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S. B. Yuste

Publications and source records attributed to S. B. Yuste.

At least 55 records · Page 3Linked to original sources
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↗
arXiv2004

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths $λ-1$ ranging from 0.1 to 1.0, in units of the diameter $σ$ of the particles. For each one of these widths, several densities $ρ$ and temperatures $T$ in the ranges $0.1\leqρσ^3\leq 0.8$ and $T_c(λ)\lesssim T\lesssim 3T_c(λ)$, where $T_c(λ)$ is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory does for long ranges and high densities.

cond-mat.stat-mech↗
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

Comment on "Mean First Passage Time for Anomalous Diffusion"

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact infinite.

cond-mat.stat-mech↗
arXiv2004

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone.

cond-mat.stat-mech↗
arXiv2003

Some exact results for the trapping of subdiffusive particles in one dimension

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is made

cond-mat.stat-mech↗
arXiv2003

On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.

math.NA↗
arXiv2003

Order statistics of Rosenstock's trapping problem in disordered media

The distribution of times $t_{j,N}$ elapsed until the first $j$ independent random walkers from a set of $N \gg 1$, all starting from the same site, are trapped by a quenched configuration of traps randomly placed on a disordered lattice is investigated. In doing so, the cumulants of the distribution of the territory explored by $N$ independent random walkers $S_N(t)$ and the probability $Φ_N(t)$ that no particle of an initial set of $N$ is trapped by time $t$ are considered. Simulation results for the two-dimensional incipient percolation aggregate show that the ratio between the $n$th cumulant and the $n$th moment of $S_N(t)$ is, for large $N$, (i) very large in comparison with the same ratio in Euclidean media, and (ii) almost constant. The first property implies that, in contrast with Euclidean media, approximations of order higher than the standard zeroth-order Rosenstock approximation are required to provide a reasonable description of the trapping order statistics. Fortunately, the second property (which has a geometric origin) can be exploited to build these higher-order Rosenstock approximations. Simulation results for the two-dimensional incipient percolation aggregate confirm the predictions of our approach.

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↗
arXiv2002

Survival probability and order statistics of diffusion on disordered media

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem we assume that, for short times, the survival probability (the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval) decays for disordered media in the same way as for Euclidean and some class of deterministic fractal lattices. This conjecture is checked by simulation on the incipient percolation aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are expressed in terms of an asymptotic series in powers of 1/ln N which is formally identical to those found for Euclidean and (some class of) deterministic fractal lattices. The agreement of the asymptotic expressions with simulation results for the two-dimensional percolation aggregate is good when the boundary is defined in terms of the chemical distance. The agreement worsens slightly when the Euclidean distance is used.

cond-mat.stat-mech↗
arXiv2001

Subdiffusion-limited single species reactions

We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. We calculate both short-time and long-time concentrations, and compare and contrast the continuous and discrete cases. Our analysis is based on the fractional diffusion equation and its discrete analog.

cond-mat.stat-mech↗
arXiv2001

Multiparticle trapping problem in the half-line

A variation of Rosenstock's trapping model in which $N$ independent random walkers are all initially placed upon a site of a one-dimensional lattice in the presence of a {\em one-sided} random distribution (with probability $c$) of absorbing traps is investigated. The probability (survival probability) $Φ_N(t)$ that no random walker is trapped by time $t$ for $N \gg 1$ is calculated by using the extended Rosenstock approximation. This requires the evaluation of the moments of the number $S_N(t)$ of distinct sites visited in a {\em given} direction up to time $t$ by $N$ independent random walkers. The Rosenstock approximation improves when $N$ increases, working well in the range $Dt\ln^2(1-c) \ll \ln N$, $D$ being the diffusion constant. The moments of the time (lifetime) before any trapping event occurs are calculated asymptotically, too. The agreement with numerical results is excellent.

cond-mat.stat-mech↗
arXiv2001

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation.

cond-mat.stat-mech↗
arXiv2001

Virial coefficients and equations of state for mixtures of hard discs, hard spheres and hard hyperspheres

The composition-independent virial coefficients of a $d$-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture [Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1] are examined. Good agreement between theoretical estimates and available exact or numerical results is found for $d=2$, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard-sphere mixtures ($d=3$) is analyzed in some detail.

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

Demixing in binary mixtures of hard hyperspheres

The phase behavior of binary fluid mixtures of hard hyperspheres in four and five dimensions is investigated. Spinodal instability is found by using a recent and accurate prescription for the equation of state of the mixture that requires the equation of state of the single component fluid as input. The role played by the dimensionality on the possible metastability of the demixing transition with respect to a fluid-solid transition is discussed. The binodal curves in the pressure--chemical potential representation are seen to lie on a common line, independent of the size ratio

cond-mat.stat-mech↗