Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models have received attention in order to include finite lifetime processes. For instance, activated chemical reactions, such as laser photolysis, exhibit a different asymptotic limit when compared with immortal walker models. A diffusion limited reaction model based on a one dimensional continuous time random walk on a lattice with evanescent walkers is presented here. The absorption probability density and the reaction rate are analytically calculated in the Laplace domain. A finite absorption rate is considered, a model usually referred to as imperfect trapping. Short and long time behaviors are analyzed.Comment: 6 pages, 3 figure
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.
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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