Coexistence Densities Research Articles

The evolution of autonomy from two cooperative specialists in fluctuating environments

From microbes to humans, organisms perform numerous tasks for their survival, including food acquisition, migration, and reproduction. A complex biological task can be performed by either an autonomous organism or by cooperation among several specialized organisms. However, it remains unclear how autonomy and cooperation evolutionarily switch. Specifically, it remains unclear whether and how cooperative specialists can repair deleted genes through direct genetic exchange, thereby regaining metabolic autonomy. Here, we address this question by experimentally evolving a mutualistic microbial consortium composed of two specialists that cooperatively degrade naphthalene. We observed that autonomous genotypes capable of performing the entire naphthalene degradation pathway evolved from two cooperative specialists and dominated the community. This evolutionary transition was driven by the horizontal gene transfer (HGT) between the two specialists. However, this evolution was exclusively observed in the fluctuating environment alternately supplied with naphthalene and pyruvate, where mutualism and competition between the two specialists alternated. The naphthalene-supplied environment exerted selective pressure that favors the expansion of autonomous genotypes. The pyruvate-supplied environment promoted the coexistence and cell density of the cooperative specialists, thereby increasing the likelihood of HGT. Using a mathematical model, we quantitatively demonstrate that environmental fluctuations facilitate the evolution of autonomy through HGT when the relative growth rate and carrying capacity of the cooperative specialists allow enhanced coexistence and higher cell density in the competitive environment. Together, our results demonstrate that cooperative specialists can repair deleted genes through a direct genetic exchange under specific conditions, thereby regaining metabolic autonomy.

Constraints on Phase Transitions in Neutron Star Matter

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities cs2>0.1 in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range Δρ/ρ<0.2 (at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined.

Neural Network Water Model Based on the MB-Pol Many-Body Potential.

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

An intermolecular potential for hydrogen: Classical molecular simulation of pressure-density-temperature behavior, vapor-liquid equilibria, and critical and triple point properties.

An intermolecular potential is reported for molecular hydrogen that combines two-body interactions from abinitio data with three-body interactions. The accuracy of the two-body potential is validated by comparison with experimental second virial coefficient data. Experimental pressure-density-temperature data are used to validate the addition of three-body interactions, often yielding very accurate predictions. Classical Monte Carlo simulations that neglect quantum effects are reported for the vapor-liquid equilibria (VLE), critical properties, and the triple point. A comparison with experimental data indicates that the effect of quantum interactions is to narrow the VLE phase envelope and to lower the critical temperature. The three-body interactions have a considerable influence on the phase behavior, resulting in good agreement with the experimental density. The critical properties of the two-body + three-body potential for hydrogen provide an alternative set of input parameters to improve the accuracy of theoretical predictions at temperatures above 100K. In the vicinity of the critical point, the coexistence densities do not obey the law of rectilinear diameters, which is a feature that has largely been overlooked in both experimental data and reference equations of state.

Spurious currents suppression by accurate difference schemes in multiphase lattice Boltzmann method

Spurious currents are often observed near curved interfaces in multiphase simulations based on diffuse interface methods. These unphysical phenomena negatively affect both computational accuracy and stability. In this paper, the origin and suppression of spurious currents are investigated using the multiphase lattice Boltzmann method driven by a chemical potential. Both the difference error and insufficient isotropy of the discrete gradient operator give rise to directional deviations in the nonideal force, leading to spurious currents. Nevertheless, a high-order finite difference scheme produces far more accurate results than a high-order isotropic difference scheme. We compare several finite difference schemes that have different levels of accuracy and resolution. When a large proportional coefficient is used, the transition region is narrow and steep, and the resolution of the finite difference scheme provides a better indication of the computational accuracy than the formal accuracy. Conversely, for a small proportional coefficient, the transition region is wide and gentle, and the formal accuracy of the finite difference gives a better indication of the computational accuracy than the resolution. Numerical simulations show that the spurious currents calculated in the three-dimensional situation are highly consistent with those in two-dimensional simulations; in particular, the two-phase coexistence densities calculated by the high-order accuracy finite difference scheme are in excellent agreement with the theoretical predictions of the Maxwell equal-area construction down to a reduced temperature of 0.2.

Interfacial properties of square-well chains from molecular dynamics simulation

ABSTRACT Square-well (SW) potential is likely the simplest potential describing attractive and repulsive interactions. However, its discontinuous functional form makes it difficult to be used in Molecular Dynamics (MD) simulation, particularly with commercial MD packages. Recently, Zerón and collaborators [Mol. Phys. 116, 3355 (2018)] have presented a parameterisation of the SW potential that allows its use for simulation packages since the intermolecular potential and force are described by continuous mathematical functions. It was validated for SW spheres. In this work, we use this reported continuous SW potential to describe for the first time the equilibrium and interfacial properties of SW chains, with potential ranges of and 1.75. Simulations for tetramers interacting with are compared with available computational data in the literature, which has allowed to validate the method for molecular chain systems. Besides, a systematic study for the potential range of has not been addressed so far, which represents valuable information for instance to discern whether different microscopic theories are capable of describing this type of system. In particular, we assess the effect of temperature, chain length, and potential range on the calculated properties, namely density profiles, coexistence densities, vapour pressures, surface tensions and critical points. Overall, with increasing the chain length, the width of the envelope of the coexistence phase increases, which results in an increase of the surface tension as well as the critical temperature at the same time that the vapour pressure and the interfacial width decrease.

Entropic Multi-Relaxation-Time Lattice Boltzmann Model for Large Density Ratio Two-Phase Flows

We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021). While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and Courant--Friedrichs--Lewy number. Here we show that the entropic multiple relaxation time model extends the stability limits of the model significantly, which allows us to reach larger Reynolds numbers for a given grid resolution. The thermodynamic properties of the solver, using the Peng--Robinson equation of state, are studied first using simple configurations. Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory. The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in 2-D and 3-D. The results are in very good agreement with theoretically predicted scaling laws and experimental data.

Towards a consistent lattice Boltzmann model for two-phase fluids

We revisit the construction of discrete kinetic models for single-component isothermal two-phase flows. Starting from a kinetic model for a non-ideal fluid, we show that, under conventional scaling, the Navier–Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limit. A scaling based on the smallness of velocity increments is then introduced, which recovers the full Navier–Stokes–Korteweg equations. The proposed model is realized on a standard lattice and validated on a variety of benchmarks. Through a detailed study of thermodynamic properties including co-existence densities, surface tension, Tolman length and sound speed, we show thermodynamic consistency, well-posedness and convergence of the proposed model. Furthermore, hydrodynamic consistency is demonstrated by verification of Galilean invariance of the dissipation rate of shear and normal modes and the study of visco-capillary coupling effects. Finally, the model is validated on dynamic test cases in three dimensions with complex geometries and large density ratios such as drop impact on textured surfaces and mercury drops coalescence.

Thermodynamic properties of Ar, Kr and Xe from a Monte Carlo-based perturbation theory with an effective two-body Lennard-Jones potential

A third-order perturbation theory is used to obtain the equilibrium properties of Ar, Kr and Xe over wide ranges of temperatures and densities. The theory belongs to the framework of the inverse temperature expansion of the Helmholtz free energy, with the perturbation terms determined from Monte Carlo simulation. The interactions are modeled by an effective two-body Lennard-Jones potential incorporating the main contribution of the three-body interactions. To this end, the ratio of three-body to two-body configuration energies have been determined also from Monte Carlo simulation. The results for the pressure and energy at supercritical temperatures are in quite good agreement with experimental data. The liquid–vapor coexistence is also reproduced fairly well, although for Ar and Kr the critical temperature is slightly overestimated as well as the liquid densities at low temperatures, and the coexistence densities of Xe are slightly overestimated for the vapor and underestimated for the liquid near the critical point. In any case, the calculations show a remarkable improvement in the predicted coexistence curve with including the three-body contribution.

The high-density equation of state in heavy-ion collisions: constraints from proton flow

A set of different equations of state is implemented in the molecular dynamics part of a non-equilibrium transport simulation (UrQMD) of heavy-ion collisions. It is shown how different flow observables are affected by the density dependence of the equation of state. In particular, the effects of a phase transition at high density are explored, including an expected reduction in mean m_T. We also show that an increase in v_2 is characteristic for a strong softening of the equation of state. The phase transitions with a low coexistence density, n_{text {CE}}<4 n_0, show a distinct minimum in the slope of the directed flow as a function of the beam energy, which would be a clear experimental signal. By comparing our results with experimental data, we can exclude any strong phase transition at densities below 4n_0.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme (DUGKS) for simulations of multiphase fluid flow, we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS. Due to the flux reconstruction procedure, additional terms that break the isotropic requirements of the pseudopotential model will be introduced. To eliminate the influences of nonisotropic terms, the expression of equilibrium distribution functions is reformulated in a moment-based form. With the isotropy-preserving parameter appropriately tuned, the nonisotropic effects can be properly canceled out. The fundamental capabilities are validated by the flat interface test and the quiescent droplet test. It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces. The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition. Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state. By directly incorporating the intermolecular interactions, the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors, which could help gain fresh insights into multiphase fluid flow.

The coexistence curve and surface tension of a monatomic water model.

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid-vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid-vapor critical point at Tc = 917.6K, ρc = 0.311gcm-3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water.

On the choice of the effective diameter in the high-temperature expansion for the Lennard–Jones fluid

A third-order perturbation theory, within the framework of the high temperature expansion, with the perturbation terms obtained from computer simulation, is used to test the performance of several prescriptions proposed in the literature to obtain the effective hard-sphere diameter for the Lennard–Jones fluid. It is found that the classical Barker–Henderson prescription provides, on the whole, the best accuracy as compared with the available simulation data for the excess energy, the equation of state and the liquid-vapour coexistence densities.

Finite-size shifts in simulated protein droplet phase diagrams.

Computer simulation can provide valuable insight into the forces driving biomolecular liquid-liquid phase separation. However, the simulated systems have a limited size, which makes it important to minimize and control finite-size effects. Here, using a phenomenological free-energy ansatz, we investigate how the single-phase densities observed in a canonical system under coexistence conditions depend on the system size and the total density. We compare the theoretical expectations with results from Monte Carlo simulations based on a simple hydrophobic/polar protein model. We consider both cubic systems with spherical droplets and elongated systems with slab-like droplets. The results presented suggest that the slab simulation method greatly facilitates the estimation of the coexistence densities in the large-system limit.

Thermodynamic properties of hard-core attractive Yukawa fluids: Single-component monomers, binary mixtures and chains

The first three perturbation terms in the inverse temperature expansion of the Helmholtz free energy of hard-core attractive Yukawa (HCAY) monomer fluids have been determined from computer simulation for several values of the range parameter. The predictions of the resulting perturbation theory for the equation of state and the excess energy are shown to be in excellent agreement with simulation data that are also reported. The theory accurately predicts also the simulation data for the liquid–vapour coexistence densities reported in the literature. Extension of the theory to HCAY binary mixtures is achieved by mapping the mixture to an effective single-component fluid and successfully compared with the simulation data reported in this work. The combination of the theory for the single-component fluid of monomers with a version of the Wertheim thermodynamic perturbation theory (TPT) also provides satisfactory results for HCAY chain fluids.

Vapor-liquid equilibrium of water with the MB-pol many-body potential.

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water's solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor-liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400K < T < 600K, we calculated properties such as equilibrium coexistence densities, vapor-liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor-liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. These results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol's application across a large swath of water's phase diagram.

Comparison and evaluation of Shan–Chen model and most commonly used equations of state in multiphase lattice Boltzmann method

A method to couple the Equation of State (EoS) with the Shan–Chen model (SC) is proposed in this paper. The difference between previously proposed approaches and the one developed here is in the manner of determining parameters of the EoS, which are a function of the critical properties of a substance. The modified relationships of the parameter that controls the strength of the inter-particle force as a function of temperature are developed for each EoS. These modified relationships eliminate the difference between pressures calculated by the SC model and each EoS. A comparison between the SC model and different popular EoSs is presented based on the proposed approach. Four models—the SC model, van der Waals EoS, Redlich–Kwong EoS, and Carnahan and Starling' EoS—are evaluated and compared, and the sign of the strength-controlling parameter (G) is discussed. The effects of the range of coexistence density, an arbitrary constant (ρo), temperature, and G on surface tension are discussed. The results of simulations show that the SC model sometimes yields negative values of surface tension when ρo is set below 1.5. Therefore, ρo should be set to 1 or ≥ 1.5.

Weak intra-guild predation facilitates consumer coexistence but does not guarantee higher consumer density

In plant communities, resource partitioning has been shown to facilitate species coexistence and, in turn, enhance community density. Such positive effects of resource partitioning in higher trophic levels are not as obvious possibly due to the occurrence of intra-guild predation (IGP). We thus built a model to explore the joint effects of IGP and resource partitioning on consumer coexistence and their collective density as rarely have studies investigated this joint effect. The model consists of two prey resources that do not directly compete with each other and two consumers that are engaged in IGP and can partition their use of the two prey resources. This model shows that the effects of IGP on consumer coexistence depend on which consumer requires the lower resource density to persist. When the IG predator is the inferior competitor, weak IGP enhances coexistence by lowering the minimum degree of partitioning that is required for coexistence; otherwise, IGP always constrains coexistence. In addition, the effects of IGP on total consumer density (Ztot) depends on which consumer has the lower maximum growth potential, defined as the difference between their maximum growth rate and mortality. Weak IGP increases Ztot when the IG predator has lower maximum growth potential; otherwise, IGP always decreases Ztot. Last, the criterion for IGP to have positive effects on consumer coexistence and Ztot are different. Our results show that weak to intermediate strengths of intra-guild predation can facilitate consumer coexistence and total community density, but consumer coexistence does not guarantee higher consumer density.

Thermodynamic properties of the 3D Lennard-Jones/spline model

The Lennard-Jones (LJ) spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at . We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be and , respectively. The triple point is estimated to and . The coexistence densities, saturation pressure, and supercritical isotherms of the LJ spline model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that the mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

An Alternative High-Density Ratio Pseudo-potential Lattice Boltzmann Model with Surface Tension Adjustment Capability

In this paper, an alternative model is presented to simultaneously achieve thermodynamic consistency, leading to high-density ratios, and surface tension adjustment capability based on the pseudo-potential lattice Boltzmann model (LBM). These features are achieved by adding two relatively simple terms, each with an adjustable coefficient, selected from the Taylor expansion of the original interaction force, one for achieving and maintaining thermodynamic consistency, and the other for adjusting the surface tension independent of the density ratio. The model also takes advantage of being independent of using SRT, MRT, 2D or 3D lattice models. The capability of the model is evaluated and verified by performing several static and dynamic benchmark test cases. First, the coexistence densities extracted for a flat interface from the model are compared with those of the Maxwell equal area rule in a wide temperature range. Results show that the thermodynamic consistency is well achieved and the coexistence densities are independent of the surface tension strength as well. Next, the well-known Laplace law for a droplet is evaluated and satisfied with the model. In addition, a wide range of surface tension values is achievable at a fixed temperature by adjusting the surface tension adjustment coefficient. After that, the ellipsoidal droplet oscillation is simulated with a good agreement between the analytical and numerical results for the oscillation period. The spurious velocities around the droplet are then evaluated and shown to be reasonable, and comparatively low even at a relatively high-density ratio around of 2400. It was found that the magnitude of these velocities can be further reduced, especially at high-density ratios, by reducing the liquid to gas dynamic viscosity ratio or equivalently increasing the gas to liquid kinematic viscosity ratio. Next, the stability, and the fascinating phenomenon of symmetric bifurcation of a rotating planar droplet are simulated and formation of two- and four-lobed shapes along with rigid rotation is presented depending on the value of the surface tension. Finally, the droplet impact on a liquid film is simulated at a relatively high-density ratio around of 720, and Reynolds number of 1440. However, the upper limit of physical parameters for simulating this phenomenon is found to be a density ratio of 720 and Re and We numbers of 6600 and 275, respectively. Effects of the surface tension strength are shown as well. The crown spread radius from the model agrees well with the analytical solution reported in the literature.