arXiv subjects

A. Santos

Publications and source records attributed to A. Santos.

At least 37 records · Page 2Linked to original sources

arXiv2016

Theoretical approaches to the structural properties of the square-shoulder fluid

A comparison of simulation results with the prediction of the structural properties of square-shoulder fluids is carried out to assess the performance of three theories: Tang--Lu's first-order mean spherical approximation, the simplified exponential approximation of the latter and the rational-function approximation. These three theoretical developments share the characteristic of being analytical in Laplace space and of reducing in the proper limit to the Percus--Yevick result for the hard-sphere fluid. Overall, the best agreement with the simulation data is obtained with the simplified exponential approximation.

cond-mat.soft↗

arXiv2015

Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.

cond-mat.stat-mech↗

arXiv2014

Role of roughness on the hydrodynamic homogeneous base state of inelastic spheres

A gas of inelastic rough spheres admits a spatially homogeneous base state which turns into a hydrodynamic state after a finite relaxation time. We show that this relaxation time is hardly dependent on the degree of inelasticity but increases dramatically with decreasing roughness. An accurate description of translational-rotational velocity correlations at all times is also provided. At a given inelasticity, the roughness parameter can be tuned to produce a huge distortion from the Maxwellian distribution function. The results are obtained from a Grad-like solution of the Boltzmann-Enskog equation complemented by Monte Carlo and molecular dynamics simulations.

cond-mat.soft↗

arXiv2013

Study of SEY degradation of amorphous carbon coatings

Deposition of low secondary electron yield (SEY) carbon coatings by magnetron sputtering onto the inner walls of the accelerator seems to be the most promising solution for suppressing the electron cloud problem. However, these coatings change their electron emission properties during long term exposure to air. The ageing process of carbon coated samples with initial SEY of about 0.9 received from CERN is studied as a function of exposure to different environments. It is shown that samples having the same initial SEY may age with different rates. The SEY increase can be correlated with the surface concentration of oxygen. Annealing of samples in air at 100-200 °C reduces the ageing rate and even recovers previously degraded samples. The result of annealing is reduction of the hydrogen content in the coatings by triggering its surface segregation followed by desorption.

physics.acc-ph↗

arXiv2012

Steady base states for non-Newtonian granular hydrodynamics

We study in this work steady laminar flows in a low density granular gas modelled as a system of identical smooth hard spheres that collide inelastically. The system is excited by shear and temperature sources at the boundaries, which consist of two infinite parallel walls. Thus, the geometry of the system is the same that yields the planar Fourier and Couette flows in standard gases. We show that it is possible to describe the steady granular flows in this system, even at large inelasticities, by means of a (non-Newtonian) hydrodynamic approach. All five types of Couette-Fourier granular flows are systematically described, identifying the different types of hydrodynamic profiles. Excellent agreement is found between our classification of flows and simulation results. Also, we obtain the corresponding non-linear transport coefficients by following three independent and complementary methods: (1) an analytical solution obtained from Grad's 13-moment method applied to the inelastic Boltzmann equation, (2) a numerical solution of the inelastic Boltzmann equation obtained by means of the direct simulation Monte Carlo method and (3) event-driven molecular dynamics simulations. We find that, while Grad's theory does not describe quantitatively well all transport coefficients, the three procedures yield the same general classification of planar Couette-Fourier flows for the granular gas

cond-mat.soft↗

arXiv2012

Rational-function approximation for fluids interacting via piece-wise constant potentials

The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived using a (semi-analytical) rational-function approximation method. The results are illustrated for the cases of a square-shoulder plus square-well potential and a shifted square-well potential and compared both with simulation data and with those that follow from the (numerical) solutions of the Percus-Yevick integral equation.

cond-mat.soft↗

arXiv2012

The penetrable-sphere fluid in the high-temperature, high-density limit

We consider a fluid of $d$-dimensional spherical particles interacting via a pair potential $ϕ(r)$ which takes a finite value $ε$ if the two spheres are overlapped ($r<σ$) and 0 otherwise. This penetrable-sphere model has been proposed to describe the effective interaction of micelles in a solvent. We derive the structural and thermodynamic functions in the limit where the reduced temperature $k_BT/ε$ and density $ρσ^d$ tend to infinity, their ratio being kept finite. The fluid exhibits a spinodal instability at a certain maximum scaled density where the correlation length diverges and a crystalline phase appears, even in the one-dimensional model. By using a simple free-volume theory for the solid phase of the model, the fluid-solid phase transition is located.

cond-mat.stat-mech↗

arXiv2011

Hydrodynamics of inelastic Maxwell models

An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model allows us to get exact results for different problems. First, the Navier--Stokes constitutive equations with explicit expressions for the corresponding transport coefficients are derived by applying the Chapman--Enskog method to inelastic gases. Second, the non-Newtonian rheological properties in the uniform shear flow (USF) are obtained in the steady state as well as in the transient unsteady regime. Next, an exact solution for a special class of Couette flows characterized by a uniform heat flux is worked out. This solution shares the same rheological properties as the USF and, additionally, two generalized transport coefficients associated with the heat flux vector can be identified. Finally, the problem of small spatial perturbations of the USF is analyzed with a Chapman--Enskog-like method and generalized (tensorial) transport coefficients are obtained.

cond-mat.soft↗

arXiv2011

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus-Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus-Yevick theory for this system and a reasonable compromise between accuracy and simplicity.

cond-mat.stat-mech↗

arXiv2010

A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-Hückel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behavior of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.

cond-mat.stat-mech↗

arXiv2009

Contact values for disparate-size hard-sphere mixtures

A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented.

cond-mat.soft↗

arXiv2008

Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.

cond-mat.soft↗

arXiv2008

Impurity in a granular gas under nonlinear Couette flow

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.

cond-mat.soft↗

arXiv2007

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.

cond-mat.stat-mech↗

arXiv2007

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. 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 for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and square-well fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.

cond-mat.stat-mech↗

arXiv2007

Aging to non-Newtonian hydrodynamics in a granular gas

The evolution to the steady state of a granular gas subject to simple shear flow is analyzed by means of computer simulations. It is found that, regardless of its initial preparation, the system reaches (after a transient period lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic regime, even at strong dissipation and for states where the time scale associated with inelastic cooling is shorter than the one associated with the irreversible fluxes. Comparison with a simplified rheological model shows a good agreement.

cond-mat.soft↗

arXiv2006

Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas

Motivated by the disagreement found at high dissipation between simulation data for the heat flux transport coefficients and the expressions derived from the Boltzmann equation by the standard first Sonine approximation [Brey et al., Phys. Rev. E 70, 051301 (2004); J. Phys.: Condens. Matter 17, S2489 (2005)], we implement in this paper a modified version of the first Sonine approximation in which the Maxwell-Boltzmann weight function is replaced by the homogeneous cooling state distribution. The structure of the transport coefficients is common in both approximations, the distinction appearing in the coefficient of the fourth cumulant $a_2$. Comparison with computer simulations shows that the modified approximation significantly improves the estimates for the heat flux transport coefficients at strong dissipation. In addition, the slight discrepancies between simulation and the standard first Sonine estimates for the shear viscosity and the self-diffusion coefficient are also partially corrected by the modified approximation. Finally, the extension of the modified first Sonine approximation to the transport coefficients of the Enskog kinetic theory is presented.

cond-mat.stat-mech↗

arXiv2006

First-order Chapman--Enskog velocity distribution function in a granular gas

A method is devised to measure the first-order Chapman-Enskog velocity distribution function associated with the heat flux in a dilute granular gas. The method is based on the application of a homogeneous, anisotropic velocity-dependent external force which produces heat flux in the absence of gradients. The form of the force is found under the condition that, in the linear response regime, the deviation of the velocity distribution function from that of the homogeneous cooling state obeys the same linear integral equation as the one derived from the conventional Chapman-Enskog expansion. The Direct Simulation Monte Carlo method is used to solve the corresponding Boltzmann equation and measure the dependence of the (modified) thermal conductivity on the coefficient of normal restitution $α$. Comparison with previous simulation data obtained from the Green--Kubo relations [Brey et al., J. Phys.: Condens. Matter 17, S2489 (2005)] shows an excellent agreement, both methods consistently showing that the first Sonine approximation dramatically overestimates the thermal conductivity for high inelasticity ($α\lesssim 0.7$). Since our method is tied to the Boltzmann equation, the results indicate that the failure of the first Sonine approximation is not due to velocity correlation effects absent in the Boltzmann framework. This is further confirmed by an analysis of the first-order Chapman-Enskog velocity distribution function and its three first Sonine coefficients obtained from the simulations.

cond-mat.stat-mech↗