Random-walk simulation of diffusion-controlled processes among static traps

Lee, Sang Bub; Kim, In Chan; Miller, Clarence A.; Torquato, Salvatore

doi:10.1103/physrevb.39.11833

Cited by 69 publications

(53 citation statements)

References 29 publications

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“…The case of stable virus (d V ¼ 0) corresponds to a problem studied mathematically in the theory of ''diffusion-limited reactions'', especially in the case of a species diffusing among a field of spherical absorbing traps (Felderhof, 1985;Richards, 1987;Lee et al, 1989;Torquato, 1991;Torquato & Yeong, 1997). We will assume that the reaction rate is infinite, i.e.…”

Section: à1=3mentioning

confidence: 99%

Spatiotemporal Dynamics of HIV Propagation

Strain

Richman

Wong

et al. 2002

Journal of Theoretical Biology

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Section: à1=3mentioning

confidence: 99%

Spatiotemporal Dynamics of HIV Propagation

Strain

Richman

Wong

et al. 2002

Journal of Theoretical Biology

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“…Sperm moved randomly with positions assessed in time increments calculated to be the minimum required for observation of a collision event, i.e. according to the 'first-passage' technique (Inamdar et al, 2007;Lee et al, 1989;Torquato and Kim, 1989).…”

Section: Analysis Of Sperm Diffusivitymentioning

confidence: 99%

Assessment of sperm chemokinesis with exposure to jelly coats of sea urchin eggs and resact: a microfluidic experiment and numerical study

Inamdar

Kim

Chung

et al. 2007

Journal of Experimental Biology

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Specific peptides contained within the extracellular layer, or jelly coat, of a sea urchin egg have been hypothesized to play an important role in fertilization, though separate accounting of the effects of chemoattraction, chemokinesis, sperm agglomeration and the other possible roles of the jelly coat have not been reported. In the present study, we used a microfluidic device that allowed determination of the differences in the diffusion coefficients of sperm of the purple sea urchin Arbacia punctulata subjected to two chemoattractants, namely the jelly coat and resact. Our objectives were twofold: (1) to experimentally determine and compare the diffusion coefficients of Arbacia punctulata spermatozoa in seawater, jelly coat solution and resact solution; and (2) to determine the effect of sea urchin sperm diffusion coefficient and egg size on the sperm-egg collision frequency using stochastic simulations. Numerical values of the diffusion coefficients obtained by diffusing the spermatozoa in seawater, resact solution and jelly coat solution were used to quantify the chemotactic effect. This allowed direct incorporation of known enlargements of the egg, and altered sperm diffusion coefficients in the presence of chemoattractant, in the stochastic simulations. Simulation results showed that increase in diffusion coefficient values and egg diameter values increased the collision frequency. From the simulation results, we concluded that type of sperm, egg diameter and diffusion coefficient are significant factors in egg fertilization. Increasing the motility of sperm appears to be the prominent role of the jelly coat.

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“…The concept of fast random walks was proposed by Muller [33] in 1956 and then broadly employed by many authors, for instance, to study diffusion-reaction processes and related first-passage problems in random packs of spheres [34,35] or near prefractal boundaries [36][37][38]. The idea consists in replacing Brownian motion by an equivalent ''spherical process'' that explores the confining domain as fast as possible.…”

Section: Fast Random Walk Algorithmmentioning

confidence: 99%

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media

Grebenkov

2011

Journal of Magnetic Resonance

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Random-walk simulation of diffusion-controlled processes among static traps

Cited by 69 publications

References 29 publications

Spatiotemporal Dynamics of HIV Propagation

Spatiotemporal Dynamics of HIV Propagation

Assessment of sperm chemokinesis with exposure to jelly coats of sea urchin eggs and resact: a microfluidic experiment and numerical study

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media

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