Reaction rate in an evanescent random walkers system

Ré, Miguel A.; Bustos, Natalia C.

doi:10.4279/pip.070003

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…COMPARISON BETWEEN RESULTS FOR CONDITIONAL ANDUNCONDITIONAL WALK LENGTHSBoth conditional and unconditional walk lengths are relevant for target search problems, hence we will compare these two quantities in the present section. Eqs (20). and(21)are the basis to compute the site-specific conditional walk lengths, whereas Eqs.…”

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confidence: 99%

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

et al. 2019

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We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly selfsimilar as one goes from one generation of the family to the next. Under these circumstances, the total probability that the walker hits a trap is determined exactly as a function of the single-step survival probability q of the mortal walker. On the n th generation graph of the family, this probability is shown to be given by the n th iterate of a certain scaling function or map q → f (q). The properties of the map then determine, in each case, the behavior of the trapping probability, the mean time to trapping, the temporal scaling factor governing the random walk dimension on the graph, and other related properties. The formalism is illustrated for the cases of a linear hierarchical lattice and the Sierpinski graphs in 2 and 3 Euclidean dimensions. We find an effective reduction of the random walk dimensionality due to the ballistic behavior of the surviving particles induced by the mortality constraint.The relevance of this finding for experiments involving travel times of particles in diffusion-decay systems is discussed.

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confidence: 99%

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

et al. 2019

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“…As one can see from the expressions in Appendix B, the walklength is given by ratios of polynomials of increasing degree, but it is not obvious how the resulting expressions depend on the lattice size N or, equivalently, on the linear size L. Were this the case, one could obtain analytic expressions similar to the formulae (16) and (17), valid in the small s limit (or consider other limits).…”

Section: Resultsmentioning

confidence: 99%

“…Recently, there has been a surge of interest in such problems [10][11][12][13][14][15][16][17][18][19][20][21][22] motivated by a large number of applications, including photosynthetic trapping [5], oocyte fertilization [13], game theory [5], radioactive decay [5,18], target deactivation problems [14] or foraging behavior [21].…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noting that the computation of the walklength of a walker subject to background trapping is a particular example of a broad class of first-passage problems for so-called mortal walkers, i.e., walkers that have a finite probability of dying as they move. Recently, there has been a surge of interest in such problems [10][11][12][13][14][15][16][17][18][19][20][21][22] motivated by a large number of applications, including photosynthetic trapping [5], oocyte fertilization [13], game theory [5], radioactive decay [5,18], target deactivation problems [14] or foraging behavior [21].…”

Section: Introductionmentioning

confidence: 99%

“…The extension of the generating function approach to deal with "mortal walkers" [10][11][12][13][14][15][16][17][18][19][20][21][22] has not only expanded the range of physical problems that can be explored using a lattice-based theory, but has also motivated the development of novel approximations for lattice Green functions, as will be illustrated later on in this study. At present, however, an approach based on lattice Green functions can be implemented only for translationallyinvariant lattices.…”

Section: Introductionmentioning

confidence: 99%

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Random walks on lattices. Influence of competing reaction centers on diffusion-controlled processes

Abad

Abil

Santos

et al. 2018

Physica A: Statistical Mechanics and its Applications

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We study diffusion-reaction processes on periodic simple cubic (sc) lattices and square planar lattices. We consider a single diffusing reactant undergoing an irreversible reaction upon first encounter with a static co-reactant placed at a given site ("one-walker problem"). We also allow for a competing reaction, namely, instantaneous trapping of the diffusing reactant at any other site (with probability s) before interacting with the static co-reactant. We use a generating function approach and Markov theory, as well as MC simulations, to determine the mean walklength n of the diffusing reactant before either of the two competing reactions takes place. To investigate the dependence of n on lattice size we compute the first, finite size corrections to the Green function of the sc lattice, correcting results reported in the literature. Using these results, space exploration properties and first-passage properties (e.g. walklength statistics, mean number of distinct sites visited, statistics of return to the origin, etc.) of both conventional (immortal) walks and mortal walks can be determined. In this context, we develop a novel approach based on a two-point Padé approximant for the Green function. Finally, we study by means of MC simulations the more complex case where both reactant and coreactant undergo synchronous nearest-neighbor displacements ("two-walker problem"). Here, we assume that reactant and co-reactant can individually be trapped with probability s at any lattice site, or can undergo an irreversible reaction on first encounter at any site. When s = 0 we find that, both for the one-walker and the two-walker problem, for lattices with (approximately) the same number of sites, the mean walklength is smaller (and hence the reaction efficiency greater) in d = 3 than in d = 2. Increasing s tends to reduce differences in system dimensionality, and distinctions between the onewalker problem and the two-walker problem. Our model provides a good starting point to develop studies on the efficiency of apparently diverse diffusion-reaction processes, such as diffusion on a partially poisoned catalytic substrate or photosynthetic trapping of excitations.

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Imperfect Trapping in a Random Walk with Both Species Mobile

Bustos¹,

Ré²

2018

APM

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It is presented here a continuous time random walk model for diffusion mediated reactions with both species mobile. The random walk is carried out over an infinite homogeneouos lattice. They are calculated the probability density for the time of reaction of a pair, the reaction rate and the time evolution of the concentration of the majority species. Analytical results are obtained in the Fourier-Laplace transform representation. Known results for a fixed trap are reobtained with appropriate marginal probabilities. It is thus justified Smoluchowski's original approximation considering the trap at a fixed position and the majority species diffusing with a coefficient sum of the individual coefficients. The results obtained are illustrated by a one dimensional model with bias.

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Reaction rate in an evanescent random walkers system

Cited by 3 publications

References 13 publications

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

First-passage properties of mortal random walks: Ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs

Random walks on lattices. Influence of competing reaction centers on diffusion-controlled processes

Imperfect Trapping in a Random Walk with Both Species Mobile

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