Solution to the Glarum model with a finite relaxation rate

Condat, C. A.

doi:10.1007/bf01313675

Cited by 21 publications

(3 citation statements)

References 24 publications

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“…En esta comunicación se presenta un modelo para procesos de reacción mediados por difusión, basado en el esquema de Caminatas Aleatorias de Tiempo Continuo (CTRW) sobre una red unidimensional, asumiendo tasas de salto arbitrarias λ A y λ T para ambas especies. Se propone así una generalización del modelo de trampa imperfecta (4,5) en redes asumiendo que la trampa T y los caminantes A son móviles. La extensión del modelo asume además una dinámica de reacción exponencial con tasa de reacción γ.…”

Section: Statistical Properties Of the Diffusion Mediated Reaction Prunclassified

Statistical properties of the diffusion mediated reaction process for a mobile imperfect trap

Bustos

Ré

2015

AnAFA

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la especie mayoritaria que denominamos aquí A, en presencia de una trampa, la especie minoritaria que denominamos T, supuesta en una posición fija. Al encontrarse una partícula A con T pueden dar lugar a una reacción, en general con una probabilidad finita. En estos modelos se supone que el coeficiente de difusión de las partćulas A es igual a la suma de los coeficientes de difusión de ambas especies. Sin embargo existen procesos en los que el modelo con ambas especies en movimiento constituye una mejor aproximación. Se considera en esta comunicación un modelo de caminata aleatoria de tiempo continuo sobre una red unidimensional en la que ambas especies pueden desplazarse. Se supone una distribución inicial uniforme de la especie mayoritaria en presencia de una trampa, representando la especie minoritaria. Aún cuando el parámetro de red es el mismo para ambas especies, los coeficientes de difusión son diferentes, estando determinados por la tasa de saltos. La reacción no es inmediata en el encuentro de ambas especies, dando lugar a realizaciones en las que los reactivos pueden separarse sin reaccionar. Se presentan resultados analíticos en el dominio

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Section: Statistical Properties Of the Diffusion Mediated Reaction Prunclassified

Statistical properties of the diffusion mediated reaction process for a mobile imperfect trap

Bustos

Ré

2015

AnAFA

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“…If we have an uniform distribution of A particles, 0 c in each lattice site, the particle concentration at site x at time t is given by (14) and, replacing (5) in (9) and then in (14), we get in the  transform representation…”

Section: Two Particles Random Walkmentioning

confidence: 99%

“…Among these models we mention imperfect trapping [14] [15] with a finite reaction rate and dynamic or gated trapping [16] [17] [18] [19] [20] when the reaction is also modulated by an another independent reaction T T ↔  that switches the trap between an active and an inactive state.…”

Section: Introductionmentioning

confidence: 99%

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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A Target Diffusion Theory for Nuclear Spin Relaxation in Ionically‐Conducting Glasses

Elliott

Owens

1991

Ber Bunsenges Phys Chem

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A theoretical mechanism is presented for nuclear spin relaxation in ionically‐conducting glasses (or disordered crystals) caused by ionic motion. This is based on the diffusion‐controlled relaxation model previously used to account for electrical relaxation in such materials: relaxation is assumed to occur at particular (interstitialcy) sites, triggered by the arrival of other diffusing ions. The experimental dependence of the spin‐lattice relaxation rate on temperature and ionic concentration can be understood on the basis of this model.

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Solution to the Glarum model with a finite relaxation rate

Cited by 21 publications

References 24 publications

Statistical properties of the diffusion mediated reaction process for a mobile imperfect trap

Statistical properties of the diffusion mediated reaction process for a mobile imperfect trap

Imperfect Trapping in a Random Walk with Both Species Mobile

A Target Diffusion Theory for Nuclear Spin Relaxation in Ionically‐Conducting Glasses

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