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

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. (paper)