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Andres Santos

Publications and source records attributed to Andres Santos.

At least 37 records · Page 2Linked to original sources
arXiv2007

Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures

In a recent paper [Phys. Rev. E \textbf{76}, 031202 (2007)], Schmidt has proposed a Fundamental Measure Density Functional Theory for one-dimensional nonadditive hard-rod fluid mixtures and has compared its predictions for the bulk structural properties with Monte Carlo simulations. The aim of this Brief Report is to recall that the problem admits an exact solution in the bulk, which is briefly summarized in a self-contained way.

cond-mat.soft↗
arXiv2007

Structure of hard-hypersphere fluids in odd dimensions

The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A {\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimension. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at $d=5$ and $d=7$ is obtained. As a byproduct of this study, an exact and explicit polynomial expression for the intersection volume of two identical hyperspheres in arbitrary odd dimensions is given.

cond-mat.stat-mech↗
arXiv2007

Simple shear flow in inelastic Maxwell models

The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through fourth degree in the simple shear flow state. First, the rheological properties (which are related to the second-degree velocity moments) are {\em exactly} evaluated in terms of the coefficient of restitution $α$ and the (reduced) shear rate $a^*$. For a given value of $α$, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third-degree and the asymmetric fourth-degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, as in the case of elastic collisions, our results show that, for a given value of $α$, the scaled symmetric fourth-degree moments diverge in time for shear rates larger than a certain critical value $a_c^*(α)$ which decreases with increasing dissipation. The explicit shear-rate dependence of the fourth-degree moments below this critical value is also obtained.

cond-mat.soft↗
arXiv2007

Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

cond-mat.soft↗
arXiv2007

Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.

cond-mat.stat-mech↗
arXiv2007

Multicomponent fluid of hard spheres near a wall

The rational function approximation method, density functional theory, and NVT Monte Carlo simulation are used to obtain the density profiles of multicomponent hard-sphere mixtures near a planar hard wall. Binary mixtures with a size ratio 1:3 in which both components occupy a similar volume are specifically examined. The results indicate that the present version of density functional theory yields an excellent overall performance. A reasonably accurate behavior of the rational function approximation method is also observed, except in the vicinity of the first minimum, where it may even predict unphysical negative values.

cond-mat.stat-mech↗
arXiv2007

Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials

It is proven that, for any soft potential characterized by a finite Fourier transform $\widetildeϕ(k)$, the virial and energy thermodynamic routes are equivalent for approximations such that the Fourier transform of the total correlation function divided by the density $ρ$ is an arbitrary function of $ρβ\widetildeϕ(k)$, where $β$ is the inverse temperature. This class includes the mean spherical approximation as a particular case.

cond-mat.soft↗
arXiv2006

Radial distribution function of penetrable sphere fluids to second order in density

The simplest bounded potential is that of penetrable spheres, which takes a positive finite value $ε$ if the two spheres are overlapped, being 0 otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of $T^*\equiv k_BT/ε$ (where $k_B$ is the Boltzmann constant and $T$ is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for $T^*\lesssim 1$ only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancelation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for $T^*\lesssim 0.73$, reaches a minimum negative value at $T^*\approx 1.1$, and then goes to zero from below as $1/{T^*}^4$ for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for $T^*\lesssim 0.7$, while the virial route is preferable if $T^*\gtrsim 0.7$.

cond-mat.stat-mech↗
arXiv2006

Test of a universality ansatz for the contact values of the radial distribution functions of hard-sphere mixtures near a hard wall

Recent Monte Carlo simulation results for the contact values of polydisperse hard-sphere mixtures at a hard planar wall are considered in the light of a universality assumption made in approximate theoretical approaches. It is found that the data seem to fulfill the universality ansatz reasonably well, thus opening up the possibility of inferring properties of complicated systems from the study of simpler ones

cond-mat.stat-mech↗
arXiv2006

A simple model kinetic equation for inelastic Maxwell particles

The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model kinetic equation that preserves the most relevant properties of the Boltzmann equation (BE) for IMP and reduces to the BGK kinetic model in the elastic limit. In the proposed kinetic model the collision operator is replaced by a relaxation-time term toward a reference Maxwellian distribution plus a term representing the action of a friction force. It contains three parameters (the relaxation rate, the effective temperature of the reference Maxwellian, and the friction coefficient) which are determined by imposing consistency with basic exact properties of the BE for IMP. As a consequence, the kinetic model reproduces the true shear viscosity and predicts accurate expressions for the transport coefficients associated with the heat flux. The model can be exactly solved for the homogeneous cooling state, the solution exhibiting an algebraic high-energy tail with an exponent in fair agreement with the correct one.

cond-mat.stat-mech↗
arXiv2006

Strong breakdown of equipartition in uniform granular mixtures

A binary mixture made of heavy and light inelastic hard spheres in the free cooling state is considered. First, the regions in the parameter space where the partial granular temperature of the heavy species is larger (or smaller) than that of the light species are analyzed. Next, the asymptotic behavior of the mean square velocity ratio in the disparate-mass limit is investigated, assuming different scaling laws for the parameters of the mixture. It is seen that two general classes of states are possible: a "normal" state and an "ordered" state, the latter representing a strong breakdown of energy equipartition.

cond-mat.stat-mech↗
arXiv2006

Are the energy and virial routes to thermodynamics equivalent for hard spheres?

The internal energy of hard spheres (HS) is the same as that of an ideal gas, so that the energy route to thermodynamics becomes useless. This problem can be avoided by taking an interaction potential that reduces to the HS one in certain limits. In this paper the square-shoulder (SS) potential characterized by a hard-core diameter $σ'$, a soft-core diameter $σ>σ'$ and a shoulder height $ε$ is considered. The SS potential becomes the HS one if (i) $ε\to 0$, or (ii) $ε\to\infty$, or (iii) $σ'\toσ$ or (iv) $σ'\to 0$ and $ε\to\infty$. The energy-route equation of state for the HS fluid is obtained in terms of the radial distribution function for the SS fluid by taking the limits (i) and (ii). This equation of state is shown to exhibit, in general, an artificial dependence on the diameter ratio $σ'/σ$. If furthermore the limit $σ'/σ\to 1$ is taken, the resulting equation of state for HS coincides with that obtained through the virial route. The necessary and sufficient condition to get thermodynamic consistency between both routes for arbitrary $σ'/σ$ is derived.

cond-mat.stat-mech↗
arXiv2006

How `sticky' are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range $λ$ at a given packing fraction and reduced temperature can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter $τ$. Such an equivalence cannot hold for the radial distribution function since this function has a delta singularity at contact in the SHS case, while it has a jump discontinuity at $r=λ$ in the SW case. Therefore, the equivalence is explored with the cavity function $y(r)$. Optimization of the agreement between $y_{\sw}$ and $y_{\shs}$ to first order in density suggests the choice for $τ$. We have performed Monte Carlo (MC) simulations of the SW fluid for $λ=1.05$, 1.02, and 1.01 at several densities and temperatures $T^*$ such that $τ=0.13$, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)]. Although, at given values of $η$ and $τ$, some local discrepancies between $y_{\sw}$ and $y_{\shs}$ exist (especially for $λ=1.05$), the SW data converge smoothly toward the SHS values as $λ-1$ decreases. The approximate mapping $y_{\sw}\to y_{\shs}$ is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for $y_{\shs}$ the solution of the Percus--Yevick equation as well as the rational-function approximation, the radial distribution function $g(r)$ of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.

cond-mat.stat-mech↗
arXiv2006

Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper we first derive the exact correlation functions of penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit $T\to\infty$ and a low-temperature approximation inspired by the exact result in the opposite limit $T\to 0$. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A perspective on the extension of both approaches to the more realistic three-dimensional case is provided.

cond-mat.stat-mech↗
arXiv2005

System of elastic hard spheres which mimics the transport properties of a granular gas

The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution $α$. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor $(1+α)/2$, relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for $α\geq 0.5$). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisions

cond-mat.stat-mech↗
arXiv2005

On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids

The energy route to the equation of state of hard-sphere fluids is ill-defined since the internal energy is just that of an ideal gas and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a square-shoulder interaction and taking the limit of vanishing shoulder width. The resulting hard-sphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hard-sphere fluids can be considered as equivalent.

cond-mat.stat-mech↗
arXiv2005

Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

The penetrable-sphere model has been introduced in the literature to describe the peculiar thermodynamic behavior of some colloidal systems. In this model the interaction potential is $ϕ(r)=ε>0$ if the two spheres are overlapped ($r<σ$) and $ϕ(r)=0$ otherwise ($r>σ$). In this paper the shear viscosity, thermal conductivity, and self-diffusion coefficients of a dilute gas of penetrable spheres are evaluated. It is found that the effective collision frequency $ν(T^*)$ grows as $\sqrt{T^*}$ up to $T^*\equiv k_BT/ε\simeq 0.25$, reaches a maximum at $T^*\simeq 0.415$ and then decays as ${T^*}^{-3/2}\log T^*$ for large temperatures. The results are applied to the hydrodynamic profiles in the steady Fourier and Couette flows.

cond-mat.stat-mech↗