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Andrés Santos

Publications and source records attributed to Andrés Santos.

117 records · Page 7Linked to original sources
arXiv2009

Solutions of the moment hierarchy in the kinetic theory of Maxwell models

In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In general, however, the drift term of the Boltzmann equation couples moments of a given order to moments of a higher order, thus preventing the solvability of the moment hierarchy, unless approximate closures are introduced. On the other hand, there exist a number of states where the moment hierarchy can be recursively solved, the solution generally exposing non-Newtonian properties. The aim of this paper is to present an overview of results pertaining to some of those states, namely the planar Fourier flow (without and with a constant gravity field), the planar Couette flow, the force-driven Poiseuille flow, and the uniform shear flow.

cond-mat.stat-mech↗
arXiv2009

Comments on "State equation for the three-dimensional system of 'collapsing' hard spheres"

A recent paper [I. Klebanov et al. \emph{Mod. Phys. Lett. B} \textbf{22} (2008) 3153; arXiv:0712.0433] claims that the exact solution of the Percus-Yevick (PY) integral equation for a system of hard spheres plus a step potential is obtained. The aim of this paper is to show that Klebanov et al.'s result is incompatible with the PY equation since it violates two known cases: the low-density limit and the hard-sphere limit.

cond-mat.soft↗
arXiv2009

Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations

We study structural and thermophysical properties of a one-dimensional classical fluid made of penetrable spheres interacting via an attractive square-well potential. Penetrability of the spheres is enforced by reducing from infinite to finite the repulsive energy barrier in the pair potentials As a consequence, an exact analytical solution is lacking even in one dimension. Building upon previous exact analytical work in the low-density limit [Santos \textit{et al.}, Phys. Rev. E \text{77}, 051206 (2008)], we propose an approximate theory valid at any density and in the low-penetrable regime. By comparison with specialized Monte Carlo simulations and integral equation theories, we assess the regime of validity of the theory. We investigate the degree of inconsistency among the various routes to thermodynamics and explore the possibility of a fluid-fluid transition. Finally we locate the dependence of the Fisher-Widom line on the degree of penetrability. Our results constitute the first systematic study of penetrable spheres with attractions as a prototype model for soft systems.

cond-mat.soft↗
arXiv2009

A branch-point approximant for the equation of state of hard spheres

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Padé [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in $d$ dimensions are also pointed out.

cond-mat.soft↗
arXiv2001

Critical Behavior of a Heavy Particle in a Granular Fluid

Behavior analogous to a second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter $ϕ$ is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field $h$ proportional to the mass ratio. A parameter $β$, measuring the fluid cooling rate relative to the impurity--fluid collision rate, is the analogue of the inverse temperature. For $β<1$ the fluid is ``normal'' with $ϕ=0$ at $h=0$, as in the case of a system with elastic collisions. For $β>1$ an ``ordered'' state with $ϕ\neq 0$ occurs at $h=0$, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function for the impurity particle near the transition are noted

cond-mat.stat-mech↗
arXiv2000

Non-Newtonian Poiseuille flow of a gas in a pipe

The Bhatnagar-Gross-Krook kinetic model of the Boltzmann equation is solved for the steady cylindrical Poiseuille flow fed by a constant gravity field. The solution is obtained as a perturbation expansion in powers of the field (through fourth order) and for a general class of repulsive potentials. The results, which are hardly sensitive to the interaction potential, suggest that the expansion is only asymptotic. A critical comparison with the profiles predicted by the Navier-Stokes equations shows that the latter fail over distances comparable to the mean free path. In particular, while the Navier-Stokes description predicts a monotonically decreasing temperature as one moves apart from the cylinder axis, the kinetic theory description shows that the temperature has a local minimum at the axis and reaches a maximum value at a distance of the order of the mean free path. Within that distance, the radial heat flows from the colder to the hotter points, in contrast to what is expected from the Fourier law. Furthermore, a longitudinal component of the heat flux exists in the absence of gradients along the longitudinal direction. Non-Newtonian effects, such as a non uniform hydrostatic pressure and normal stress differences, are also present.

cond-mat.stat-mech↗
arXiv1996

Long Wavelength Instability for Uniform Shear Flow

Uniform Shear Flow is a prototype nonequilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the Navier-Stokes equations and shown to apply at both low and high densities. Next, higher order rheological effects are included using a model kinetic theory. The results are compared favorably to those from Monte Carlo simulation.

cond-mat↗