Diffusion and survival in a medium with imperfect traps

Nieuwenhuizen, Th. M.; Brand, Helmut R.

doi:10.1007/bf01015563

Cited by 12 publications

(13 citation statements)

References 12 publications

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“…Due to the presence of arbitrarily large trap-free regions where the walker can survive for a long time, the survival probability decays slower than exponentially, following a stretched exponential function with stretching exponent α = d/(d + 2) for Euclidean host lattices [13][14][15][16][17] and α = d s /(d s + 2) for fractals [11][12][13]. The same asymptotic behavior was also found to hold for randomly distributed imperfect traps [18,19]. While some authors argue that stretched exponential long-time decay due to this mechanism occurs only when f (t) drops to extremely low values and thus is not practically observable, more recent simulations show that the mechanism may manifest itself in an experimentally observable range of values of f (t) [20].…”

Section: Introductionmentioning

confidence: 63%

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Random walks with fractally correlated traps: Stretched exponential and power-law survival kinetics

Plyukhin

2016

Phys. Rev. E

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We consider the survival probability f (t) of a random walk with a constant hopping rate w on a host lattice of fractal dimension d and spectral dimension ds ≤ 2, with spatially correlated traps. The traps form a sublattice with fractal dimension da < d and are characterized by the absorption rate wa which may be finite (imperfect traps) or infinite (perfect traps). Initial coordinates are chosen randomly at or within a fixed distance of a trap. For weakly absorbing traps (wa ≪ w), we find that f (t) can be closely approximated by a stretched exponential function over the initial stage of relaxation, with stretching exponent α = 1 − (d − da)/dw, where dw is the random walk dimension of the host lattice. At the end of this initial stage there occurs a crossover to power law kinetics f (t) ∼ t −α with the same exponent α as for the stretched exponential regime. For strong absorption wa w, including the limit of perfect traps wa → ∞, the stretched exponential regime is absent and the decay of f (t) follows, after a short transient, the aforementioned power law for all times.

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Section: Introductionmentioning

confidence: 63%

“…According to the heuristic argument in Section 2, the survival probability for weakly absorbing traps is expected to be characterized by stretched exponential decay (18) with the exponent…”

Section: D Lattice With Traps On the Cantor Setmentioning

confidence: 99%

Random walks with fractally correlated traps: Stretched exponential and power-law survival kinetics

Plyukhin

2016

Phys. Rev. E

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“…For several decades such one-dimensional trapping problems have been extensively analysed in the literature (see, e.g., [43][44][45] and references therein). In particular it can be shown (see, e.g., [46]) that the tail of the sojourn time distribution has a stretched exponential form P (t u ) ∼ exp(−a (ln(1/ρ τ )) 2/3 t 1/3 u ) due to the survival of particles in arbitrarily large trap-free regions. However, we are interested in the mean and variance which are not much influenced by the tail of the distribution.…”

Section: Disordered Model As Trapping Problemmentioning

confidence: 99%

Traffic of cytoskeletal motors with disordered attachment rates

Grzeschik¹,

Harris²,

Santen³

2010

Phys. Rev. E

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Motivated by experimental results on the interplay between molecular motors and tau proteins, we extend lattice-based models of intracellular transport to include a second species of particle which locally influences the motor-filament attachment rate. We consider various exactly solvable limits of a stochastic multiparticle model before focusing on the low-motor-density regime. Here, an approximate treatment based on the random-walk behavior of single motors gives good quantitative agreement with simulation results for the tau dependence of the motor current. Finally, we discuss the possible physiological implications of our results.

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“…The simplest example of inhomogeneous reaction-diffusion system is the trapping of diffusing particle by traps [23]. The density of particles for trapping reaction with randomly distributed traps has been know to show a stretched exponential behavior [24][25][26], self-segregation [27][28][29][30], and self-organization around traps [31][32][33][34]. Random growth and trapping of diffusing particle can be used to model inhomogeneous population models [35,36].…”

Section: Introductionmentioning

confidence: 99%

Population extinction in an inhomogeneous host–pathogen model

Bagarti

2016

Physica A: Statistical Mechanics and its Applications

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We study inhomogeneous host-pathogen dynamics to model the global amphibian population extinction in a lake basin system. The lake basin system is modeled as quenched disorder. In this model we show that once the pathogen arrives at the lake basin it spreads from one lake to another, eventually spreading to the entire lake basin system in a wave like pattern. The extinction time has been found to depend on the steady state host population and pathogen growth rate. Linear estimate of the extinction time is computed. The steady state host population shows a threshold behavior in the interaction strength for a given growth rate.

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Diffusion and survival in a medium with imperfect traps

Cited by 12 publications

References 12 publications

Random walks with fractally correlated traps: Stretched exponential and power-law survival kinetics

Random walks with fractally correlated traps: Stretched exponential and power-law survival kinetics

Traffic of cytoskeletal motors with disordered attachment rates

Population extinction in an inhomogeneous host–pathogen model

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