arXiv subjects

Andrés Santos

Publications and source records attributed to Andrés Santos.

At least 73 records · Page 4Linked to original sources

arXiv2018

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component $i$ to be approximately proportional to $2σ_i+\langleσ\rangle$, where $σ_i$ is the diameter of the disk and $\langleσ\rangle$ is the mean diameter.

cond-mat.soft↗

arXiv2018

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures

A detailed comparison between the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL)equation of state of hard-sphere mixtures is made with Molecular Dynamics (MD) simulations of the same compositions. The Labík and Smith simulation technique [S. Labík and W. R. Smith, Mol. Simul. \textbf{12}, 23-31 (1994)] was used to implement the Widom particle insertion method to calculate the excess chemical potential, $βμ_0^\text{ex}$, of a test particle of variable diameter, $σ_0$, immersed in a hard-sphere fluid mixture with different compositions and values of the packing fraction, $η$. Use is made of the fact that the only polynomial representation of $βμ_0^\text{ex}$ which is consistent with the limits $σ_0\to 0$ and $σ_0\to\infty$ has to be of the cubic form, i.e., $c_0(η)+\overline{c}_1(η)σ_0/M_{1}+\overline{c}_2(η)(σ_0/M_{1})^2+\overline{c}_3(η)(σ_0/M_{1})^3$, where $M_{1}$ is the first moment of the distribution. The first two coefficients, $c_0(η)$ and $\overline{c}_1(η)$, are known analytically, while $\overline{c}_2(η)$ and $\overline{c}_3(η)$ were obtained by fitting the MD data to this expression. This in turn provides a method to determine the excess free energy per particle, $βa^\text{ex}$, in terms of $\overline{c}_2$, $\overline{c}_3$, and the compressibility factor, $Z$. Very good agreement between the BMCSL formulas and the MD data is found for $βμ^\text{ex}_0$, $Z$, and $βa^\text{ex}$ for binary mixtures and continuous particle size distributions with the top-hat analytic form. However, the BMCSL theory typically slightly underestimates the simulation values, especially for $Z$, differences which the Boublík-Carnahan-Starling-Kolafa formulas and an interpolation between two Percus-Yevick routes capture well in different ranges of the system parameter space.

cond-mat.soft↗

arXiv2018

Impact of roughness on the instability of a free-cooling granular gas

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014)], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly degenerate transversal (shear) mode and a longitudinal ("heat") mode are unstable with respect to long enough wavelength excitations. The instability is driven by the shear mode above a certain inelasticity threshold; at larger inelasticity, however, the instability is driven by the heat mode for an inelasticity-dependent range of medium roughness. Comparison with the case of a granular gas of inelastic smooth spheres confirms previous simulation results about the dual role played by surface friction: while small and large levels of roughness make the system less unstable than the frictionless system, the opposite happens at medium roughness. On the other hand, such an intermediate window of roughness values shrinks as inelasticity increases and eventually disappears at a certain value, beyond which the rough-sphere gas is always less unstable than the smooth-sphere gas. A comparison with some preliminary simulation results shows a very good agreement for conditions of practical interest.

cond-mat.soft↗

arXiv2017

Equation of state of polydisperse hard-disk mixtures in the high-density regime

A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about $0.01$ is sufficient to avoid crystallization and explore the metastable fluid branch.

cond-mat.soft↗

arXiv2017

One-dimensional fluids with second nearest-neighbor interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $p_1(r)$, is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $p_1(r)$ is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

cond-mat.soft↗

arXiv2017

Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio ($q=0.4$ and $q=0.5$), a value of the nonadditivity parameter $Δ=0.3$), and five values of the mole fraction of the species with the biggest diameter ($x_1=0.1$, $0.3$, $0.5$, $0.7$, and $0.9$). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs Ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state.

cond-mat.soft↗

arXiv2017

When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids

Under certain conditions, two samples of fluid at different initial temperatures present a counterintuitive behavior known as the Mpemba effect: it is the hotter system that cools sooner. Here, we show that the Mpemba effect is present in granular fluids, both in uniformly heated and in freely cooling systems. In both cases, the system remains homogeneous, and no phase transition is present. Analytical quantitative predictions are given for how differently the system must be initially prepared to observe the Mpemba effect, the theoretical predictions being confirmed by both molecular dynamics and Monte Carlo simulations. Possible implications of our analysis for other systems are also discussed.

cond-mat.soft↗

arXiv2017

Thermal properties of an impurity immersed in a granular gas of rough hard spheres

We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of the theoretical solution by comparing with computer simulations. For this, we use two independent computer data sets, from molecular dynamics (MD) and from Direct Simulation Monte Carlo method (DSMC). Both approach well, with different degrees, the kinetic theory within a reasonable range of parameter values.

cond-mat.soft↗

arXiv2016

Chemical potential of a test hard sphere of variable size in a hard-sphere fluid

The Labík and Smith Monte Carlo simulation technique to implement the Widom particle insertion method is applied using Molecular Dynamics (MD) instead to calculate numerically the insertion probability, $P_0(η,σ_0)$, of tracer hard-sphere (HS) particles of different diameters, $σ_0$, in a host HS fluid of diameter $σ$ and packing fraction, $η$, up to $0.5$. It is shown analytically that the only polynomial representation of $-\ln P_0(η,σ_0)$ consistent with the limits $σ_0\to 0$ and $σ_0\to\infty$ has necessarily a cubic form, $c_0(η)+c_1(η)σ_0/σ+c_2(η)(σ_0/σ)^2+c_3(η)(σ_0/σ)^3$. Our MD data for $-\ln P_0(η,σ_0)$ are fitted to such a cubic polynomial and the functions $c_0(η)$ and $c_1(η)$ are found to be statistically indistinguishable from their exact solution forms. Similarly, $c_2(η)$ and $c_3(η)$ agree very well with the Boublík-Mansoori-Carnahan-Starling-Leland and Boublík-Carnahan-Starling-Kolafa formulas. The cubic polynomial is extrapolated (high density) or interpolated (low density) to obtain the chemical potential of the host fluid, or $σ_{0}\toσ$, as $βμ^{\text{ex}}=c_0+c_1+c_2+c_3$. Excellent agreement between the Carnahan-Starling and Carnahan-Starling-Kolafa theories with our MD data is evident.

cond-mat.soft↗

arXiv2016

Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for fractal dimension [M. Heinen et al., Phys. Rev. Lett. \textbf{115}, 097801 (2015)], a good agreement being observed.

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arXiv2015

Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force

We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the Direct Simulation Monte Carlo method) we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called "lifted-tennis-ball" behavior).

cond-mat.soft↗

arXiv2015

Multi-particle critical correlations

We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to the $k$-particle ones and their derivatives with respect to the density. Critical exponents corresponding to generalized compressibility equations resulting from the hierarchy are shown to grow linearly with the order of correlations. We prove that the critical behaviour requires taking into account correlation functions of arbitrary order. It is however only a necessary condition. Indeed, approximate closures of the hierarchy obtained by expressing higher order correlations in terms of lower order ones (Kirkwood's superposition approximation and its generalizations) turn out to be inconsistent with the critical behaviour.

cond-mat.stat-mech↗

arXiv2015

Equation of state for five-dimensional hyperspheres from the chemical-potential route

We use the Percus-Yevick approach in the chemical-potential route to evaluate the equation of state of hard hyperspheres in five dimensions. The evaluation requires the derivation of an analytical expression for the contact value of the pair distribution function between particles of the bulk fluid and a solute particle with arbitrary size. The equation of state is compared with those obtained from the conventional virial and compressibility thermodynamic routes and the associated virial coefficients are computed. The pressure calculated from all routes is exact up to third density order, but it deviates with respect to simulation data as density increases, the compressibility and the chemical-potential routes exhibiting smaller deviations than the virial route. Accurate linear interpolations between the compressibility route and either the chemical-potential route or the virial one are constructed.

cond-mat.stat-mech↗

arXiv2015

Virial coefficients and demixing in the Asakura-Oosawa model

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out.

cond-mat.soft↗

arXiv2015

The effective colloid interaction in the Asakura-Oosawa model. Assessment of non-pairwise terms from the virial expansion

The relevance of neglecting three- and four-body interactions in the coarse-grained version of the Asakura-Oosawa model is examined. A mapping between the first few virial coefficients of the binary nonadditive hard-sphere mixture representative of this model and those arising from the coarse-grained (pairwise) depletion potential approximation allows for a quantitative evaluation of the effect of such interactions. This turns out to be especially important for large size ratios and large reservoir polymer packing fractions.

cond-mat.soft↗

arXiv2015

Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram

A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of stickiness on the spinodal curves and on the effective solute-solute potential is analyzed. In the opposite nonadditive case, the solvent-solvent diameter is zero and the model can then be reckoned as an extension of the well-known Asakura-Oosawa model with additional sticky solute-solvent interaction. This latter model has the property that its exact effective one-component problem involves only solute-solute pair potentials for size ratios such that a solvent particle fits inside the interstitial region of three touching solutes. In particular, we explicitly identify the three competing physical mechanisms (depletion, pulling, and bridging) giving rise to the effective interaction. Some remarks on the phase diagram of these two complementary models are also addressed through the use of the Noro-Frenkel criterion and a first-order perturbation analysis. Our findings suggest reentrance of the fluid-fluid instability as solvent density (in the first model) or adhesion (in the second model) is varied. Some perspectives in terms of the interpretation of recent experimental studies of microgels adsorbed onto large polystyrene particles are discussed.

cond-mat.soft↗

arXiv2014

Transport coefficients of a granular gas of inelastic rough hard spheres

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

cond-mat.stat-mech↗

arXiv2014

Fourth virial coefficient of additive hard-sphere mixtures in the Percus-Yevick and hypernetted-chain approximations

The fourth virial coefficient of additive hard-sphere mixtures, as predicted by the Percus-Yevick (PY) and hypernetted-chain (HNC) theories, is derived via the compressibility, virial, and chemical-potential routes, the outcomes being compared with exact results. Except in the case of the HNC compressibility route, the other five expressions exhibit a common structure involving the first three moments of the size distribution. In both theories the chemical-potential route is slightly better than the virial one and the best behavior is generally presented by the compressibility route. Moreover, the PY results with any of the three routes are more accurate than any of the HNC results.

cond-mat.stat-mech↗