Monte Carlo Simulation of NanoCommunications with the Diffusion Equation

We apply computational simulation such as the Monte Carlo technique to calculate observables which are of importance to characterize biological systems in the nano level such as bacteria. Essentially we focus on the calculation of the mobility of physical observables by using the Diffusion's equation. For this end we make use of the cylindrical coordinate system by which ones obtains the solutions depending on the Bessel functions. It has a certain similarity with the well-known Jackson's potential by which the potential of a single charged object in point inside of a geometrical system based in a cylinder is proportional to Bessel functions. We assume that the electrical configuration of the fluid dynamics is dictated by the diffusion's equation. With the closed-form solutions we calculate the temporal evolutions of the fluid from the respective electric force by assuming that the nano biological system is composed by positive and negative ions. Under this view we establish the relations of nano communications from events derived purely from a Coulomb-like force. In this manner we perform Monte Carlo simulations by assuming that the nano networks are achieving nano-communications from electric repulsion or attraction forces. Thus, we estimate the net displacement of a bacteria population. This formulation might be entirely of interest for ends of advanced networking such as Internet of Nano-Things[1].