arXiv subjects

M. Lopez de Haro

Publications and source records attributed to M. Lopez de Haro.

16 recordsLinked to original sources

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↗

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↗

arXiv2006

On the radial distribution function of a hard-sphere fluid

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.

cond-mat.stat-mech↗

arXiv2005

Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid

The contact values $g(σ,σ')$ of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution $f(σ)$ are considered. A ``universality'' assumption is introduced, according to which, at a given packing fraction $η$, $g(σ,σ')=G(z(σ,σ'))$, where $G$ is a common function independent of the number of components (either finite or infinite) and $z(σ,σ')=[2 σσ'/(σ+σ')]μ_2/μ_3$ is a dimensionless parameter, $μ_n$ being the $n$-th moment of the diameter distribution. A cubic form proposal for the $z$-dependence of $G$ is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express $G(z)$ in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2005

Thermodynamics of the Transformation of Gravitational Waves into Matter Quantums for a Vacuum Space Model

It is shown that the entropy of low density monochromatic gravitational waves, waves required for the stabilization of the crystalline structure of vacuum cosmic space, varies with the volume in the same manner as the entropy of an ideal gas formed by particles. This implies that close enough to the big-bang event the energy of all the 10 to the 120 power gravitational waves, under an adiabatic compression process, which stabilizes the crystalline structure of vacuum space behaves thermodynamically as though it is consisted of a number nB = 10 to the 80 power of independent energy or matter quanta (neutrons). PACS numbers: 03.50.De, 03.65.-w, 04.20.-q, 61.50.-f, 65.50.+m, 98.80.Ft, 97.60.Lf

physics.gen-ph↗

arXiv2005

Demixing can occur in binary hard-sphere mixtures with negative non-additivity

A binary fluid mixture of non-additive hard spheres characterized by a size ratio $γ=σ_2/σ_1<1$ and a non-additivity parameter $Δ=2σ_{12}/(σ_1+σ_2)-1$ is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit $d\to\infty$) a demixing transition with a critical consolute point at a packing fraction scaling as $η\sim d 2^{-d}$ is found, even for slightly negative non-additivity, if $Δ>-{1/8}(\lnγ)^2$. Arguments concerning the stability of the demixing with respect to freezing are provided.

cond-mat.stat-mech↗

arXiv2005

On the effective one-component description of highly asymmetric hard-sphere binary fluid mixtures

The phase diagram of a binary fluid mixture of highly asymmetric additive hard spheres is investigated. Demixing is analyzed from the exact low-density expansions of the thermodynamic properties of the mixture and compared with the fluid-fluid separation based on the effective one-component description. Differences in the results obtained from both approaches, which have been claimed to be equivalent, are pointed out and their possible origin is discussed. It is argued that to deal with these differences new theoretical approximations should be devised.

cond-mat.soft↗

arXiv2004

Equation of state of non-additive $d$-dimensional hard-sphere mixtures

An equation of state for a multicomponent mixture of non-additive hard spheres in $d$ dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard spheres proposed by us [A. Santos, S. B. Yuste, and M. López de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on the known exact second and third virial coefficients and requires as input the compressibility factor of the one-component system. A comparison is carried out both to another recent theoretical proposal based on a similar philosophy and to the available exact results and simulation data in $d=1$, 2, and 3. Good general agreement with the reported values of the virial coefficients and of the compressibility factor of binary mixtures is observed, especially for high asymmetries and/or positive nonadditivities.

cond-mat.soft↗

arXiv2004

Rescaled density expansions and demixing in hard-sphere binary mixtures

The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.

cond-mat.stat-mech↗

arXiv2002

Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal

The contact values $g_{ij}(σ_{ij})$ of the radial distribution functions of a $d$-dimensional mixture of (additive) hard spheres are considered. A `universality' assumption is put forward, according to which $g_{ij}(σ_{ij})=G(η, z_{ij})$, where $G$ is a common function for all the mixtures of the same dimensionality, regardless of the number of components, $η$ is the packing fraction of the mixture, and $z_{ij}$ is a dimensionless parameter that depends on the size distribution and the diameters of spheres $i$ and $j$. For $d=3$, this universality assumption holds for the contact values of the Percus--Yevick approximation, the Scaled Particle Theory, and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque approximation. Known exact consistency conditions are used to express $G(η,0)$, $G(η,1)$, and $G(η,2)$ in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above conditions (a quadratic form and a rational form) are made for the $z$-dependence of $G(η,z)$. For one-dimensional systems, the proposals for the contact values reduce to the exact result. Good agreement between the predictions of the proposals and available numerical results is found for $d=2$, 3, 4, and 5.

cond-mat.stat-mech↗

arXiv2002

Equation of state of a multicomponent d-dimensional hard-sphere fluid

A simple recipe to derive the compressibility factor of a multicomponent mixture of d-dimensional additive hard spheres in terms of that of the one-component system is proposed. The recipe is based (i) on an exact condition that has to be satisfied in the special limit where one of the components corresponds to point particles; and (ii) on the form of the radial distribution functions at contact as obtained from the Percus-Yevick equation in the three-dimensional system. The proposal is examined for hard discs and hard spheres by comparison with well-known equations of state for these systems and with simulation data. In the special case of d=3, our extension to mixtures of the Carnahan-Starling equation of state yields a better agreement with simulation than the already accurate Boublik-Mansoori-Carnahan-Starling-Leland equation of state.

cond-mat.stat-mech↗

arXiv2001

Light-scattering spectrum of a viscoelastic fluid subjected to an external temperature gradient

The light-scattering spectrum for a Maxwell fluid in a steady state due to the presence of an external temperature gradient is computed. In such a fluid heat conduction is assumed to be governed by the classical Fourier law. The calculation is carried out through the use of fluctuating hydrodynamics. The effect of the non-Newtonian character of the fluid in the resulting spectrum is discussed.

cond-mat.stat-mech↗

arXiv2001

Comment on "Theory and computer simulation for the equation of state of additive hard-disk fluid mixtures"

A flaw in the comparison between two different theoretical equations of state for a binary mixture of additive hard disks and Monte Carlo results, as recently reported in C. Barrio and J. R. Solana, Phys. Rev. E 63, 011201 (2001), is pointed out. It is found that both proposals, which require the equation of state of the single component system as input, lead to comparable accuracy but the one advocated by us [A. Santos, S. B. Yuste, and M. López de Haro, Mol. Phys. 96, 1 (1999)] is simpler and complies with the exact limit in which the small disks are point particles.

cond-mat.stat-mech↗

arXiv2000

Relaxation in kinetic models on alternating linear chains

A restricted dynamics, previously introduced in a kinetic model for relaxation phenomena in linear polymer chains, is used to study the dynamic critical exponent of one-dimensional Ising models. Both the alternating isotopic chain and the alternating-bond chain are considered. In contrast with what occurs for the Glauber dynamics, in these two models the dynamic critical exponent turns out to be the same. The alternating isotopic chain with the restricted dynamics is shown to lead to Nagel scaling for temperatures above some critical value. Further support is given relating the Nagel scaling to the existence of multiple (simultaneous) relaxation processes, the dynamics apparently not playing the most important role in determining such scaling.

cond-mat↗

arXiv2000

Nagel scaling and relaxation in the kinetic Ising model on a n-isotopic chain

The kinetic Ising model on a n-isotopic chain is considered in the framework of Glauber dynamics. The chain is composed of N segments with n sites, each one occupied by a different isotope. Due to the isotopic mass difference, the n spins in each segment have different relaxation times in the absence of the interactions, and consequently the dynamics of the system is governed by multiple relaxation mechanisms. The solution is obtained in closed form for arbitrary n, by reducing the problem to a set of n coupled equations, and it is shown rigorously that the critical exponent z is equal to 2. Explicit results are obtained numerically for any temperature and it is also shown that the dynamic susceptibility satisfies the new scaling (Nagel scaling) proposed for glass-forming liquids. This is in agreement with our recent results (L. L. Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys. Rev. Lett. 84, 1507 (2000)), which relate this new scaling function to multiple relaxation processes.

cond-mat.stat-mech↗

arXiv1999

Nagel scaling, relaxation and universality in the kinetic Ising model in an alternating isotopic chain

The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model with Glauber dynamics on an alternating isotopic chain are examined. The analysis provides to our knowledge the first connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may also exhibit plateau regions and does not hold for low temperatures.

cond-mat.stat-mech↗