Simple stochastic model for random waste absorption of an algae cell: Analytic approach

Abstract

Over the past few decades, research on water quality using biological treatment has been considerably done. The problem of how the algae dynamically absorb waste is of great important both environmental and biological science particularly concerning a problem of waste water treatment. With this regards, we have applied a model in which a Brownian agent interacts with a spin or clock in 1D to describe and predict the system of waste absorption by algae. We assumed that the waste particles executing Brownian like motion and occasionally absorbed by algae. Analytic results are presented and discussed in connection with the waste absorption by algae. It was found that the absorption nature is dominated by the exponential like nature. How this model can be improved to better understanding or match with the real system is also elaborated.