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Biomedical subjects

L Acedo

Publications and source records attributed to L Acedo.

8 recordsLinked to original sources
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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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

Diffusion in lattice Lorentz gases with a percolation threshold.

A mean-field approximation for the diffusion coefficient in lattice Lorentz gases with an arbitrary mixture of pointlike stochastic scatterers in the low-density limit is proposed. In this approximation, the diffusion coefficient is directly related to the first return probability of the moving particle in the corresponding Cayley tree through an effective ring operator. A renormalization scheme for the approximate determination of the first return probability is constructed. The predictions of this mean-field theory and those of the repeated ring approximation (RRA) are compared with computer simulation results for models in which a fraction x(B) of the scatterers are deterministic backscatterers, so that the diffusion coefficient vanishes beyond a certain percolation threshold x(c)(B). The approximation proposed in this paper is seen to be in good agreement with the simulation results, in contrast to the RRA, which already fails to give the correct percolation threshold.

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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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