination shells, and the larger simulations also included the complete second coordination shell. The equations of state, for densities spanning the fluid, metastable fluid, and solid regimes, were determined. Using molecular dynamics simulations with the hyperspheres tethered to lattice sites allowed the computation of the free energy for each of the crystal lattices relative to the fluid phase. From these free energies, the fluid-crystal coexistence region was determined for the E6, D6, and A6 lattices. Pair correlation functions for all the examined states were computed. Interestingly, for all the states examined, the pair correlation functions displayed neither a split second peak nor a shoulder in the second peak. These behaviors have been previously used as a signature of the freezing of the fluid phase for hard hyperspheres in two to five dimensions.