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S B Yuste

Publications and source records attributed to S B Yuste.

11 recordsLinked to original sources
PubMed2004

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.

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PubMed2004

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.

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PubMed2004

Average shape of fluctuations for subdiffusive walks.

We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a tablelike form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.

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PubMed2003

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>>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 Phi(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 nth cumulant and the nth 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 the 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.

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PubMed2002

Equation of state of additive hard-disk fluid mixtures: a critical analysis of two recent proposals.

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

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PubMed2002

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.

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PubMed2001

Order statistics of the trapping problem.

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the mth moment of the time t(j,N) elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi(M)(t) that no particle of an initial set of M=N,N-1,...,N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi(M)(t), and it is found that for a large range of trap concentrations the mth moment of t(j,N) goes as x(-m) and its variance as x(-2), x being ln(2/d)(1-c)ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.

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PubMed2001

Subdiffusion-limited A+A 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.

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PubMed2000

Territory covered by N random walkers on fractal media: the Sierpinski gasket and the percolation aggregate.

We address the problem of evaluating the number S(N)(t) of distinct sites visited up to time t by N noninteracting random walkers all starting from the same origin in fractal media. For a wide class of fractals (of which the percolation cluster at criticality and the Sierpinski gasket are typical examples) we propose, for large N and after the short-time compact regime, an asymptotic series for S(N)(t) analogous to that found for Euclidean media: S(N)(t) approximately S(N)(t)(1-Delta). Here S(N)(t) is the number of sites (volume) inside a hypersphere of radius L[ln(N)/c]1/v where L is the root-mean-square chemical displacement of a single random walker, and v and c determine how fast 1-Gamma(t)(l) (the probability that a given site at chemical distance l from the origin is visited by a single random walker by time t) decays for large values of l/L: 1-Gamma(t)(l) approximately exp[-c(l/L)(v)]. For the fractals considered in this paper, v=d(l)w/((d(l)w)-1), d(l)w being the chemical-diffusion exponent. The corrective term Delta is expressed as a series in ln(-n)(N)ln(m) ln(N) (with n> or =1 and 0< or =m< or =n), which is given explicitly up to n=2. This corrective term contributes substantially to the final value of S(N)(t) even for relatively large values of N.

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PubMed1999

Territory covered by N random walkers.

The problem of evaluating the number of distinct sites S(N)(t) covered up to time t by N random walkers is revisited. For the nontrivial time regime and for N>>1 we show how to get the asymptotic behavior of S(N)(t) and we calculate the main and first two corrective terms. The mth corrective term decays mildly as 1/ln(m) N. For d-dimensional (d=1,2,3) simple cubic lattices, the main term is the volume of the hypersphere of radius [(ln N(2))2Dt/d](1/2), D being the diffusion constant, and the corrective terms account for the roughening of the surface of the set of visited sites.

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