arXiv subjects

Andrés Santos

Publications and source records attributed to Andrés Santos.

At least 55 records · Page 3Linked to original sources

arXiv2020

Structural and Thermodynamic Properties of Hard-Sphere Fluids

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus--Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixture are also discussed.

cond-mat.soft↗

arXiv2020

Enskog kinetic theory of rheology for a moderately dense inertial suspension

The Enskog kinetic theory for moderately dense inertial suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the background fluid on suspended particles is modeled via a viscous drag force plus a Langevin-like term defined in terms of the background temperature. In a previous paper [Hayakawa et al., Phys. Rev. E 96, 042903 (2017)], Grad's moment method with the aid of a linear shear-rate expansion was employed to obtain a theory which gave good agreement with the results of event-driven Langevin simulations of hard spheres for low densities and/or small shear rates. Nevertheless, the previous approach had a limitation of applicability to the high shear-rate and high density regime. Thus, in the present paper, we extend the previous work and develop Grad's theory including higher order terms in the shear rate. This improves significantly the theoretical predictions, a quantitative agreement between theory and simulation being found in the high-density region (volume fractions smaller than or equal to $0.4$).

cond-mat.stat-mech↗

arXiv2020

Mpemba effect in molecular gases under nonlinear drag

We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.

cond-mat.stat-mech↗

arXiv2020

Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated

cond-mat.soft↗

arXiv2019

Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit

The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann--Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions. This allows us to obtain explicit analytical expressions for the temperature ratios. On the computational side, two different techniques are used. First, the kinetic equations are numerically solved by the direct simulation Monte Carlo (DSMC) method. Second, molecular dynamics simulations for dilute gases are performed. Comparison between theory and simulations shows a general good agreement. This means that (i) the impact of the molecular chaos ansatz on the temperature ratios is not significant (except at high inelasticities and/or big impurities) and (ii) the simple Maxwellian approximation yields quite reliable predictions.

cond-mat.soft↗

arXiv2019

Energy Production Rates of Multicomponent Granular Gases of Rough Particles. A Unified View of Hard-Disk and Hard-Sphere Systems

Granular gas mixtures modeled as systems of inelastic and rough particles, either hard disks on a plane or hard spheres, are considered. Both classes of systems are embedded in a three-dimensional space ($d=3$) but, while in the hard-sphere case the translational and angular velocities are vectors with the same dimensionality (and thus there are $d_{\text{tr}}=3$ translational and $d_{\text{rot}}=3$ rotational degrees of freedom), in the hard-disk case the translational velocity vectors are planar (i.e., $d_{\text{tr}}=2$ translational degrees of freedom) and the angular velocity vectors are orthogonal to the motion plane (i.e., $d_{\text{rot}}=1$ rotational degree of freedom). This complicates a unified presentation of both classes of systems, in contrast to what happens for smooth, spinless particles, where a treatment of $d$-dimensional spheres is possible. In this paper, a kinetic-theory derivation of the (collisional) energy production rates $ξ_{ij}^{\text{tr}}$ and $ξ_{ij}^{\text{rot}}$ (where the indices $i$ and $j$ label different components) in terms of the numbers of degrees of freedom $d_{\text{tr}}$ and $d_{\text{rot}}$ is presented. Known hard-sphere and hard-disk expressions are recovered by particularizing to $(d_{\text{tr}},d_{\text{rot}})=(3,3)$ and $(d_{\text{tr}},d_{\text{rot}})=(2,1)$, respectively. Moreover, in the case of spinless particles with $d=d_{\text{tr}}$, known energy production rates $ξ_{ij}^{\text{tr}}=ξ_{ij}$ of smooth $d$-dimensional spheres are also recovered.

cond-mat.soft↗

arXiv2019

Kinetic Theory of Soft Matter. The Penetrable-Square-Well Model

The penetrable-square-well (PSW) pair interaction potential is defined as $ϕ(r)=ε_r$ if the two interacting particles are overlapped ($r<σ$), $ϕ(r)=-ε_a$ inside a corona ($σ λ$). Thus, the potential reduces to the conventional square-well (SW) one in the limit $ε_r\to\infty$ and to the penetrable-sphere (PS) potential if $ε_a\to0$ or $λ\toσ$. This paper aims at studying the temperature dependence of the Navier--Stokes transport coefficients of a dilute gas of particles interacting via the PSW model. By exploiting the fact that the PSW scattering process is analogous to that of a light ray passing through two concentric spherical media with different refractive indices, the scattering angle is analytically derived as a function of the impact parameter and the relative velocity of the colliding particles; depending on the values of those two quantities, collisions can be soft, hard, or grazing. Next, by standard application of known general results from the Chapman--Enskog method, the Navier--Stokes transport coefficients in the first-order approximation are numerically evaluated. It is found that the PSW coefficients are practically indistinguishable from the SW ones for temperatures low enough ($k_BT\lesssim 0.2 ε_r$), there exists a transition regime ($0.2 ε_r\lesssim k_BT\lesssim 10ε_r$) where the transport coefficients interpolate between the SW and the PS ones, and finally the PSW coefficients are comparable to the PS ones for high enough temperatures ($k_BT\gtrsim 10ε_r$). The results are applied to the temperature profiles of the planar Fourier flow.

cond-mat.soft↗

arXiv2019

Intruders in disguise: Mimicry effect in granular gases

In general, the total kinetic energy in a multicomponent granular gas of inelastic and rough hard spheres is unequally partitioned among the different degrees of freedom. On the other hand, partial energy equipartition can be reached, in principle, under appropriate combinations of the mechanical parameters of the system. Assuming common values of the coefficients of restitution, we use kinetic-theory tools to determine the conditions under which the components of a granular mixture in the homogeneous cooling state have the same translational and rotational temperatures as those of a one-component granular gas (``mimicry'' effect). Given the values of the concentrations and the size ratios, the mimicry effect requires the mass ratios to take specific values, the smaller spheres having a larger particle mass density than the bigger spheres. The theoretical predictions for the case of an impurity immersed in a host granular gas are compared against both DSMC and molecular dynamics simulations with a good agreement.

cond-mat.soft↗

arXiv2019

Large Mpemba-like effect in a gas of inelastic rough hard spheres

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.

cond-mat.soft↗

arXiv2019

Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres

Starting from a recent derivation of the energy production rates in terms of the number of translational and rotational degrees of freedom, a comparative study on different granular temperatures in gas mixtures of inelastic and rough disks or spheres is carried out. Both the homogeneous freely cooling state and the state driven by a stochastic thermostat are considered. It is found that the relaxation number of collisions per particle is generally smaller for disks than for spheres, the mean angular velocity relaxing more rapidly than the temperature ratios. In the asymptotic regime of the undriven system, the rotational-translational nonequipartition is stronger in disks than in spheres, while it is hardly dependent on the class of particles in the driven system. On the other hand, the degree of component-component nonequipartition is higher for spheres than for disks, both for driven and undriven systems. A study of the mimicry effect (whereby a multicomponent gas mimics the rotational-translational temperature ratio of a monocomponent gas) is also undertaken.

cond-mat.soft↗

arXiv2019

On the emergence of large and complex memory effects in nonequilibrium fluids

Control of cooling and heating processes is essential in many industrial and biological processes. In fact, the time evolution of an observable quantity may differ according to the previous history of the system. For example, a system that is being subject to cooling and then, at a given time $t_{w}$ for which the instantaneous temperature is $T(t_w)=T_{\mathrm{st}}$, is suddenly put in contact with a temperature source at $T_{\mathrm{st}}$ may continue cooling down temporarily or, on the contrary, undergo a temperature rebound. According to current knowledge, there can be only one "spurious" and small peak/low. However, our results prove that, under certain conditions, more than one extremum may appear. Specifically, we have observed regions with two extrema and a critical point with three extrema. We have also detected cases where extraordinarily large extrema are observed, as large as the order of magnitude of the stationary value of the variable of interest. We show this by studying the thermal evolution of a low density set of macroscopic particles that do not preserve kinetic energy upon collision, i.e., a granular gas. We describe the mechanism that signals in this system the emergence of these complex and large memory effects, and explain why similar observations can be expected in a variety of systems.

cond-mat.soft↗

arXiv2018

Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function $g(r)$ was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of $g(r)$ up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus--Yevick, and Martynov--Sarkisov closures. Finally, the Fisher--Widom and Widom lines are obtained in the case of the triangle-well model.

cond-mat.soft↗

arXiv2018

Finite-size estimates of Kirkwood-Buff and similar integrals

Recently, Krüger and Vlugt [Phys. Rev. E 97, 051301(R) (2018)] have proposed a method to approximate an improper integral $\int_0^\infty \text{d}r\, F(r)$, where $F(r)$ is a given oscillatory function, by a finite-range integral $\int_0^L \text{d}r\, F(r) W(r/L)$ with an appropriate weight function $W(x)$. The method is extended here to an arbitrary (embedding) dimensionality $d$. A study of three-dimensional Kirkwood-Buff integrals, where $F(r)=4πr^2h(r)$, and static structure factors, where $F(r)=(4π/q) r\sin(qr) h(r)$, $h(r)$ being the pair correlation function, shows that, in general, a choice $d\neq 3$ (e.g., $d=7$) for the embedding dimensionality may significantly reduce the error of the approximation $\int_0^\infty \text{d}r\, F(r)\simeq \int_0^L \text{d}r\, F(r) W(r/L)$.

physics.comp-ph↗

arXiv2018

Velocity Distribution and Cumulants in the Unsteady Uniform Longitudinal Flow of a Granular Gas

The uniform longitudinal flow is characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$ is the strain rate, a uniform density $n(t)\propto a(t)$, and a uniform granular temperature $T(t)$. Direct simulation Monte Carlo solutions of the Boltzmann equation for inelastic hard spheres are presented for three (one positive and two negative) representative values of the initial strain rate $a_0$. Starting from different initial conditions, the temporal evolution of the reduced strain rate $a^*\propto a_0/\sqrt{T}$, the non-Newtonian viscosity, the second and third velocity cumulants, and three independent marginal distribution functions has been recorded. Elimination of time in favor of the reduced strain rate $a^*$ shows that, after a few collisions per particle, different initial states are attracted to common "hydrodynamic" curves. Strong deviations from Maxwellian properties are observed from the analysis of the cumulants and the marginal distributions.

cond-mat.soft↗

arXiv2018

Relative Entropy of a Freely Cooling Granular Gas

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in the quasi-smooth limit.

cond-mat.soft↗

arXiv2018

Properties of the Homogeneous Cooling State of a Gas of Inelastic Rough Particles

In this work we address the question of whether a low-density system composed of identical rough particles may reach hydrodynamic states (also called \textit{normal} states), even if energy is not conserved in particle collisions. As a way to measure the ability of the system to present a hydrodynamic behavior, we focus on the so-called homogeneous cooling state of the granular gas and look at the corresponding relaxation time as a function of inelasticity and roughness. We report computer simulation results of the sixth- and eighth-order cumulants of the particle velocity distribution function and study the influence of roughness on their relaxation times and asymptotic values. This extends the results of a previous work [Phys. Rev. E \textbf{89}, 020202(R) (2014], where lower-order cumulants were measured. Our results confirm that the relaxation times are not necessarily longer for stronger inelasticities. This implies that inelasticity by itself does not preclude hydrodynamics. It is also observed that the cumulants associated with the angular velocity distribution may reach very high values in a certain region of (small) roughness and that these maxima coincide with small orientational correlation points.

cond-mat.soft↗

arXiv2018

Structural properties of the Jagla fluid

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, $g(r)$, from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of $g(r)$ in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher--Widom and Widom lines of the Jagla fluid are obtained.

cond-mat.soft↗

arXiv2018

Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, $Δs$, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), $s_\text{ex}$, and the pair-correlation contribution, $s_2$. Thus, the RMPE represents the net contribution to $s_\text{ex}$ due to spatial correlations involving three, four, or more particles. A heuristic `ordering' criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension $1<d<3$ has been proposed [Santos, A.; López de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both $d$ and the packing fraction $ϕ$. It is observed that, for any given dimensionality $d$, the RMPE takes negative values for small densities, reaches a negative minimum $Δs_{\text{min}}$ at a packing fraction $ϕ_{\text{min}}$, and then rapidly increases, becoming positive beyond a certain packing fraction $ϕ_0$. Interestingly, while both $ϕ_{\text{min}}$ and $ϕ_0$ monotonically decrease as dimensionality increases, the value of $Δs_{\text{min}}$ exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality $d\simeq 2.38$. A plot of the scaled RMPE $Δs/|Δs_{\text{min}}|$ shows a quasiuniversal behavior in the region $-0.14\lesssimϕ-ϕ_0\lesssim 0.02$.

cond-mat.soft↗