Modeling the dynamics of polymer chains in water solution. Application to sensor design

摘要

This paper is devoted to a mathematical model of a chaotic dynamics of a polymer chain in water. The model consists of a parabolic equation that is derived according to the self-consistent field approach. This model is employed for the numerical simulation of a biological sensor that detects the presence of a specific protein in the fluid. The sensor is absolutely simple and seems to be new. Besides that, the suggested equation is interesting from the mathematical point of view. It includes a non-local operator of integration not only over the past time interval as in the problems with memory but also over the future time interval. It is unusual for parabolic problems.